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It is well known that the inertial actuator can be used as the passive vibration absorber if the natural frequency of the inertial actuator is closed to the targeted structural resonance frequency. Typically, the inertial actuator as a passive or semi-active vibration absorber can only control a single structural resonance at a time. In this study, a simple and practical multiple-degree-of-freedom (MDOF) vibration absorber, which is based on a single inertial actuator and a parallel connection of multiple low-pass filters as controller, is proposed to damp multiple structural resonances simultaneously. The control performance of the proposed MDOF vibration absorber is the combined control effects for both passive absorber and active absorber. It means that the multiple-mode structural vibration can be reduced effectively by using a single inertial actuator. Additionally, the proposed controller can be designed by low-cost analogue circuit and allows directly using acceleration feedback. The performance of the MDOF vibration absorber is first analyzed both numerically and experimentally. Then the proposed MDOF vibration absorber is applied to control the vibration of multiple resonances of a cantilever beam. The experimental results show that multimodal damping can be generated by the proposed MDOF vibration absorber.

A large part of research on membrane mufflers focuses on the sound insulation performance of the membrane, and there is less research on the sound absorption performance of the membrane. In most cases, membrane mufflers only have some narrow absorption peaks in the low frequency band. In this paper, a micro-perforated dielectric elastomer membrane sound absorber is introduced to broaden the sound absorption frequency band of the membrane in the low frequency band. Different initial thickness, perforation aperture, and perforation spacing of the dielectric elastomer membranes were designed and fabricated, and the effect of the variation of the parameters was investigated by testing the sound absorption performance of the structural specimens. It was found that increasing the initial thickness of the membrane, appropriately decreasing the perforation aperture, and appropriately controlling the perforation spacing could improve the sound absorption performance of the structure. And based on the perforated membrane, a ring electrode structure was further designed to realize the electrically adjustable sound absorption frequency of the membrane. After the membrane with the ring electrode structure was perforated in the central region, the sound absorption band of the membrane was broadened significantly, and the applied voltage could realize the electrically adjustable sound absorption performance of the structure in the low frequency band.

In this study, a new methodology is presented to detect the sensor fault for piezoelectric array based on the filtered frequency response function (FRF) shapes. The proposed method does not require prior knowledge about healthy piezoelectric array. First, the imaginary parts of FRFs from the piezoelectric array during vibration are measured and normalized to obtain the FRF shapes in different frequencies. Then the irregularities in these FRF shapes are extracted by using high-pass filter with properly chosen cut-off frequency. These abnormal irregularities on the filtered FRF shape curves indicate the location of the faulty sensor, due to the irregularity of FRF shapes introduced by the faulty piezoelectric element. The proposed sensor fault method is experimentally demonstrated on a clamped-clamped steel beam mounted with piezoelectric buzzer array. Two common piezoelectric sensor fault types including sensor breakage and debonding are evaluated. The experimental results indicate that the proposed method has great potential in the detection of the sensor fault for piezoelectric array as it is simple and does not require the FRF data of the healthy sensor array as a baseline.

Goal for the present research is investigating the effect of scale effect on free vibration of piezoelectric sandwich nanobeams on Winkler foundation. For this purpose, the effects of nonlocal parameters and strain gradient parameters on the free vibration of the model are studied. Based on the nonlocal strain gradient theory and Timoshenko beam theory, the nonlinear vibration of piezoelectric sandwich nanobeams on Winkler foundation is investigated. The nonlinear governing equations and boundary conditions are derived using the Hamilton's principle. The partial differential equation is transformed into ordinary differential equation by Galerkin's method, and then the nonlinear vibration of piezoelectric nanobeam is numerically analyzed using the Runge-Kutta method. The results show that the nonlinear frequency ratio decreases with the increase of length-to-thickness ratio. When the nonlocal parameter is not less than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness softening effect. When the nonlocal parameter is not greater than the strain gradient length scale parameter, the piezoelectric nanobeam exhibits stiffness hardening effect. It is also observed that both large length-to-thickness ratios and shear deformation can attenuate the nonlocal strain gradient effect. In addition, changes in the external applied voltage have a significant effect on the natural frequency of the piezoelectric nanobeams and increasing the thickness of the piezoelectric layer can enhance the structural stiffness.

