In this paper a continuous flow sonochemical

In this paper, a continuous flow sonochemical reactor is developed and used to continuously produce a metastable crystal structure in the form of high aspect ratio CdS platelets. The sub 10nm thick order EHop-016 exhibit good particle size control without the use of surfactants. The method is compared with batch sonochemistry and conventional heating to delineate the advantages.

Development of a continuous flow sonochemical reactor
A flow cell reactor was developed to couple an ultrasonic (US) horn with the nanoparticle chemistry of interest. Ultrasound attenuates as a function of distance in front of the horn. Attenuation is an exponential function, strongly dependent on the attenuation coefficient (α) as given by [17]where I is intensity at distance d from the source, I0 being initial intensity. The acoustic pressure amplitude as a function of distance from the horn has been modeled using the equation [18].where P(d) is the acoustic pressure amplitude as a function of distance d, ρ is the density of the liquid, c is velocity of sound in the liquid, v is the velocity amplitude of the horn, λ is the wavelength of the sound and a is the radius of the horn tip.
A key factor in the design of the flow cell was to reduce the residence time of the flow chemistry within the reactor. Shorter residence times would lead to the potential for higher, more uniform power densities adjacent to the horn and less exposure to bulk temperatures. A horn with a maximum power inverter rating of 750W (model VCX 750) and an interfacing flow cell (630-0495) were acquired from Sonics and Materials, Inc. To reduce fluid residence time within the flow cell, the internal volume of flow cell was modified through the use of an insert. Fig. 1 shows a schematic of the internal volume of the reactor with and without the flow insert. The flow cell insert reduced the flow cell volume from 65ml to 8ml. The critical dimension in the insert was the clearance between the horn outer diameter and the inner diameter of the insert itself. This had to be sufficiently larger than the critical bubble size in order to prevent vapor lock restricting the outflow of processed reactants. The flow insert was made of UHMWPE due to its low density, high elasticity, high softening point and low cost.
The use of the insert was found to provide several benefits. First, Fig. 2 shows the effect of the flow cell insert on the time needed for the bulk temperature to reach steady state in pure water. It can be clearly observed that it takes approximately one-third the amount of time to reach 70°C for pure water. Second, the curve collected without the insert shows several points at which the temperature suddenly drops off. This is due to temperature accumulation adjacent to the horn leading to bubble accumulation and disruption of power transfer. This suggests that the use of the flow cell insert led to better temperature uniformity within the flow cell as originally intended. A schematic of the final continuous flow setup is shown in Fig. 3.

Experimental methods
Based on prior literature [10], a cadmium chloride and thiourea reactant chemistry was chosen for sonochemical synthesis of cadmium sulfide nanoparticles. This chemistry involves processing at 85°C [19,20]. The reaction mechanism involves forming a cadmium–thiourea complex – Cd[SC(NH2)2](OH)2 which is aided by ammonia released from ammonium chloride–ammonium hydroxide buffer. This controls the release of Cd ions for precipitation into CdS and hence affects the kinetics of the reaction, aimed at controlling the particle size. Table 2 shows the conditions chosen for the reaction in batch and continuous modes. The chemistry was first evaluated in batch mode to check feasibility.
Since the boiling point of pure water is very close to the reaction temperature of 85°C, highly localized hot spots can result in vapor phase formation leading to flow disruption, i.e., vapor lock. Hence an azeotropic mix consisting of water and ethylene glycol in a 1:1 volume was used, elevated the boiling point to 107°C [21]. The nanoparticles were quenched at the outlet, washed, dried and used for observation. A FEI TITAN Chemi-STEM (Portland, OR, USA) operating at 200kV was used to image the nanoparticles. A Bruker-AXS D8 Discover X-ray diffraction unit (Madison, WI, USA) was used for phase analysis using XRD patterns. A SX-100 CAMECA electron microprobe analyzer (Gennevillier, France) was used to evaluate the composition of nanoparticles using wave dispersive spectroscopy (WDS). Unlike energy dispersive spectroscopy (EDS), WDS uses the wave nature of X-rays and Bragg’s diffraction of the X-rays produced when an electron beam hits the surface of the sample. This has significant advantages over traditional EDS as it has better energy resolution, better detection of lighter elements and higher signal to noise ratio. A few milligrams of the nanoparticles were formed into a pellet on a glass substrate for this compositional analysis.

