Piezoelasticity Theory Research Articles

Thermoelastic analysis of functionally graded carbon nanotube reinforced composite cylindrical panel embedded in piezoelectric sensor and actuator layers

Based on theory of piezo-elasticity, bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel attached to thin piezoelectric layers subjected to thermal, mechanical loads and or electric field is investigated. It is assumed that thermo-elastic constants of the structure are independent of temperature gradient. In this paper, uniformly and various cases of functionally graded CNT distribution along the radial direction of host layer are considered. Governing differential equations are solved analytically by using the Fourier series expansion along axial and circumferential direction and state-space technique across the radial direction. Temperature, stress and displacement fields as well as induced electric voltage in sensor layer are obtained and used to study the thermo-piezoelastic behavior of hybrid FG-CNTRC cylindrical panel. Accuracy of present approach is validated by comparing the numerical results with the available reported results in literatures. Parametric studies are carried out to assess the effects of CNT volume fraction, case of CNT distribution along the radial direction, surface thermal/mechanical surface boundary conditions, applied voltage on the bending behavior of FG-CNTRC hybrid cylindrical panel.

Transient sound radiation from an impulsively excited piezoelectric composite hollow sphere in a wedge-shaped acoustic domain

The exact 3D linear piezoelasticity theory, the linear acoustic wave equation, and the classical method of images are employed for the coupled acousto-elastodynamic time response analysis of an arbitrarily thick two-layered elasto-piezoelectric composite hollow sphere that is freely suspended in a perfect acoustic wedge with impenetrable (rigid/compliant) boundaries, while subjected to arbitrary (non-axisymmetric) non-stationary electro-mechanical excitations. Problem solution is attained by application of the method of eigen-function expansion, a revised form of translational addition theorems for modified spherical Bessel functions in Laplace transform domain, and Durbin’s numerical inversion algorithm with an advanced (modified Cesàro) convergence improvement scheme. Numerical simulations include selected radiated pressure time signatures of a water-submerged air-filled PZT4/aluminum spherical shell driven by a pair of external diametrical short duration mechanical pulses. The effects of sphere wall thickness, wedge opening (apex) angle (γ=π/6,π/4,π/2) and surface condition (hard or pressure-release) are examined. Also, some noteworthy features of the transient fluid/structure interaction are recognized through proper 2D visualizations of the internal and external sound fields. Lastly, accuracy of the proposed acousto-elastic model is confirmed with the help of a commercial FEA software in addition to comparison with the available data.

Unified solutions for piezoelectric bilayer cantilevers and solution modifications

Based on the theory of piezoelasticity, the static performance of a piezoelectric bilayer cantilever fully covered with electrodes on the upper and lower surfaces is studied. Three models are considered, i.e., the sensor model, the driving displacement model and the blocking force model. By establishing suitable boundary conditions and proposing an appropriate Airy stress function, the exact solutions for piezoelectric bilayer cantilevers are obtained, and the effect of ambient thermal excitation is taken into account. Since the layer thicknesses and material parameters are distinguished in different layers, this paper gives unified solutions for composite piezoelectric bilayer cantilevers including piezoelectric bimorph and piezoelectric heterogeneous bimorph, etc. For some special cases, the simplifications of the present results are compared with other solutions given by other researches based on one-dimensional constitutive equations, and some amendments have been found. The present investigation shows: (1) for a PZT-4 piezoelectric bimorph, the amendments of tip deflections induced by an end shear force, an end moment or an external voltage are about 19.59%, 23.72% and 7.21%, respectively; (2) for a PZT-4-Al piezoelectric heterogeneous bimorph with constant layer thicknesses, the amendments of tip deflections induced by an end shear force, an end moment or an external voltage are 9.85%, 11.78% and 4.07%, respectively, and the amendments of the electrode charges induced by an end shear force or an end moment are both 1.04%; (3) for a PZT-4-Al piezoelectric heterogeneous bimorph with different layer thicknesses, the maximum amendment of tip deflection approaches 23.72%, and the maximum amendment of electrode charge approaches 31.09%. The present solutions can be used to optimize bilayer devices, and the Airy stress function can be used to study other piezoelectric cantilevers including multi-layered piezoelectric cantilevers under corresponding loads.