Considering the internal and external disturbances in actual engineering structure, a composite active vibration control method is proposed for an all-clamped piezoelectric panel. First, the theoretical modal analysis and laser vibrometer are employed to obtain the natural frequency and mode shape of the panel, for reasonable arrangement of actuator and accelerometer. Second, a nonlinear extended state observer is introduced to estimate the total disturbances, i.e., modeling uncertainties, high-order harmonics, coupling and external excitations. Third, the estimated value is used to compensate and attenuate the influence of the total disturbances in real time. In addition, the feedback controller based on the proportional differential and acceleration feedback method is designed to enhance the vibration suppression performance of the whole system. Finally, a semi-physical platform is built in MATLAB/Simulink real-time environment with the NI-PCIe6343 acquisition card to verify the effectiveness and superiority of the proposed method.

Inertial actuators (IAs) are often used as control units in active noise and vibration control systems. It is well-known that the IA's natural frequency should be far below that of the structure under control to ensure good stability margins. However, under normal circumstances, an IA with low natural frequency either increases the additional weight or causes unwanted static displacement of the IA's proof-mass. In this study, an IA with virtual mass is presented to reduce the IA's natural frequency without changing its physical design. The virtual mass of the IA is realized by using the proof-mass acceleration feedback as a local loop within the IA. Thus, the IA's natural frequency can be shifted to low frequency for active control application. The proposed IA with virtual mass is then applied to actively control a clamped beam's vibration based on the velocity feedback control system. The experimental results show that the stability of the control system and the control performance can be improved significantly as the IA's natural frequency is reduced with virtual mass.

To realize structural vibration control,a two parameters H2 optimization design was proposed to optimize the tuning ratio and damping ratio for electromagnetic tuned mass damper (EMTMD). The control effect of this two parameters optimization design is better than that of classical tuned mass damper (TMD).For this two parameters optimization,the most important thing is that the inductance of the coil can be set very small and the external load resistance can be positive ,which can avoid the use of complex negative impedance circuit. If Ref.[6] were designed according to the H2 optimization of two parameters, the EMTMD can be used for multi-modal vibration control of structures without connecting negative inductance and negative resistance spontaneously.

A new type of deep subwavelength acoustic metamaterial (AMM) absorber with 100% ventilation is presented in this study. The proposed ventilation absorber consists of coiled-up half-wave resonators (HWRs) and quarter-wave resonators (QWRs). First, the sound absorption and sound transmission performances for absorbers were analyzed considering the thermal viscosity dissipation. Then, the prototype with ten HWRs and three QWRs composed of acrylic plates was manufactured based on the theoretical model. The acoustic performance of the absorber was tested in an air-filled acoustic impedance tube to determine the sound absorption and transmission loss performances. Good agreement was found between the measured and theoretically predicted results. The experimental results show that the proposed ventilation AMM absorber is able to achieve sound absorption in a range between 330 Hz and 460 Hz with a thickness of only 32 mm (about 3% of the wavelength in the air). Furthermore, the sound transmission loss can achieve 17 dB from 330 Hz to 460 Hz. The main advantage of the proposed absorber is that it can be completely ventilated in duct noise control.

Helmholtz resonators (HRs) are widely used to reduce narrow frequency band noise. In this paper, by using microphone and loudspeaker in HR as sensor and actuator, a sweeping HR with time-varying natural frequency, which can eliminate the complexity of changing the physical dimension of HR during operation, is developed. The natural frequency of the HR is continuously swept by using a time-varying Proportional-Integral (PI) controller. The main advantage of the proposed sweeping HR is without requiring of the accuracy value of the targeted control frequency. Finally, the experimental results are presented to verify the control performance of the proposed sweeping HR. Noise reduction of 6 dB in the 120–170 Hz band was obtained when one sweeping HR was installed in a rigid duct.