br Results The acoustic emission collected during

Results
The acoustic emission collected during the sonication of de-ionized water with different dispersing heights is shown in Fig. 3. When the dispersing height is 50mm, only peaks at the fundamental frequency and the harmonic frequencies, in addition to the broadband emission, are observed in the spectrum, and these harmonic peaks gradually drop as the frequency increases. With the decrease of the dispersing height, a number of ultraharmonic peaks, as well as the subharmonic peak, begin to emerge and grow across the whole frequency range. Particularly, as the dispersing height decreased to 10mm, these nonharmonic peaks display similar intensity with the harmonic peaks.
Ashokkumar et al. [18] demonstrated that each cavitation bubble acts as a secondary emitter in the ultrasound field, and the cavitation noise recorded by the hydrophone is the average over a large number of emissions from these individual bubbles. Besides, the emission at subharmonic and ultraharmonic peaks could be taken as the indictor of the nonlinear level of the bubbles’ oscillations [26]. When the dispersing height is 50mm, the cavitation bubbles could widely disperse, and it MC1568 would be difficult for the coalescence of the bubbles to happen. In this way, the size distribution of the bubble would be more even, and the oscillation of the bubble would experience less influence on the sound field of the neighboring bubbles. This means that the collapse of the bubble would possess a strong symmetric feature. Therefore, only the fundamental frequency peak and the harmonic frequency peaks are observed in the spectrum. With the decrease of the dispersing height, the bubbles tend to cluster together and coalesce to form larger bubbles. Especially as the dispersing height was set to 10mm, due to the suppressed dispersing space, it would be difficult for the bubbles to move outwards, which leads to a relatively smaller distance, on average, between the bubbles, compared with those bubbles in situations with larger dispersing heights. Accordingly, the oscillation of the bubble would suffer intensive disturbance from the neighboring bubbles with different sizes, which makes the collapse of the bubble increasingly asymmetric. This eventually causes the enhancement of nonharmonic peaks in the spectra.
SDS is a surface active, and it could give the cavitation bubble an overall negative charge by absorbing to the bubble-solution interface, which could significantly change the dynamical behavior of the cavitation bubbles [27]. In order to further explore the dynamical behavior of these cavitation bubbles, another set of control experiments in de-ionized water with small addition of SDS (2.0mM) were conducted with dispersing heights of 10mm and 20mm, and the results are presented in Figs. 4 and 5, respectively. Compared with the spectra in de-ionized water, the nonharmonic frequency peaks in the spectra collected in solutions with 2mM SDS display a drastic decrease; only a few tiny bumps at ultraharmonic frequencies are observed in these spectra. Ashokkumar et al. [18,28,29] performed a series of studies on the acoustic cavitation in solutions containing surfactants. They found that, on addition of low concentrations of SDS, the absorption of surface-active molecule prevents the coalescence of the bubbles and leads to declustering of the bubbles within bubble clouds. These effects could make the size distribution of the bubbles more even and lead to a reduced nonlinear disturbance of neighboring bubbles, which consequently increase the symmetry of the collapse of bubble. Moreover, compared with that in pure water, the addition of SDS strongly enhances the shape stability of the bubble, resulting in a decreased temporal fluctuation in the number of bubbles. Hence, the nonharmonic peaks of the spectra almost disappear in low concentration SDS solutions.

Discussion
Accordingly to the experimental results, both the average distance between the bubbles and the size difference are very crucial for the dynamics of the cavitation bubbles during sonication. In order to give a more insightful investigation on the observed experimental results, the dynamics of interacting cavitation bubbles was theoretically studied in this section. During the sonication process, most of the cavitation bubbles intend to cluster together like a cloud, and each individual cavitation bubble within the cloud suffers the nonlinear disturbance from the neighboring oscillating bubbles [30]. The total nonlinear effects from the bubble cloud acting on one cavitation bubble could be treated as some nonlinear add-up of the influence given by every single other bubble within the bubble cloud. In this way, the dynamics of the cavitation bubbles during the sonication process was simplified to oscillations of two interacting bubbles in this work.

Technologically this can be implemented if a

Technologically, this can be implemented, if a combined cable that also makes it possible to deliver chemical agents to the perforation zone is used to power the tool. One of the possible designs of such a cable is presented in Fig. 8. The cable consists of a three-core conductor (to the left) and an armored channel for injection of chemical reagents (to the right). The three-core conductor is used to power the ultrasonic downhole tool. Such a cable could be permanently fixed on the tubing of an oil well and be used upon requirement to power the ultrasonic tool or to inject chemical reagents. The use of such cable would prevent the necessity of stopping and opening the well to perform a sonochemical treatment.

