Piezoelectric Actuator Layers Research Articles

Active vibration control of rotating smart bidirectional FGPTC subjected to internal mechanical shock

This study considers the active vibration control of a sandwich truncated cone, whose intermediate layer is made of bidirectional functionally graded (FG) porous material bonded with integrated piezoelectric actuator and sensor layers on its outer and inner surfaces. The material properties of the bidirectional functionally graded porous truncated cone (FGPTC), with even and uneven porosity distributions along the length and thickness directions, are changed using a power law function. The governing motion equations utilize the two-dimensional (2D) axisymmetric theory of elasticity rather than simple shell theories. The solving of the governing motion equations is accomplished through the utilization of graded finite element and Newmark methods. The study investigates the impact of dimensions, parameters, and porosity types on transient response behavior, including the semi-vertex angle and the ratio of truncated cone length to outer radius. Furthermore, the effects of power index, porosity volume fractions, rotational velocities, and boundary conditions are examined. Active vibration control (AVC) of the piezoelectric FGPTC is achieved by employing a closed-loop control algorithm based on velocity feedback. Several numerical simulations are conducted to evaluate the effectiveness of the proposed active vibration control system in reducing structural vibrations. The results demonstrate significant reductions in vibration amplitudes and improved structural stability achieved through the active control approach.

Vibration Characteristics of FML Cylindrical Shell Bonded by Thin Piezoelectric Actuator and Sensor Layer with and Without Fluid–Structure Interaction Resting on Pasternak Elastic Foundation

The present study investigates the vibration analysis of cylindrical shells composed of fiber metal laminate (FML) with embedded piezoelectric layers, undergoing fluid-structure interaction (FSI) and resting on a Pasternak elastic foundation based on the principles of three-dimensional elasticity theory. Using the state space approach, the equations of motion were derived under simply supported boundary conditions. The natural frequencies of the FML cylindrical shell, accounting for the presence of a moving fluid, were computed by solving the eigenfrequency equations. The study examined the influence of various parameters, including boundary conditions, length-to-radius ratio, fluid type, fluid velocity, circumferential wave number, and radius-to-thickness ratio, on glass-reinforced aluminum laminate (GLARE), aramid-reinforced aluminum laminate (ARALL), and carbon-reinforced aluminum laminate (CARALL). A constant composite/metal volume ratio was assumed. The results obtained were validated by comparing with natural frequency values from the existing literature, confirming the agreement and convergence with previous studies. The results confirm that the highest natural frequency values are assigned to the CARALL, ARALL and GRALE structures in descending order. Furthermore, an increase in fluid flow velocity through the cylindrical shell correlates with a reduction in natural frequency.

Hybrid Fuzzy PID Sound Radiation Control of a Functionally Graded Porous GPL-Reinforced Plate with Piezoelectric Sensor and Actuator Layers

This paper is the first attempt to investigate the sound radiation control of a functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) plate integrated with piezoelectric face sheets. A spatial state-space formulation based on the linear 3D piezoelasticity theory is utilized to derive a semi-analytic solution for the coupled vibroacoustic response of the simply-supported arbitrarily thick composite plate. A comprehensive parametric study examines the effect of GPLs’ distribution, weight fraction, and porosity parameters of the core layer on the radiated sound power. Then, the best material configuration is selected to be actively controlled. A hybrid Fuzzy Proportional-Integral-Derivative (FPID) controller, which utilizes an FPID controller integrated with a classical PID controller, is employed to mitigate sound radiation from the smart sandwich plate via the volume velocity approach. The gain parameters of the proposed controller are tuned using the Bat optimization algorithm. Finally, the performance of the active control strategy in attenuating radiated sound power is investigated through several numerical simulations. Results show the proposed control scheme's robustness and rapid disturbance rejection performance.