Analysis of Dynamic Properties of Piezoelectric Structure under Impact Load

An analytical model of the dynamic properties is established for a piezoelectric structure under impact load, without considering noise and perturbations in this paper. Based on the general theory of piezo-elasticity and impact mechanics, the theoretical solutions of the mechanical and electrical fields of the smart structure are obtained with the standing and traveling wave methods, respectively. The comparisons between the two methods have shown that the standing wave method is better for studying long-time response after an impact load. In addition, good agreements are found between the theoretical and the numerical results. To simulate the impact load, both triangle and step pulse loads are used and comparisons are given. Furthermore, the influence of several parameters is discussed so as to provide some advices for practical use. It can be seen that the proposed analytical model would benefit, to some extent, the design and application (especially the airport runway) of the related smart devices by taking into account their impact load performance.

Active Transient Sound Radiation Control from a Smart Piezocomposite Hollow Cylinder

Abstract The linear 3D piezoelasticity theory along with active damping control (ADC) strategy are applied for non-stationary vibroacoustic response suppression of a doubly fluid-loaded functionally graded piezolaminated (FGPM) composite hollow cylinder of infinite length under general time-varying excitations. The control gain parameters are identified and tuned using Genetic Algorithm (GA) with a multi-objective performance index that constrains the key elasto-acoustic system parameters and control voltage. The uncontrolled and controlled time response histories due to a pair of equal and opposite impulsive external point loads are calculated by means of Durbin’s numerical inverse Laplace transform algorithm. Numerical simulations demonstrate the superior (good) performance of the GA-optimized distributed active damping control system in effective attenuation of sound pressure transients radiated into the internal (external) acoustic space for two basic control configurations. Also, some interesting features of the transient fluid-structure interaction control problem are illustrated via proper 2D time domain images and animations of the 3D sound field. Limiting cases are considered and accuracy of the formulation is established with the aid of a commercial finite element package as well as comparisons with the current literature.

Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

ABSTRACTThe linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba2NaNb5O15/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.

General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

Based on the fundamental equations of piezoelasticity of quasicrystals (QCs), with the symmetry operations of point groups, the plane piezoelasticity theory of onedimensional (1D) QCs with all point groups is investigated systematically. The governing equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the operator method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

Multi-Objective Robust Active Vibration Control of an Arbitrary Thick Piezolaminated Beam

A multi-objective mixed / robust output feedback control synthesis with additional regional pole placement constraints in a linear matrix inequalities (LMI) framework is adopted for active vibration suppression of a simply supported, arbitrary thick, piezolaminated beam with continuously integrated sensor and actuator layers, in the face of high frequency unmodeled dynamics (residual uncertainties) and external disturbance. The structural formulation is based on a spatial state-space approach using the exact linear two-dimensional piezoelasticity theory and involving local/global transfer matrices. To assist control system design, subspace-based multivariable system identification is carried out by using the first four modes in the frequency range of 0–4000 rad/sec for control purpose, while the remaining high frequency (residual) modes in the control bandwidth are left as the uncertainty of modeling. The dynamic performance of vibration control system is demonstrated in both frequency and time domains for a three-layered sandwich beam including three pairs of piezoelectric actuator/sensor (Ba2NaNb5O15/PZT4) segments asymmetrically collocated on both sides of an orthotropic core for two different types of loading (i.e., impulsive load and random disturbance). The accuracy of dynamic analysis is established with the aid of a commercial finite element package and the data available in the literature.

Active vibration control of an arbitrary thick smart cylindrical panel with optimally placed piezoelectric sensor/actuator pairs

Active vibration suppression of a simply supported, arbitrarily thick, transversely isotropic circular cylindrical host panel, integrated with spatially distributed piezoelectric actuator and sensor layers, is investigated based on the linear three dimensional exact piezo-elasticity theory. To assist control system design, system identification is conducted by applying a frequency domain subspace approximation method based on N4SID algorithm using the first few structural modes of the system. The state space model is constructed from system identification and used for state estimation and development of control algorithm. The optimal electrode configuration for the collocated piezoelectric actuator–sensor pair is found by applying a genetic optimization procedure based on maximization of a quantifiable objective function considering the controllability, observability and spillover prevention of the identified system. A linear quadratic Gaussian (LQG) optimal controller is subsequently designed and simulated based on the identified model of optimally configured smart structure in order to actively control the system response in both frequency and time domains. The dynamic performance and effectiveness of the optimized vibration control system is demonstrated for two different types of external mechanical excitations (i.e., impulsive load and white noise disturbance). The accuracy of dynamic analysis is established with the aid of a commercial finite element package and the data available in the literature.