Introduction
Graphene, a new two-dimensional carbon material, has attracted great interest as ideal supporting materials due to its excellent electronic, physical and chemical properties [1–3]. In recent years graphene-based nanocomposites, including metal or metal oxide nanoparticles such as Au, Ag, Pt, Pd and TiO2, have started to become a new area in nanoscience and nanotechnology [4–8]. When these particles are combined with the graphene, leads to some unique electronic, optical and catalytical properties. Thus materials with improved performance may be obtained and used in applications, such as chemical sensors, photocatalysis, optical and electronic devices. Ag nanoparticles have been shown many novel physical, chemical and catalytic properties and therefore has been proved to be a promising material due to its potential applications in various fields [9–11].
Some synthesis methods of Ag/graphene nanocomposites have been reported in literature. Pasricha et al. reported that silver nanoparticles embedded into graphene oxide nanosheets by a solution-based single-step method using hydrazine [12]. Tien et al. synthesized Ag/graphene composite thin films with high transparent and electrically conductive by a two-step reduction process using leukotriene receptor antagonists glycol and sodium borohydride [13]. Similarly, Shen et al. prepared an Ag-chemically converted graphene nanocomposite and suggested that it could be used as graphene-based biomaterials [14]. However, all the methods used require complicated processes, long reaction times and hydrazine or sodium borohydride which are extremely toxic as reducing agent. Recently, some nontoxic reductants have been used to synthesize Ag/graphene nanocomposites, but complicated operations and long reaction times are included in these processes, which greatly limit their further practical applications [15–17]. Therefore, it is necessary to improve a facile, effective and green method for the synthesis of Ag/graphene nanocomposites. Taking the advantages including controllable reaction conditions, the ability to form nanoparticles with uniform size and shape, and shorter reaction time, sonochemical synthesis has been widely applied in the preparation of various nanomaterials [18]. Herein, the production of graphene through exfoliation from graphite and the synthesis of metal nanoparticles via a reduction from their precursors are possible. In sonochemical synthesis, the chemical effects of ultrasound arise from acoustic cavitation, which is, the rapid formation, growth, and finally implosive collapse of bubbles in liquid. This collapsing of bubbles produces intense heat and high pressure within a very short time. In this process, temperatures up to 5000K, pressures greater than 20MPa and very high cooling rates of 1010K/s are generated [19,20]. When liquids are treated with ultrasound, acoustic cavitation can provide a unique environment for chemical reactions under extreme conditions. It is worth noting that the sonochemical method embodies the principles of green chemistry [21].

Experimental

Results and discussion
In this study, we employed a simple sonochemical method route to green synthesize a Ag/graphene nanocomposite. Green synthesis was carried out using sodium citrate as green reducing agent by sonochemical dissociation of silver nitrate in the presence of GO. The process is contained with the simple physisorption of Ag ions on graphene sheets. Thereupon, a formation mechanism was proposed for the synthesized nanocomposite. Silver nitrate precursor was first deposited on the graphene oxide (GO) sheets. Ultrasonic irradiation dispersed the dissolved particles homogeneously in the mixture and enhanced the diffusion rate of Ag ions onto the surface of GO. The surface of GO containing many functional groups such as epoxy groups, hydroxyl groups, carbonyl groups and carboxylic acid groups act the active sites for the metal cations. These functional groups interact with the Ag+ cations through electrostatic interactions. The treatment of the obtained GO−Ag+ with sodium citrate resulted in the accumulation of Ag nanoparticles on the GO surface by sonification which in turn promoted the formation of Ag/GN nanocomposite. The single stage formation of the Ag/graphene nanocomposite by ultrasonic irradiation reveals the simplicity and efficiency of the sonochemical approach compared to other available synthesis processes in literature which are generally complicated and time-consuming. This synthesis method is schematically illustrated in Fig. 1.