Electro-Mechanical Buckling of Shallow Segments of Functionally Graded Porous Toroidal Shell Covered by Piezoelectric Actuators

The current work deals with the mechanical buckling behavior of saturated porous toroidal shell segments sandwiched by piezoelectric actuator layers. Material properties of the porous shells with nonuniform distributed porosities are assumed to vary as a specific function of the thickness and porosity parameters. The nonlinear equations of the sandwich toroidal shell having either positive or negative Gaussian curvature are obtained on the basis of Biot’s poroelasticity theory. The energy method as the minimum potential energy principle is applied to derive the governing equations of the sandwich shells. The buckling equations of the piezo-porous sandwich shells under various types of mechanical loading are established by employing the adjacent equilibrium criterion. The governing equations as a set of the coupled partial differential equations are solved using an analytical method including the Airy stress function. Closed-form solutions are derived for shallow segments of the sandwich toroidal shell with positive/negative Gaussian curvature under lateral pressure, axial compression, and hydrostatic pressure loadings. Novel numerical results are presented in this work to show the effects of important factors such as the piezoelectric layer thickness, applied voltage, shell geometrical ratio, and variation of the porosity coefficient on the buckling behavior of these structures.

Vibration Analysis of Two-dimensional Functionally Graded Plate with Piezoelectric Layers using the Classical Theory of Plates

In this article, two-dimensional functional materials have been used using the power law in them, which is a good measure to obtain the properties of a composite material of metal and ceramic. At first, the equations of motion were obtained using Hamilton's method and solved by the GDQ method, and finally, the accuracy of the obtained answers was compared with the existing articles. In the following, the dynamic model of the sheet with two piezoelectric actuator layers at the top and bottom was investigated and the obtained equations were solved using the Ritz method.

Vibration control of an axially loaded composite beam bonded with Piezoelectric actuator and sensor layers on a Winkler–Pasternak foundation and under transverse excitation force based on first-order shear deformation theory

Vibration control of an axially loaded composite beam bonded with Piezoelectric actuator and sensor layers on a Winkler–Pasternak foundation and under transverse excitation force based on first-order shear deformation theory

Thermo-Electro-Mechanical Analysis of Micropolar FGP Cylindrical Shell Covered with Piezoelectric Actuator Layers

An investigation is performed in this paper to analyze the nonlinear thermo-electro-mechanical response of long sandwich cylindrical shells with functionally graded porous (FGP) core and thin piezoelectric actuator layers. The FGP core of the sandwich shell is assumed to be temperature- and microstructure-dependent. It is assumed that the sandwich shell is subjected to uniform lateral pressure loading in a thermo-electrical environment. The equilibrium equations of the shell with infinite length are established with the aid of the virtual displacement principle and von Kármán kinematic assumptions. The governing equations are obtained in terms of displacement components based on the first-order shear deformation model of shallow cylindrical shells and the modified couple stress theory. These nonlinear differential equations are analytically solved for a sandwich shell having both the simply-supported and clamped–clamped edge conditions by employing a two-step perturbation technique. Analytical closed-form solutions are determined as a relationship including the load parameter and the mid-span deflection. The comparison examples are made with the existing results in the literature for a simple functionally graded shell, where good agreement is obtained. It is shown that the nonlinear response of the sandwich shell is highly dependent upon the temperature variation, power law index, porosity coefficient, couple stress parameter, piezoelectric layers, and geometrical parameters of the shell.