Nonlinear vibration and instability of a visco-Pasternak coupled double-DWBNNTs-reinforced microplate system conveying microflow

The present article deals with the nonlinear vibration and instability analysis of a bonded double-smart composite microplate system (DSCMPS) conveying microflow based on nonlocal piezoelasticity theory. Two microplates are connected together by visco-Pasternak medium and both of them made of poly-vinylidene fluoride reinforced by double walled boron nitride nanotubes (DWBNNTs). Modified Navier–Stokes relation is used to evaluate fluid–microplate interaction considering the effects of bulk viscosity and slip boundary condition. Energy method and Hamilton's principle are employed to derive motion equations with regard to von Kármán geometric nonlinearity. Also, charge equation is used to consider electromechanical coupling. Due to existence of nonlinear terms, the governing equations are solved with the help of the differential quadrature method (DQM). A detailed parametric study is conducted to elucidate the effects of the flow velocity, fluid viscosity, Knudsen number, type of elastic medium, temperature change, small scale, aspect ratio, volume fraction, and orientation angle of the DWBNNTs on the vibration and instability behaviors of the coupled DSCMPS. This study might be helpful for the design of nano-electro-mechanical systems/ micro-electro-mechanical systems.

Active sound radiation control of a submerged piezocomposite hollow sphere

A spatial state-space approach based on the linear three-dimensional exact piezoelasticity theory along with the Helmholtz equations for the internal/external acoustic domains are employed to describe the coupled vibroacoustic response of an arbitrarily thick, spherically isotropic, functionally graded, radially polarized piezolaminated hollow sphere, immersed in and filled with ideal compressible fluids, and under the actions of arbitrary (non-axisymmetric) distributed time-harmonic transverse mechanical excitations at its inner and/or outer boundaries. A frequency domain subspace–based identification technique is applied to estimate the coupled fluid-structure dynamics of the system in the controller design stage. Subsequently, a standard linear quadratic Gaussian optimal controller is synthesized and simulated based on the identified model, and the optimal control input voltages for suppressing the sensor output voltage (total radiated power) of the submerged sphere are calculated for selected weighting parameters associated with the system response and control input. Numerical simulations establish the effectiveness of the selected (partial/full) sensor/actuator configuration in conjunction with the adopted control strategy for attenuating the predicted sound radiation response of an air-filled, water-submerged, sandwich piezocomposite (PZT4/steel/PZT4) sphere, in both frequency and time domains. Also, the trade-off between dynamic performance and control effort penalty is examined for impulsive and Gaussian random external mechanical disturbances. Furthermore, the effect of piezoelectric material gradient variation on sound radiation control performance of the smart piezocomposite structure is briefly discussed. The validity of the acousto-elastic model is demonstrated by use of a commercial finite element package as well as by comparison with the data available in the literature.

Solution modification of a piezoelectric bimorph cantilever under loads

Most of the previous investigations on the static performances of piezoelectric bimorph cantilevers are based on the elementary theory of piezo-elasticity. In fact, one fundamental problem has not been solved yet from the view of the theory of piezo-elasticity, that is, a piezoelectric bimorph cantilever covered fully with electrodes on the upper and lower surfaces and subjected to a transversely concentrated load at the free end of the beam. The major obstacle to find the solution is the equipotential conditions on both the upper and lower surfaces of the cantilever. In this article, by establishing suitable boundary conditions and introducing an appropriate Airy stress function, the analytical solutions of a piezoelectric bimorph cantilever under three different loading conditions have been obtained. Numerical analysis is also conducted and the results are consistent with the present theoretical predictions. This investigation amends the corresponding works given by other investigations based on the elementary theory. It is found that the amendments to the end deflections of a PZT-4 piezoelectric bimorph cantilever caused by an end shear force, an end moment, or a voltage difference between the upper and lower surfaces are about 10.46%, 12.78%, and 3.52%, respectively. In addition, it is also found that these amendments depend just on the material parameters, have nothing to do with the geometric parameters of the bimorph cantilever. The Airy stress function proposed in this article can also be used to study other different piezoelectric cantilevers including multilayer piezoelectric cantilevers under corresponding loads.