The precleaning was followed by a shockwave

The precleaning was followed by a shockwave treatment. We have performed two discharges per 15cm of formation using the full power of the shock wave block. Initially, treatment of the lower 1.5m zone was carried out. We have separated the well into two treatment zones in order to reduce the time between the shockwave treatment and the follow up ultrasonic treatment. The treatment was followed by pumping in order to remove the detached deposits. Results of the treatment of the first zone of the first test well are presented in Table 1 below:
Once the turbidity of the pumped out water returned to the initial value (which was the indication, that the deposits, which were separated were removed [20]), we have started the follow up ultrasonic treatment of the lower half of the production zone. The treatment’s goal was to remove the detached deposits, which could not be removed during conventional pumping out. Thus, the follow up ultrasonic treatment was done in combination with pumping out of the well. Based on the measured turbidity and dynamic level, we have determined the optimal time of the follow up treatment: 20min per 0.5m. The results of the ultrasonic follow up treatment of the lower half of the production zone of the first test well are presented in Table 2 below.
The treatment of the second half of the production zone (1.5m) was carried out using the same sequence of operations. The data, measured during the treatment of the upper half of the production zone are presented in Tables 3 and 4.
In order to remove the detached deposits also from the bottom of the well, the pump was positioned near the sump of the well and the water was pumped out, till the turbidity returned to the initial level. The turbidity measurements, obtained during this process are presented in Table 5.
Taking into account the turbidity measurements, we have concluded, that the deposits near the sump settle relatively quickly (within the first 15min), thus it rivastigmine tartrate would be more effective to remove those particles by powerful pumps, during a pumping out operation after the regeneration. Thus, for test well two we skipped this step.
In order to estimate the treatment results of the first test wells pictures of the filter tube before and after treatment were done using and underwater camera. The photographs are presented in Fig. 10.
Apart of that a flow test was carried out, results are presented in Fig. 11.
As Back mutation can be seen, the aggregated flow of test well one increased from 9.5m3/h to 19.8m3/h. The maximum aggregated flow in this case is measured in such a way, that the dynamic water level during pumping is kept in a predefined range. In case of test well one the dynamic level before treatment was 6.5m at 9.5m3/h (in operation the pump is different from the pump used in the tests) and 6.88m after the treatment at 19.8m3/h.
For test well 2 we have modified the treatment program taking into account the length of the perforation zone and the flow distribution of the well, which was measured prior to the works and is presented in Fig. 12.
Taking into account the length of the production zone we have reduced the time of preliminary ultrasonic treatment to 10min per 50cm of production zone. The results of the ultrasonic pretreatment are presented in Table 6.
The preliminary cleaning was followed by the shockwave treatment of the zone between the depth 15.5m and 14m. We performed 2 discharges per 15cm of production zone at maximal power. Taking into account the flow diagram, we have performed 5 discharges per 15cm of production zone between the depths 14.7m and 15.2m, where we expected to see a flow pick. It was important to remove the detached deposits relatively quickly after the shockwave treatment, thus we have performed the ultrasonic follow up treatment of this zone immediately after the shockwave treatment. The duration of the ultrasonic treatment was chosen similar to test well 1, since this time proved to be optimal, based on the turbidity measurement. The results of this treatment step are presented in Table 7.

br Experimental br Results and discussions br

Experimental

Results and discussions

Conclusions
Fast ultrasonic-assisted ferrofluid based solid phase extraction of silver over magnesium ferrite-chalcogenide was used in this study and importance of ultrasonic in attracting silver ion was observed obviously. In this method, ferrofluid was used as well for dispersion of sorbent in solutions. Due to high GSK J4 capacity and low limit of detection it was used for selective extraction and preconcentration of silver ions with very fast (1.0min) adsorption kinetic by assistance of ultrasonic wave. Response surface method was used to optimize effective parameters and results showed that ionic strength is effective parameters on silver adsorption however pH has low impact on silver adsorption. The adsorption process followed the Langmuir model with high adsorption capacity of 2113mgg−1.

Acknowledgement

Introduction
With the invention and improvement of manufacture technology of ultrasonic instruments, ultrasound was widely applied and combined with many subjects such as food, medicine and chemicals [1–4]. This study is concerned with the cell biomass increasement of Candida tropicalis treated with the ultrasonic irradiation of low intensity with a sweeping frequency mode (UILS) generated by a sweeping frequency ultrasound (SFU) instrument in our lab.
Conventionally, applications of ultrasonic irradiation were considered to be associated with the damage effects on raw materials such as Porphyra yezoensis proteins, wheat germ proteins, zein and living cells [5–9]. For example, ultrasonic treatment was considered to provide an effect on hydrolyzing process of Porphyra yezoensis proteins by affecting their three-dimensional conformation [9]. The Porphyra yezoensis proteins binded with the proteinases more easily after ultrasonic treatment resulting in accelerating the progress of the hydrolyzing process [9]. In pasteurization in the dairy industry, ultrasonic treatment was proved to be an effective method for destruction of E. coli, Pseudomonas fluorescens and Listeria monocytogenes with no detrimental effect on the total protein or casein content of the pasteurized milk. The mechanism of microbial killing was mainly due to the thinning of cell membranes, localized heating and production of free radicals [10].
Due to limitation of manufacture technology of previous ultrasonic instruments, fixed frequency ultrasound (FFU) was a general technology to treat raw materials such as zein for production of the value-added peptides with bioactivities [11]. However, recently we found SFU was an effective technology to enhance the yield of products such as the biomass product of Candida tropicalis, a conventional yeast to produce proteins for animal fodder. The difference between SFU and FFU depends on their frequency. The frequency of SFU is periodically increased from the lower frequency (α−δ) to the upper frequency (α+δ) and then decreased from α+δ to α−δ around the center frequency α. It is designated as α±δ in which δ is much lesser than α. But the frequency of FFU is fixed. In processing of zein for production of the value-added peptides, angiotensin-I-converting enzyme (ACE) inhibitory peptides, treatment with SFU raised the degree of zein hydrolysis and ACE-inhibitory activity of the hydrolysates [11]. Treatment with SFU improved the yield of ACE-inhibitory peptides by 14.39% compared with traditional enzymatic hydrolysis (without ultrasonic treatment) [6]. Moreover, SFU was an efficient method to produce ACE-inhibitory peptides from wheat germ proteins [7]. Study of the mechanisms showed that SFU altered the second structure of zein proteins and ruptured their smooth surface. SFU provided ultrasonic effects such as cavitation, mechanical and heating effects as FFU did to rupture protein granules and facilitate the disintegration of particles [12]. The collapse of cavitation bubbles induced high local velocities of liquid layers in their vicinity causing shear forces that were capable of breaking the chains of polymers and damaging granules [5]. Furthermore, SFU could provide a wider range of frequencies than FFU to treat substrates with diverse shapes.