In this work, a double-layer honeycomb microperforated structure with adjustable back-cavity’s height is designed based on cylinder honeycomb structure and microperforated panel (MPP). The sound absorption performance can be changed by adjusting the height of back-cavity. Thus, a better absorption performance is achieved by changing the position of the inner MPP. Acoustic impedance of the structure was calculated based on transfer matrix method. The sound absorption coefficient of the structure was obtained by finite element method (FEM). Meanwhile, the 3D printing technology was used to produce the experimental samples. The experimental results demonstrate that the sound absorption coefficient of the structure is greater than 0.8 in the range of 750–1250 Hz, greater than 0.9 in the range of 2297–3592 Hz, and above 0.5 in the range of 500–4000 Hz. In addition, the feasibility of achieving adjustable sound absorption by means of changing the height of the back-cavity is verified by theoretical, simulation, and experimental results. The structure proposed in this work can realize the function of wide-band and better sound absorption performance by changing the position of the inner MPP, which can be applied to effectively reduce different frequencies noise.

The sound absorption performance of micro-perforated plate (MPP) is mainly restricted by four parameters: cavity depth, aperture, plate thickness and perforation rate. The concept of change rate of sound absorption coefficient is introduced, which is taken as the measuring standard to judge the influence of changing these parameters on the sound absorption performance of MPP. Generally, the parameter sensitivity of MPP sound absorber from large to small is as follows: cavity depth, aperture, perforation rate, plate thickness. According to the characteristic that the resonant frequency of MPP will shift when the cavity depth changes, combined with the acoustoelectric analogy principle, two kinds of single-layer honeycomb micro-perforated plate (HMPP) structures with different cavity depth are designed by using particle swarm optimization algorithm. Simulation and experimental results show that the structures can use their own different depth of honeycomb cores to achieve the purpose of broadband sound absorption. The feasibility of using particle swarm optimization algorithm to design broadband sound absorber is verified. In addition, through the contrastive analysis of the two structures, compared to the four regions HMPP, the experimental results of the seven regions HMPP are closer to the theoretical and simulation results, which is consistent with the characteristics of particle swarm optimization (PSO): the more optimization parameters are, the better the performance is.

To reduce the noise in a ventilated system, three-dimensional (3D)-printed sound absorbers, based on multiple spiral waveguides, are proposed in this letter. A waveguide unit consists of a fixed-length cylindrical straight tube and a certain number of spiral tubes. The geometrical parameters of the spiral waveguides can be flexibly regulated, aided by the 3D digital modeling method to control the phase of the sound wave. Experimental results show that the proposed sound absorber can obtain the sound transmission loss (STL) about 9.6 dB in a frequency range of 300-1250 Hz with an 18% ventilation ratio.

All-clamped plate structures are usually subject to strong coupling, model uncertainties and system time-delay. To address these challenges, this work proposes a novel vibration control method based on a linear active disturbance rejection controller (LADRC) with time-delay compensation (TDC-LADRC). The mathematical model of the piezoelectric plate is first established based on system identification with an auxiliary variable method. Then ADRC is designed for the delay-free part by a smith predictor with a novel differentiator. An extended state observer (ESO) is drawn to estimate the internal and external disturbances, such as mode errors, higher harmonics and external environmental excitations. Then, real-time compensation is introduced via feed-forward mechanism to attenuate their adverse effects, so that optimal vibration suppression performance can be achieved by the proposed controller. Finally, based on NI-PCIe6343 acquisition card, an experimental set-up is designed to verify and compare the performance of the proposed TDC-LADRC against the traditional LADRC and the traditional predictor based LADRC (PLADRC). Comparative experimental results show that the proposed TDCLADRC possesses the best disturbance rejection and vibration suppression performance.