Investigating the effect of fluid-structure interaction on the vibrations of fiber-metal laminated cylindrical shells bonded by piezoelectric actuator and sensor layer

این پژوهش به بررسی ارتعاشات پوسته های استوانه ای چند لایه الیاف-فلزی آلومینیوم با لایه های تعبیه شده پیزوالکتریک که دارای اندرکنش سیال-سازه است بر اساس تئوری الاستیسیته سه بعدی می پردازد. با استفاده از رویکرد فضای حالت معادلات حرکت برای شرایط مرزی تکیه گاهی ساده بدست آمدند. فرکانس های طبیعی پوسته استوانه چند لایه فیبر فلز شامل سیال محرک با حل معادله فرکانس ویژه حاصل شدند. اثر پارامترهای مختلف مثل طول به شعاع، سرعت سیال، عدد موج محیطی و شعاع به ضخامت برای آلومینیوم تقویت شده با الیاف کربن مورد بررسی قرار گرفت. نسبت حجمی کامپوزیت/فلز ثابت در نظر گرفته شد. تاکنون پژوهشی بروی پوسته های استوانه ای چند لایه الیاف-فلزی آلومینیوم با لایه های تعبیه شده پیزوالکتریک که دارای اندرکنش سیال-سازه انجام نشده است . موضوع بسیار جدیدی است. مطابقت و همگرایی نتایج پژوهش حاضر با مقایسه نتایج فرکانس های طبیعی گزارش شده در ادبیات تائید گردید و بیانگردقت بالای نتایج حاصل از این پژوهش می باشد.

Wave Propagation in Smart Sandwich Plates with Functionally Graded Nanocomposite Porous Core and Piezoelectric Layers in Multi-Physics Environment

This research provides a mathematical model and solution for investigating wave propagation in graphene platelets (GPLs)-reinforced functionally graded (FG) metal foam plates integrated with piezoelectric actuator and sensor layers resting on an orthotropic visco-Pasternak medium in magneto-electro-thermo environment. The FG porous nanocomposite core and the actuator piezoelectric layer are exposed to steady magnetic and electric fields, respectively. The electric potential between two piezoelectric layers is governed by a proportional-derivative controller. The Halpin–Tsai micromechanics model and the Kelvin–Voigt model are adopted to express the effective elastic modulus of the FG porous nanocomposite core and material viscoelasticity of the core and piezoelectric layers, respectively. The governing equations of smart FG porous nanocomposite plates under thermal environment are derived grounded on the refined third-order shear deformation theory. Upon the validated theoretical model, the wave velocities and frequencies in plates are obtained by solving governing equations analytically. Finally, the effects of material viscoelasticity, porosity distribution and coefficient, GPL distribution and weight fraction, the plate and GPL geometries and external environment on wave propagation characteristics are demonstrated comprehensively. This work provides guidance on tunable control of wave propagation in smart sandwich plates affected by complex external environments.

Closed form solutions for thermo-mechanical buckling analysis of shallow piezo-laminated spherical shells

Thermo-mechanical buckling analysis of laminated spherical shells bounded with the piezoelectric actuator layers has been presented in this article. Applied loads are a combination of thermal, mechanical and electrical loads. Derivations of equilibrium and stability equations are based on the classical laminated shell theory and Sanders’s nonlinear kinematic relations. The analysis employs the Galerkin method to achieve closed-form formulas for the buckling loads of the piezo-laminated spherical shell. Effects of applied actuator voltage, voltage sign, geometrical parameters of the shell (length, diameter, and thickness), material properties, and layout of composite layers on the buckling strength are investigated. Analytical solutions are obtained for three types of thermal loading, and one thermo-mechanical loading condition. The results are validated by the known data in the literature.

Cancelation of acoustic scattering from a smart hybrid ERF/PZT-based double‐wall composite spherical shell structure