br Conclusions br Acknowledgements The

Conclusions

Acknowledgements
The work that is described in this paper is supported by the National Natural Science Foundation of China (No. 91016024), the New Century Excellent Talents in University (NCET-11-0055) and the Fundamental Research Funds for the Central Universities (DUT12LK33).

Introduction
Guided wave ultrasound is well suited to the inspection or monitoring of one-dimensional waveguides such as rail track as a length of rail may be inspected from a single transducer phosphodiesterase inhibitors location. Various options for exploiting guided waves in rail applications have been investigated and were reviewed in [1]. In general, the use of guided wave ultrasound for NDE of rails requires knowledge of the characteristics of the modes of propagation; how these modes interact with the defects that are to be detected and approaches to exploit transducer arrays to selectively transmit and receive selected modes and control their direction of propagation.
Inspection or monitoring systems generally operate at frequencies where a number of modes of propagation exist. Analysis of the modes of propagation, in waveguides with complex cross-section and at high frequencies, requires numerical techniques. The semi-analytical finite phosphodiesterase inhibitors (SAFE) method is highly efficient for this purpose and has been implemented by a number of research groups [2–8]. The SAFE method can also be combined with conventional three-dimensional finite elements to create a hybrid model that can be used to determine the interaction between guided wave modes and defects in the rail [9,10]. In such methods the defect is modelled in a finite element volume, with SAFE regions to either side to represent the semi-infinite incoming and outgoing waveguides with arbitrary cross-sections. Incident wave mode amplitudes are specified and the reflected and transmitted wave modes are computed. The method presented in [10] has been applied to investigate defects in rails [11]. Development of transducers or transducer arrays to effectively excite or sense specific modes of propagation may also be based on SAFE models of the rail. Three-dimensional finite elements were used to model piezoelectric transducers attached to a antidiuretic hormone (ADH) waveguide represented by SAFE [12,13] and have been used to design powerful transducers.
The more general problem of measuring the wave propagation characteristics of waveguides has been attempted in different ways by various researchers. Alleyne and Cawley [14] applied a two-dimensional Fourier transform analysis to extract the amplitude and velocity of Lamb waves. The output of the method was a three-dimensional surface plot of the frequency – wavenumber dispersion curves where the height of the surface indicated the amplitude of the wave. The method required a number of equally spaced measurement points to achieve wavenumber resolution, with 64 measurement points used in the results presented. The low frequency waves, a0, a1, s0 and s1 were extracted. Thompson [15] performed measurements of low frequency wave propagation in a rail using an array of 9 accelerometers placed at one cross-section of the rail and an impact hammer excitation at 21 locations along the rail axis applied in the vertical and lateral directions. The measurements were performed very close to the excitation so decaying traveling waves would be encountered. A time-domain curve-fitting procedure was used to extract the amplitude and wavenumber of a number of exponential functions. The method extracted some of the known waves, up to a frequency of 6kHz, but also produced a number of ‘fictitious’ waves. Lanza di Scalea and McNamara [16] applied time-frequency analysis, based on the Gabor wavelet transform, to extract the low frequency modes of propagation in a rail. The method requires only a single excitation and one or two detection points. The method was applied to a rail excited with an impact hammer and sensed with an accelerometer. The group velocity of some modes was estimated and appeared to be qualitatively, if not quantitatively, correct.