Surface stress, initial stress and Knudsen-dependent flow velocity effects on the electro-thermo nonlocal wave propagation of SWBNNTs

This paper investigates the electro-thermal nonlocal wave propagation of fluid-conveying single-walled Boron Nitride nanotubes (SWBNNTs) using nonlocal piezoelasticity with surface stress, initial stress and Knudsen-dependent flow velocity effect. SWBNNT is embedded in a vicsoelastic medium which is simulated as visco-Pasternak foundation. Using Euler–Bernoulli beam (EBB) model, Hamilton׳s principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. A detailed parametric study is conducted, focusing on the combined effects of the electric parameters, viscoelastic medium, initial stress, surface stress, Knudsen number (Kn) and small scale on the wave propagation behaviour of the fluid-conveying SWBNNT. The results show that for smaller values of wave number the dispersion relation for different fluid viscosities seems to be similar. At the higher values of wave numbers, increase in the wave frequency values is remarkable due to increase in fluid viscosity. The electric field as a smart controller, surface effect, initial stress, temperature change and slip velocity effect have significant role on the wave frequency. The results of this work is hoped to be of use in design and manufacturing of smart MEMS/NEMS in advanced medical applications such as drug delivery systems with great applications in biomechanics.

Piezoelectric energy harvesting from traffic-induced pavement vibrations

This paper focuses on the development and experimental testing of a potential clean energy source for powering the remote equipment used in transportation infrastructure. Traditional power sources (i.e., power cables and batteries) are excessively expensive or infeasible in this type of application. A compression-based roadway energy harvester has been developed that can be embedded into pavement to scavenge electrical energy from traffic-induced vibrations. The proposed roadway harvester employs a group of piezoelectric harvesting units to convert traffic-induced vibrations into electrical energy, and each single harvesting unit contains three piezoelectric multilayer stacks. According to the linear theory of piezoelasticity, a two-degree-of-freedom electromechanical model of the piezoelectric harvesting unit was developed to characterize its performance in generating electrical energy under external excitations. Experimental testing in the laboratory was conducted to investigate the output power properties of the harvesting unit and shows good agreement with the theoretical analysis. Based on the testing results of the harvesting unit, the capability of the proposed roadway harvester has been theoretically evaluated and demonstrated that it has the ability to generate sufficient energy for driving common electrical equipment used in transportation infrastructure.

Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories

Based on nonlocal piezoelasticity theory, dynamic stability of double-walled boron nitride nanotubes (DWBNNTs) conveying viscose fluid is studied by incorporating Euler–Bernoulli beam theory, Timoshenko beam theory, and cylindrical shell theory. The surface stress effects are considered based on Gurtin–Murdoch continuum theory. The DWBNNT is embedded in visco-Pasternak medium and the nonlinear van der Waals forces between the inner and outer surface of the DWBNNT is taken into account. Using von Kármán geometric nonlinearity, the governing equations are derived based on Hamilton’s principle. In order to obtain the dynamic instability region of DWBNNT, incremental harmonic balance method is applied. The detailed parametric study is conducted, focusing on the combined effects of the nonlocality, surface stress, fluid velocity, and surrounding medium on the dynamic instability region of DWBNNT. Furthermore, dynamic instability region of Euler–Bernoulli beam theory, Timoshenko beam theory, and cylindrical shell theory are compared to each other. Numerical results indicate that neglecting the surface stress effects, the difference between dynamic instability region of three theories becomes remarkable.

Nonlocal piezoelasticity based wave propagation of bonded double-piezoelectric nanobeam-systems

Piezoelectric nanobeam (PNB) offer the possibility of being used in micro-electromechanical systems and nano-electromechanical systems and the dynamic testing of such structures often produces stress wave propagation in them. This work concerns with the size-dependent wave propagation of double-piezoelectric nanobeam-systems (DPNBSs) based on Euler–Bernoulli beam model. The two piezoelectric nanobeams are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. Nonlocal piezoelasticity theory is used to derive the general differential equation based on Hamilton’s principal to include those scale effects. Particular attention is paid to the wave propagation piezoelectric control of the coupled system in three cases namely in-phase wave propagation, out-of-phase wave propagation and wave propagation when one PNB is stationary. In three mentioned cases, an analytical method is proposed to obtain phase velocity; cut-off and escape frequencies of the DPNBSs. Results indicate that the imposed external voltage is an effective controlling parameter for wave propagation of the coupled system. Furthermore, the phase velocity of in-phase wave propagation is independent of elastic medium stiffness.