This research develops a novel composite beam integrating a flexible printed circuit board (FPCB) sensor membrane with polyvinylidene fluoride (PVDF) arrays for accurately extracting modal curvature in a convenient way, which can be easily used in the potential aerospace applications of in-situ structure damage detection or structure health monitoring. The proposed composite beam structure consists of a metal beam, a FPCB sensor membrane and a periodic array of identical rectangular PVDF films. Specifically, a periodic array of identical rectangular PVDF films is encapsulated in the FPCB sensor membrane, and the FPCB sensor membrane is integrated with the metal beam. Since the lead wire, sensors, the protective layer of sensor and the host beam structure are of one-piece construction in the proposed structure, the proposed structure has the self-sensing function that the discrete curvature of modal shapes of the metal beam can be directly obtained by using the experiment modal analysis (EMA) method and no other sensors. Results show that the proposed structure has good self-sensing performance and can directly extract the modal curvature information without any numerical differential calculation. In addition, the proposed structure restrains surrounding noise and improves the stability of the sensor array signal since the sensor array is encapsulated with the metal beam under the same condition.

This article aims to investigate stability and vibration behavior of carbon nanotube-reinforced composite beams supported by classical and nonclassical boundary conditions. To include significant effects of shear deformation and rotary inertia, Timoshenko beam theory is used to formulate the coupled equations of motion governing buckling and vibration analyses of the beams. An effective mathematical technique, namely Chebyshev collocation method, is employed to solve the coupled equations of motion for determining critical buckling loads and natural frequencies of the beams with different boundary conditions. The accuracy and reliability of the proposed mathematical models are verified numerically by comparing with the existing results in the literature for the cases of classical boundary conditions. New results of critical buckling loads and natural frequencies of the beams with nonclassical boundary conditions including translational and rotational springs are presented and discussed in detail a...

An adjustable sound absorption frequency honeycomb-microperforated panel (ASAFHM) structure is designed in this study. The ASAFHM structure is a unit of a honeycomb-microperforated panel (MPP) structure. A mechanical rotating mechanism was used to change the sound absorption property of MPP added in the middle of the ASAFHM core. An equivalent hybrid honeycomb-MPP model, which can be calculated using acoustoelectric analogy and transfer matrix methods, is described to predict the sound absorption of the ASAFHM structure. Experimental results demonstrate that the peak frequency can shift by approximately 14.2%. Furthermore, the maximum 0.8 absorption bandwidth can be broadened to 188% by adjustable absorption baffles under different angles. The relationship between perforation ratio and resonant frequency fitted linearly in this study can be used to design sound absorbers under complex noise environments. This study provides an effective method to adjust the sound performance of sound absorbers. The proposed honeycomb-MPP structure herein is applicable to sound absorption.

It is well-known that the acoustic sound performance of double-plate structures deteriorates rapidly around the mass-air-mass resonance frequency. In this study, a electromagnetic shunt damper (EMSD) connected between incident and radiating plate is used to improve the sound transmission loss at low frequency ranges. The EMSD consists of a coil, a permanent magnet, and a specially designed shunt circuit. First, a full structural-acoustic coupling modal model is developed to analyze the vibration and acoustical behaviour of the double-plate structures with EMSD system. Then two EMSD shunt circuit configurations, namely negative resistance (NR) and negative resistance series with capacitance (NR-C), are proposed to control the sound transmission. The control performance of the EMSD is investigated based on different parameters of the shunt circuits. Finally, the experiment was performed to verify the proposed theoretical model of EMSD. The numerical and experimental results show that, the sound transmission loss around the mass-air-mass resonance frequency can be improved significantly by using the EMSD with NR or NR-C shunt circuit. However, EMSD cannot control the first in-phase mode of the double-plate structure.

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

This paper investigates the dynamic response of Timoshenko beams made of functionally graded materials (FGMs). The beams are supported by various classical and non-classical boundary conditions. By using Timoshenko beam theory to establish the governing equations of motion for describing the vibration behavior of the beams, the significant effects of shear deformation and rotary inertia are taken into account. Different mathematical models that is the power law, exponential and Mori–Tanaka models are used to describe material composition across the beam thickness. To predict accurate vibration behavior of the beams, the Chebyshev collocation method (CCM) is applied to solve the vibration problem of such beams. According to the numerical results, it is revealed that the proposed modeling and analysis method can provide accurate frequency results of the beams as compared to some cases in the literature. New frequency results of the beams with different material compositions and boundary conditions are also presented for future comparison and development.