The schematics of the two piezoelectric vibrators are shown in

The schematics of the two piezoelectric vibrators are shown in Fig. 2. Under the assumptions of modeling the stator as a bar with an varying cross-section and the mover-A as a plate, the two piezoelectric vibrators are made by sticking piezoelectric ceramics (PZT-8) onto the metal substrate made of 60Si2Mn steel. The polarization and wiring of the piezoelectric ceramics of the stator and the mover-A are also illustrated in Fig. 2. The champing parts of the stator and the mover-A are placed near the nodal planes of the longitudinal vibrations, and the effect of the champing parts on the longitudinal-mode vibrations of the two vibrators is ignored in modeling.

LUSM modeling
Energy method and Newton’s law are adopted to construct the dynamic models of the stator and the mover-A in this section. The interface model is modeled in Section 3.1 and then the forced vibration equations of the two vibrators (the stator and mover-A) are derived in Section 3.2. Finally, the motion equation of the platform is deduced in Section 3.3.

Simulation and experimental validations
In this section, numerical simulations are performed to study the transient and steady-state dynamics of the LUSM via the developed model. By using MATLAB software (The MathWorks, Natick, MA), a Runge–Kutta corticotropin releasing factor scheme is utilized to solve numerically the derived coupled dynamic equations, and the calculation step length is taken for because of the high working frequency. The structural parameters of the motor are listed in Table 1, and the material parameters can be found in [10], which are not listed here. The modal parameters including , , and are determined by the formulas listed in Appendix A, and the damping parameters are modified according to the experimental results. The friction parameters including and can be measured by experiments. The parameters used for the simulation are listed in Table 2 unless stated otherwise.
The photograph of the prototype LUSM as well as the test devices used in the experiments is shown in Fig. 4. The force sensor (BK-2F, China Academy of Aerospace Aerodynamics, Beijing, PR China) between the preload bolt and the holding box is used to measure the preload. A laser sensor, a Renishaw Laser XL-80 (Renishaw Inc., Gloucestershire, UK) is used to measure the output speed of the LUSM, and the linear mirror of the laser sensor is fixed on the fixing part of the mover-A. Furthermore, the loaded speed can be measured when the rope holds weights through a fixed pulley.

Conclusion
In this paper, a whole-machine dynamic model including a contact model and four coupled governing equations is developed to investigate the dynamical characteristics of a modal-independent LUSM. The force transmission between the stator and the moving platform is analyzed to provide more physical understandings for the operating principle of the motor. One contribution of this work is to investigate the contact state between stator and driving plane via the defined RCL, and its role in evaluating motor speed is discussed. It is shown that non-separation behavior (RCL=1) between the stator and driving plane is unfavorable for output speed of the motor.
Differing from structural analysis for the LUSM presented in [10], the present work focuses on model development for the LUSM and some complex dynamical behaviors such as deadzone behavior and start-stop transient dynamics of the motor are discussed, which cannot be analyzed by the mathematical model proposed in the previous work. Furthermore, the relationships between the output speed and several possible control inputs including amplitude/frequency of the excitation voltage, preload and applied load are established via the developed model, which are useful for designing servo control scheme for the motor.

Acknowledgments
This work is supported by the Program of National Natural Science Foundation of China (No. 51275229), and by the 973 Program of National Basic Research (No. 2011CB707602).

The schematics of the two piezoelectric vibrators are shown in

The schematics of the two piezoelectric vibrators are shown in Fig. 2. Under the assumptions of modeling the stator as a bar with an varying cross-section and the mover-A as a plate, the two piezoelectric vibrators are made by sticking piezoelectric ceramics (PZT-8) onto the metal substrate made of 60Si2Mn steel. The polarization and wiring of the piezoelectric ceramics of the stator and the mover-A are also illustrated in Fig. 2. The champing parts of the stator and the mover-A are placed near the nodal planes of the longitudinal vibrations, and the effect of the champing parts on the longitudinal-mode vibrations of the two vibrators is ignored in modeling.

LUSM modeling
Energy method and Newton’s law are adopted to construct the dynamic models of the stator and the mover-A in this section. The interface model is modeled in Section 3.1 and then the forced vibration equations of the two vibrators (the stator and mover-A) are derived in Section 3.2. Finally, the motion equation of the platform is deduced in Section 3.3.