Active vibration control of a thick piezolaminated beam with imperfectly integrated sensor and actuator layers

A spatial state-space formulation based on the linear two-dimensional piezoelasticity theory and involving local/global transfer matrices is applied to investigate the active vibration suppression of a simply supported, arbitrarily thick, orthotropic elastic beam, imperfectly integrated with spatially distributed piezoelectric actuator and sensor layers on its top and bottom surfaces, respectively. A linear spring-layer model is adopted to simulate the bonding imperfections between the host structure and the piezoelectric layers. To assist control system design, system identification is conducted by applying a frequency domain subspace approximation method with N4SID algorithm. The state space model is constructed from system identification and used for state estimation and development of control algorithm. A linear quadratic Gaussian (LQG) controller is subsequently designed and simulated based on the identified model in order to actively control the response of the smart structure. The accuracy of analysis is established with the aid of a commercial finite element package.

Active vibration control of an arbitrary thick piezolaminated beam with imperfectly integrated sensor and actuator layers

A spatial state-space formulation based on the linear twodimensional piezoelasticity theory and involving local/global transfer matrices is applied to investigate the active vibration suppression of a simply supported, arbitrarily thick, orthotropic elastic beam, imperfectly integrated with spatially distributed piezoelectric actuator and sensor layers on its top and bottom surfaces, respectively. A linear spring-layer model is adopted to simulate the bonding imperfections between the host structure and the piezoelectric layers. To assist control system design, system identification is conducted by applying a frequency domain subspace approximation method with N4SID algorithm based on the first five structural modes of the system. The state space model is constructed from system identification and used for state estimation and development of control algorithm. A linear quadratic Gaussian (LQG) optimal controller is subsequently designed and simulated based on the identified model in order to actively control the response of the smart structure in both frequency and time domains.

Nonlocal Timoshenko beam model for dynamic stability of double-walled boron nitride nanotubes conveying nanoflow

Based on nonlocal piezoelasticity theory, dynamic stability of double-walled boron nitride nanotube conveying viscous fluid is investigated using Timoshenko beam theory. Double-walled boron nitride nanotube is surrounded in visco-Pasternak medium and conducts the internal fluid. Modified Navier–Stokes relation is used to evaluate fluid–double-walled boron nitride nanotube interaction considering the effects of bulk viscosity and slip boundary condition. Mechanical harmonic excitation and thermal loadings are exerted on double-walled boron nitride nanotube with zero electrical boundary condition. Nonlinear van der Waals forces between the inner and outer layers of double-walled boron nitride nanotube are taken into account. Hamilton’s principle is utilized to derive governing equations with regard to von Kármán geometric nonlinearity. Charge equation is used to consider the coupling of electric potential and mechanical displacement. Space and time domains are discretized using Galerkin and incremental harmonic balance approaches. Finally the eigenvalue equations are solved based on the iterative method to derive dynamic instability regions. The detailed parametric study is conducted, focusing on the combined effects of aspect ratio, nonlocal parameter, fluid velocity, Knudsen number, thermal changes, van der Waals forces and surrounding medium on dynamic instability regions of double-walled boron nitride nanotube.

Induced nonlocal electric wave propagation of boron nitride nanotubes

Axial displacement and electric wave propagation of single-walled Boron-Nitride nanotubes (SWBNNTs) induced by alternating current (AC) are investigated in this study. A single-walled zigzag structure BNNT is modeled based on nonlocal piezoelasticity theory and Euler-Bernoulli beam (EBB). Equations correspond to lateral displacement have been obtained. Using Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the higher order of governing equations are derived. Analytical solution is applied to solve governing equations. Also the axial and lateral displacement of a SWBNNT and electric potential induced by AC through it are presented. The detailed parametric study is conducted, focusing on the remarkable effects of the half wave number on the behavior of the SWBNNT. The results indicate applying alternating field, leads to propagation of axial displacement along the SWBNNT. Also the result of this study can be useful to design and manufacture of smart micro/nano-electro-mechanical systems in advanced biomechanics applications by controlling axial and lateral displacements.