The theory for calculation and/or measurement of sound power based on the classical velocity-based radiation mode (V-mode) approach is well established for planar structures. However, the current V-mode theory is limited in scope in that it can only be applied to conventional motion sensors (i.e., accelerometers). In this study, in order to estimate the sound power of vibrating beam and plate structure by using polyvinylidene fluoride (PVDF) films as sensors, a PVDF-based radiation mode (C-mode) approach concept is introduced to determine the sound power radiation from the output signals of PVDF films of the vibrating structure. The proposed method is a hybrid of vibration measurement and numerical calculation of C-modes. The proposed C-mode approach has the following advantages: (1) compared to conventional motion sensors, the PVDF films are lightweight, flexible, and low-cost; (2) there is no need for special measuring environments, since the proposed method does not require the measurement of sound fields; (3) In low frequency range (typically with dimensionless frequency kl < 4), the radiation efficiencies of the C-modes fall off very rapidly with increasing mode order, furthermore, the shapes of the C-modes remain almost unchanged, which means that the computation load can be significantly reduced due to the fact only the first few dominant C-modes are involved in the low frequency range. Numerical simulations and experimental investigations were carried out to verify the accuracy and efficiency of the proposed method.

This study is concerned with design of a tuneable vibration absorber by using an inertial actuator (IA) with its proof-mass acceleration used as feedback signal. Acceleration feedback control loop can produce virtual mass effect, and the natural frequency of the IA can be shifted. The main advantage of the proposed IA-based tuneable vibration absorber is that the control loop is very simple and does not require any low-pass filter or integrator. Finally, the experimental results are presented to verify the tuning capability and control performance of the proposed vibration absorber.

This paper presents the results of the experimental vibroacoustical and modal testing of a triple pane insulating glazing structure. The testing was performed in the sound transmission facility using acoustic excitation, force excitation and a laser scanning vibrometer for measurement of frequency response functions and volume velocity. The results of the identification include the modal mass, damping and stiffness, vibratory modes and volume velocity distribution. A new measurement method is presented in order to identify the global vibratory modes of all three combined transparent glass panes simultaneously. These results are essential for updating the analytical model of triple glazing for calculation and prediction of sound transmission loss over a wide frequency range. The calculated and measured sound transmission loss is presented and discussed.

The Adomian decomposition method (ADM) and high-pass filters are employed in this study to investigate the free vibrations and damage detection of cracked Euler-Bernoulli beams. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the mode shapes can be determined for beams consisting of an arbitrary number of cracks under general boundary conditions in a recursive way. Then, a highpass filter is used to extract the irregularity profile from the corresponding mode shape. The location and size of the cracks in the beam can be determined by the peak value of the irregularity profile. The numerical results for different locations and depths of cracks on the damaged beam under different boundary conditions are presented. The results show that the proposed method is effective and accurate. The experimental work for aluminium cantilever beams with one and two cracks was performed to verify the proposed method. The successful detection of cracks in the beam demonstrates that the proposed method has great potential in crack detection of beam-type structures, as it is simple and does not require the mode shapes of an uncracked beam as a baseline.

In this paper, a solution to the problem of finding the shape of piezoelectric modal sensors for non-uniform Euler–Bernoulli beams with rectangular cross-sections is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function as well as the beam width and thickness function. Based on the DTM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes for beams consisting of an arbitrary number of steps can be determined through a recursive way. The solution is obtained by solving a set of algebraic equations with only five unknown parameters. Furthermore, the method can be extended to obtain an approximate solution of the second spatial derivative of the mode shapes for any type of non-uniform beams. Then the shapes of the piezoelectric modal sensors for arbitrary non-uniform Euler–Bernoulli beam with rectangular cross-section are obtained. Finally, several numerical examples are given to demonstrate the feasibility of the proposed modal sensors with various boundary conditions.

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of tapered Euler–Bernoulli beams with a continuously exponential variation of width and a constant thickness along the length under various boundary conditions. Based on ADM the governing differential equation for the tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions and non-uniformity ratios are presented. The accuracy is assured from the convergence and comparison published results.