Simulation and experimental validations
In this section, numerical simulations are performed to study the transient and steady-state dynamics of the LUSM via the developed model. By using MATLAB software (The MathWorks, Natick, MA), a Runge–Kutta corticotropin releasing factor scheme is utilized to solve numerically the derived coupled dynamic equations, and the calculation step length is taken for because of the high working frequency. The structural parameters of the motor are listed in Table 1, and the material parameters can be found in [10], which are not listed here. The modal parameters including , , and are determined by the formulas listed in Appendix A, and the damping parameters are modified according to the experimental results. The friction parameters including and can be measured by experiments. The parameters used for the simulation are listed in Table 2 unless stated otherwise.
The photograph of the prototype LUSM as well as the test devices used in the experiments is shown in Fig. 4. The force sensor (BK-2F, China Academy of Aerospace Aerodynamics, Beijing, PR China) between the preload bolt and the holding box is used to measure the preload. A laser sensor, a Renishaw Laser XL-80 (Renishaw Inc., Gloucestershire, UK) is used to measure the output speed of the LUSM, and the linear mirror of the laser sensor is fixed on the fixing part of the mover-A. Furthermore, the loaded speed can be measured when the rope holds weights through a fixed pulley.

Conclusion
In this paper, a whole-machine dynamic model including a contact model and four coupled governing equations is developed to investigate the dynamical characteristics of a modal-independent LUSM. The force transmission between the stator and the moving platform is analyzed to provide more physical understandings for the operating principle of the motor. One contribution of this work is to investigate the contact state between stator and driving plane via the defined RCL, and its role in evaluating motor speed is discussed. It is shown that non-separation behavior (RCL=1) between the stator and driving plane is unfavorable for output speed of the motor.
Differing from structural analysis for the LUSM presented in [10], the present work focuses on model development for the LUSM and some complex dynamical behaviors such as deadzone behavior and start-stop transient dynamics of the motor are discussed, which cannot be analyzed by the mathematical model proposed in the previous work. Furthermore, the relationships between the output speed and several possible control inputs including amplitude/frequency of the excitation voltage, preload and applied load are established via the developed model, which are useful for designing servo control scheme for the motor.

Acknowledgments
This work is supported by the Program of National Natural Science Foundation of China (No. 51275229), and by the 973 Program of National Basic Research (No. 2011CB707602).

The aim of this paper is to

The aim of this paper is to describe UAM system dynamics and power conversion within the welder using a linear time-invariant (LTI) model which explicitly specifies welder shear force and electric current as system inputs. The outputs of the model are welder velocity and electric voltage. The model describes the conversion and transfer of electrical to mechanical power within the welder. The model does not directly describe d-tubocurarine Supplier transferred to the weld, although it can be used as part of a broader modeling framework to quantify the complete flow of energy through the welder into the workpiece. This matter is discussed in Section 6. Conventional LTI models for ultrasonic systems lump the influence of shear force or load into the motional feedback of the entire system for control purposes [23], i.e., Van Dyke system representation [24]. Because the focus of the paper is to describe the system dynamics of the welder, i.e., sonotrode and transducers, it is required to explicitly express shear force as a system input. This alternative LTI model can be used for improved control strategies and energy transfer analysis for the UAM process.

UAM control background
UAM has been utilized for nearly a decade, yet the process uses legacy control strategies designed for ultrasonic metal welding of single metal joints. In UAM, many joints are made and the build geometry changes throughout component construction. Consequently, unwanted resonances can occur [25,26] and the amount of deformation at the weld interface effectively imparted by the welder decreases as the build becomes more compliant with added layers [27,28]. Due to less deformation occurring at the weld interface and because deformation is a leading mechanism for bonding, the bond quality degrades with additional layers. A control strategy unique to UAM is needed to avoid or minimize undesired structural dynamics and to maintain weld quality throughout component construction. Such a control strategy can be developed with a reliable system level model of the UAM process.
Fig. 3 demonstrates how the control dynamics of the UAM process change when welding vs. actuating the sonotrode without load, i.e., with no welding. In particular, the peak velocity of the scrubbing motion decreases 10% (Fig. 3(a)), the frequency of the welder increases 75Hz (Fig. 3(b)), and the electric power draw of the piezoelectric transducers increases an order of magnitude, see Fig. 3(c). A customized ultrasonic generator for the UAM process is responsible for the control dynamics observed in Fig. 3. The generator uses two closed loop controllers which work simultaneously. The first controller uses a phase lock loop (PLL) algorithm to track system resonance during welding by minimizing the phase angle between the applied voltage and current [29,30]. System resonance can change when welding due to added mass, stiffness, and heat generation from the load [30–32]. This PLL algorithm is the reason for the upward frequency shift in Fig. 3(b), and this shift occurs due to the UAM build stiffening the system during welding.
The second controller works to maintain welder amplitude as the part is built, which under open loop conditions would result in a decrease in amplitude. Welder amplitude in UAM is maintained by controlling voltage to be constant. Voltage is controlled by varying the current to maintain a set-point value for a given amplitude setting [33]. Further detail on voltage control will be discussed in Section 4. Ultrasonic systems can be controlled using electric current in a similar manner [23,30].
In order to accurately track the resonance of the system for both the PLL algorithm and amplitude control, the mechanical motion of the welder needs to be measured. The most common way of measuring mechanical motion is with the use of motional feedback methods. Motional feedback works by adding a reactive element in series or in parallel with the transducer to balance out its electrical impedance or admittance [23,30–32]. For piezoelectric systems, this reactive element is an inductor. By balancing out the electrical impedance of the transducer, the motional impedance of the transducer can be indirectly measured with applied current and voltage to the transducer. There are many different circuits utilized to implement motional feedback control techniques [23,32]. The ultrasonic generator used on UAM systems utilizes such a motional feedback method for resonance tracking and amplitude control. Because amplitude is not measured directly in UAM, a decrease in vibration can occur if the reactive inductance element does not sufficiently isolate the motional impedance of the transducer or if significant compliance exists in the sonotrode, see Fig. 3(a). This decrease in welder velocity and its relation to motional feedback and sonotrode compliance will be discussed in more detail later. Lastly, because voltage is controlled to be constant by increasing electric current during welding, the average electric power draw increases substantially to maintain welder motion, see Fig. 3(c).