The Adomian modified decomposition method (AMDM) is employed in this paper to investigate the free vibrations of N elastically connected parallel Euler–Bernoulli beams, which are continuously joined by a Winkler-type elastic layer. The proposed AMDM method can be used to analyze the vibration of beam system consisting of an arbitrary number of beams. By using boundary conditions the natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The numerical results for different boundary conditions, beam numbers and the stiffness of the Winkler-type elastic layer are presented. It is shown that the AMDM offers an accurate and effective method of free vibration analysis of multiple-connected beams with arbitrary boundary conditions.

In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a cantilever beam with intermediate support is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function. By using boundary condition and continuity condition equations at intermediate support, the closed-form series solution of the second spatial derivative of the mode shapes can be determined based on DTM. Then the shapes of the designed modal sensors are obtained. Finally, numerical examples are given to demonstrate the feasibility of the proposed modal sensors for the cantilever beam with intermediate support.

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of the Euler-Bernoulli beams with multiple cross-section steps. The proposed ADM method can be used to analyze the vibration of beams consisting of an arbitrary number of steps through a recursive way. The solution can be obtained by solving a set of algebraic equations with only three unknown parameters. Furthermore, the method can be extended to obtain an approximate solution to vibration problems of any type of non-uniform beams. Several numerical examples are presented and compared to those given in the paper. It is shown that the ADM offers an accurate and effective method of free vibration analysis of multiple-stepped beams with arbitrary boundary conditions.

In this article, a solution to the problem of finding the shape of piezoelectric modal sensors for a non-uniform beam with continuously exponential varying width under general boundary conditions is proposed using the Adomian modified decomposition method (AMDM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function and the beam width function. Based on the AMDM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then, the shapes of the designed modal sensors are obtained. Finally, several numerical examples are given to demonstrate the feasibility of the proposed modal sensors with various boundary conditions.

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of a stepped Euler–Bernoulli beam consisting of two uniform sections. Each section is considered a substructure which can be modeled using ADM. By using boundary condition and continuity condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions, step ratios and step locations are presented. Comparing the results using ADM to those given in the literature, excellent agreement is achieved.

The theory of the Adomian modified decomposition method (AMDM) for solving linear and nonlinear differential equations is well established. However, the solutions obtained by using the current AMDM are valid only for a very small region. In this paper, a new aftertreatment technique is proposed to improve the accuracy of the AMDM during a wide region. Based on the proposed aftertreatment technique, the truncated series solution obtained by the AMDM can be expressed as another series in terms of the independent sine and cosine trigonometric functions. Two numerical examples are presented and compared to those obtained from the numerical 4th-order Runge-Kutta algorithm. It is shown that the AMDM with the proposed aftertreatment technique offers an accurate and effective method for solving nonlinear differential equations in a wide applicable region.

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.

In this paper, a spontaneous Rayleigh-Brillouin scattering spectrometer is developed to measure the gaseous spontaneous Rayleigh-Brillouin scattering profiles over the pressure range from 1 to 5 atm for a wavelength of 532nm at a constant room temperature of 296K and a 90o scattering angle. In order to make a direct comparison between the experimentally obtained spectrum and the theoretical spectrum calculated from the Tenti S6 model, the measured spontaneous Rayleigh-Brillouin scattering signal is deconvolved by the Wiener filtering. The purpose is to remove the effect on the spectrum by the transmission function of the Fabry-Perrot scanning interferometer. The results of the comparison show that the deconvolved spectra are consistent with the theoretical spectra calculated from the Tenti S6 model, and thus confirm that the deconvolution based on the Wiener filter is able to process the measured spectra and improve the spectral resolution. Some factors that influence the accuracy of deconvolution are analyzed and discussed. At the same time, another comparison between the raw experimentally obtained spectra and the theoretical spectra calculated by convolving the Tenti S6 model with instrument function of the measurement system is performed in the same experimental condition. The results of the two comparisons show that, compared with the raw experimentally obtained spectrum, the deconvolved spectrum matches the theoretically calculated spectrum more accurately under lower pressure (≤2atm) than under relative higher pressure (>2atm).

This paper presents an experimental investigation of passively control of sound transmission through a double glazed window by using arrangement of Helmholtz resonators (HRs), which are commonly used for narrow band control application. The laboratory experiments were performed placing the window between reverberation chamber and anechoic chamber. The window was subject to diffuse field, approximate normal wave and oblique wave acoustic excitations. Three sets of HRs were designed and installed in cavity of window. The sound control performances at far-field were measured. The control performances from varying the number of HRs, incident acoustic field, excitation sources (band-limited white noise and traffic noise examples) are presented and discussed in detail. It is shown that a considerable reduction of the transmitted sound pressure levels has been achieved around the mass–air–mass resonance frequency (50–120 Hz). The obtained reductions in the transmitted sound pressure illustrate the potentials of HRs for improving the sound insulation characteristics of double glazed window. The experimental results also indicate that only tuning the HRs to the mass–air–mass resonance frequency does not guarantee the best possible insulation of the sound transmission.

Piezoelectric transducers have been used extensively as the distributed actuators and sensors in active control of structural vibrations. Piezoelectric actuator/sensors are distributively bonded on or embedded in the host structure and have the inherent advantage of integrating over their surface area, which leads to potentially more robust implementations as compared to implementations that use shaker/accelerometers. For this reason piezoelectric actuator/sensors have attracted more and more attention in recent years. In this paper, a theoretical analysis is presented of the active control of a vibrating beam using collocated triangular and rectangular piezoelectric actuator/sensor pairs. The aim of this study is to generate points of zero displacements and zero slopes at any designated position. So the control systems impose a virtual clamped boundary condition at the control position on the beam, in which both displacement and slope are driven to zero. Two independent single-input single-output (SISO) control systems similar to direct velocity feedback (DVFB) are implemented, i.e. for the rectangular pair the voltage signal measured by a triangular piezoelectric sensor is electronically multiplied by a fixed gain and fed directly back to a collocated piezoelectric actuator. The triangular and rectangular piezoelectric actuator/ sensor pairs positioned at one end of the beam are used to measure and control the displacement and slope of the structure respectively. The active control systems are unconditionally stable for any type of primary disturbance acting on the structure due to the collocated actuator/sensors. It should be noted that the presented control strategy is different to DVFB. In DVFB, when the control gain is increased, the vibration energy of the beam is initially reduced at resonance frequencies because of the active damping effect. However this effect does not continue. When large control gains are implemented, the overall kinetic energy of the beam is increased to the same or even higher values than those of the beam without control systems because the vibration of the beam is rearranged into a new set of lightly damped resonance frequencies. Imposing a virtual clamped boundary condition at the control position is clearly more complicated than DVFB, because in addition to the zero displacement constraints, the zero slope constraints must also be satisfied. The proposed control system allows for certain points of the structure to remain stationary without using any rigid supports. Furthermore, such control systems have the potential to create a region of nearly zero vibration for any ‘excitation’ frequency. This means that no progressive waves or reflected waves exist in the designated region, thus significantly reducing the vibration level in that region of the beam. The control systems impose a virtual clamped boundary condition at the control position on the beam in which the displacement and slope are driven to zero. As a result, the vibration of the actively controlled beam can be described in terms of two beams clamped at the control position. A numerical analysis is then performed to verify the proposed control system. It is found that the new resonance frequencies and mode shapes seen in the simulations are consistent with the natural frequencies and natural modes of the controlled beam derived analytically. The capability of the proposed method for generating a zero-vibration region is also numerically demonstrated.