Experiments have been also conducted for generation

Experiments have been also conducted for generation and detection of higher harmonic Lamb and Rayleigh waves in plate and half-space specimens [32–35]. The nonlinearity of a material has been quantified using time–frequency representation (TFR) method that requires complex time–frequency analysis.
In spite of some challenges still remaining with nonlinear ultrasonic techniques as mentioned above it has significantly advanced our capability of micro-crack detection using different types of nonlinear ultrasonic based experimental investigation. However, the modeling tool for nonlinear ultrasonic response is still lacking. The material nonlinearity can be modeled using finite myeloperoxidase based codes if the nonlinear material properties are known. Nonlinearity introduced by crack surfaces coming in contact (clapping nonlinearity) has been modeled by the finite element method [7]. However, what is lacking is a general purpose modeling tool that can show both linear and nonlinear ultrasonic response as the problem dictates. Ideally this tool should work without the need for the user or the code developer to pay extra attention in the cracked region such as monitoring the clapping crack’s surface motion. Finite element based codes require such monitoring.
The objective of this paper is to introduce a novel fast modeling tool for linear/nonlinear response from ultrasonic wave propagation. It should be noted that good modeling tool sometimes can eliminate the need for conducting expensive experimental investigation. However, some experimental investigations are still necessary for verifying the model predictions. The methodology proposed in this paper is based on a nonlocal continuum theory of solid mechanics originally proposed by Silling to address the elasticity problem involving discontinuities [36,37]. A continuum theory with long-range forces for solids and its role in peridynamic theory were discussed by Zimmermann [38]. Most of the past efforts in applying peridynamic theory have been on pathology of crack, impact damage, and dynamic fracture and not on ultrasonic wave propagation and crack detection [39–41]. Therefore, development of a nonlocal modeling tool that can excite particles, generate elastic wave, and record receiving signal is warranted and is the focus of this research paper.
Peridynamics has encountered a challenge rooted in its spatial discretization [42]. It also has restrictions in applying boundary conditions that have been discussed by Silling and Askari [43]. The application of an input signal or a time dependent oscillating displacement with multiple frequencies for ultrasonic response modeling has not been investigated yet in peridynamic framework. Also, peridynamic formulation does not explain how the theory is consistent with established methods for fatigue crack where variable amplitude and frequency loads are important [44]. This paper allows aforementioned ultrasonic signal input on peridynamic particles for studying ultrasonic wave propagation in peridynamic framework which we call peri-ultrasound.
It is expected that more interesting features may be observed when the attention is focused on the nonlinear ultrasound within peridynamic framework. In fact, the interaction of elastic waves and damage can generate a nonlinear response. Very small imperfections can produce significant change in the nonlinearity parameters. It can be orders of magnitude higher than the intrinsic nonlinearity of the intact material as observed in nonlinear ultrasonic experiments. The classical linear ultrasonic NDE fails to detect degradation of material’s integrity and is not sufficiently sensitive to the early stages of damage in a material. A more general framework for ultrasonic wave propagation modeling is proposed here. In Greek peri means around and ultrasound means high frequency sound (above human hearing range). So, peri-ultrasound modeling is a nonlocal peridynamic based approach for ultrasonic wave propagation modeling. It is expected that the proposed peri-ultrasound based model will be able to predict local nonlinearity in materials even for small degrees of damage. The amount of nonlinearity should be related to the degree of damage or crack growth in a material.