In this paper, structural sound and vibration control using passive and semi-active shunt piezoelectric damping circuits is presented. A piezoelectric patch with an electrical shunt circuit is bonded to a base structure. When the structure vibrates, the piezoelectric patch strains and transforms the mechanical energy of the structure into electrical energy, which can be effectively dissipated by the shunt circuit. Hence, the shunt circuit acts as a means of extracting mechanical energy from the base structure. First, different types of shunt circuits (such as RL series circuit, RL parallel circuit and RL-C circuit), employed in the passive damping arrangement, are analyzed and compared. By using the impedance method, the general modelling of different shunt piezoelectric damping techniques is presented. The piezoelectric shunt circuit can be seen as additional frequency-dependence damping of the system. One of the primary concerns in shunt damping is to choose the optimal parameters for shunt circuits. In past efforts most of the proposed tuning methods were based on modal properties of the structure. These methods are used to minimize the response of a particular structural mode whilst neglecting the contribution of the other modes. In this study, a design method based on minimization of the sound power of the structure is proposed. The optimal parameters for shunt circuits are obtained using linear quadratic optimal control theory. In general, the passive shunt circuit techniques are an effective method of modal damping. However, the main drawback of the passive shunt circuit is that the shunt piezoelectric is very sensitive to tuning errors and variations in the excitation frequency. To overcome this problem, the pulse-switching shunt circuit, a semi-active continuous switching technique in which a RL shunt circuit is periodically connected to a bonded piezoelectric patch, is introduced as structural damping. The switch law for pulse-switching circuit is discussed based on the energy dissipation technique. Compared with a standard passive piezoelectric shunt circuit, the advantages of the pulse-switching shunt circuit is a small required shunt inductance, a lower sensitivity to environmental changes and easier tuning. Very low external power for the switch controller is required so it may be possible to extract this energy directly from the vibration of the structure itself. Numerical simulations are performed for each of these shunts techniques focusing on minimizing radiated sound power from a clamped plate. It is found that the RL series, RL parallel and pulse-switching circuits have basically the same control performance. The RL–C parallel circuit allows us to reduce the value of the inductance L due to the insertion of an external capacity C. However, the control performance will be reduced simultaneously. The pulse-switching circuit is more stable than RL series circuit with regard to structural stiffness variations. Finally, experimental results are presented using an RL series/parallel shunt circuit, RL-C parallel shunt circuit and pulse-switching circuit. The experimental results have shown that the vibration and noise radiation of a structure can be reduced significantly by using these shunt circuits. The theoretical and experimental techniques presented in this study provide a valuable tool for effective shunt piezoelectric damping.

This paper presents an overview of recent results concerning active and passive control of sound transmission through double wall structures. First, the analytical simulations are presented for the active control of sound transmission through double wall structures. These are based on a coupling structural-acoustic modal model using piezoelectric materials and loudspeaker/microphones as actuator/sensors. The numerical results show the potential for employing piezoelectric sensor/actuators to improve sound transmission loss. In addition, some useful conclusions are obtained. When, for example, a volume velocity sensor is applied to a radiating plate, sound transmission loss will improve significantly, no matter what type of actuators (i.e. loudspeakers or PZT actuators on either plate) are used. With a loudspeaker/microphone configuration should be avoided for same thickness double wall structures, etc. Furthermore, current research activities on the control of sound transmission through double wall structures also include an arrangement of Helmholtz resonators (HRs) placed within the wall cavity for the passive control of sound transmission through a double wall structure. The current research goal is to find optimal parameters of HRs (damping ratio, numbers, natural frequency, etc.) in order to maximize the improvement of the transmission loss over a specified frequency range. An analytical model of fully coupled structural-acoustic-HRs within a double wall structure is established. Results indicate that tuning the HRs to the mass–air–mass resonance frequency does not guarantee the best possible improvement of the sound transmission loss. Using the frequency averaged sound transmission loss as the cost function to optimize the natural frequency of the HRs is a more effective method to find the HRs tuning frequency for maximizing the improvement of the transmission loss. The aim of this paper is to illustrate the potential of the active control approach using smart piezoelectric materials and different control actuators (i.e. loudspeakers in the cavity, PZT actuators applied to one of the plates) to improve the transmission loss through double wall structures. Additionally, new results on tuning and placement of HRs are presented. Both of these are based upon a refined model of the systems and offer good physical insight into the active and passive control of sound transmission through double wall structures.