A coupled multiphysics vibroacoustic model is developed for axisymmetric scattering of plane progressive time-harmonic sound waves from a fluid-filled and submerged smart hybrid double concentric composite spherical shell that incorporates noncollocated piezoelectric (PZT) and electrorheological fluid (ERF) actuator layers. The dynamic equations of motion for the PZT- and ERF-based sandwich shells are independently derived using Hamilton’s variational principle, Kirchhoff-Love thin shell formulation, Maxwell's electrodynamics equations, and Kelvin-Voigt viscoelastic constitutive model. The frequency-domain multi-input/multi-output (MIMO) sliding mode control (SMC) strategy is then applied to activate the sound scattering cancelation capability of the triply-coupled smart structure through collaborative active/semi-active operation of the built-in actuator elements. Extensive numerical simulations reveal the remarkable broadband attenuation of both types of wide and narrow resonance peaks arising in the calculated far-field backscattering spectra that are primarily linked to various types of interacting fluid- and shell-borne peripheral waves. Also, the near-field effectiveness and cloaking potentials of proposed smart hybrid design in realizing partial or complete acoustic invisibility with respect to the incident sound field are explored at selected frequencies. In particular, the superior 3 D acoustic cloaking capabilities of the PZT/ERF and ERF/ERF configurations are established noting the low actuation energy advantage of the ERF element.

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

Nonlinear vibration of conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch

In this study, nonlinear vibration of a conical shell with a piezoelectric sensor patch and a piezoelectric actuator patch is evaluated. The strain displacement relation is considered to be nonlinear and based on that the equations of motion and piezoelectric sensor output signal are extracted. For the first time, nonlinear electromechanical equations of motion for the conical shell with a piezoelectric sensor layer and a piezoelectric actuator layer are extracted in detail and presented. The producer of extraction of conical shell electromechanical equations of motions is presented for further clarifications. The output signal of the piezoelectric sensor patch considering the nonlinear strain displacement equation of motion is derived. For controlling the vibration actively, a proportional controller is defined by which the applied actuator signal is determined. The nonlinear electromechanical equations of motion are expanded based on conical shell strains. By applying the Galerkin method, the nonlinear time-domain equations are extracted. The complicated attained equations are solved using the harmonic balance method. Conical shell nonlinear frequency response in uncontrolled condition and controlled condition is computed and compared with each other. The frequency response shows that the active vibration control of the conical shell increases the nonlinearity of the system and reduces the vibration amplitude. In addition, free nonlinear vibration of the proposed system is calculated and presented. The results show higher impacts of piezoelectric patches on the conical shell free vibration response and they can reduce the vibration amplitude dramatically.

Vibration control of cantilever beam using poling tuned piezoelectric actuator

This paper presents active vibration control of smart cantilever beam using poling tuned piezoelectric actuator. The vibrating response of piezo-laminated cantilever beam is modeled using a lumped parameter approach. The fuzzy logic controller is used to control the vibration and 49 rules have been established to develop the controller. Sensor voltage and derivative of sensor voltage are considered as inputs while the actuator voltage is considered as an output. Different piezoelectric materials are considered for analysis to improve the performance of the piezoelectric actuator layer using poling tuning phenomena which further enhances the control performance. In Poling tuning phenomena, poling is done at an angle due to which different piezoelectric strain coefficients i.e., transverse (d31 mode), longitudinal (d33 mode), and shear (d15 mode) are activated simultaneously and start contributing toward effective piezoelectric strain coefficient. The poling angle corresponding to the maximum magnitude of effective piezoelectric strain coefficient is called an optimized poling angle. Significant enhancement of 60.78% in control performance in PMN-0.42PT is observed at optimum poling angle of whereas, BT-NNb shows 36.75% improvement in control performance at an optimum poling angle On the other hand, PZT-7A shows a minimum improvement of 15.53% at optimum poling angle

Control of sound transmission into a hybrid double-wall sandwich cylindrical shell

A 3D analytical model is formulated for diffuse sound field transmission control through a smart hybrid double concentric sandwich circular cylindrical shell structure in presence of external and internal air gap mean flows. The multi-input multi-output sliding mode control is applied to enhance the sound transmission loss characteristics via direct control action of a uniform force piezoelectric actuator layer along with semi-active variation of the stiffness/damping characteristics of the electrorheological fluid core layer incorporated in a non-collocated configuration within the external or internal shell structure. Extensive numerical simulations examine the uncontrolled/controlled diffuse field sound transmission loss spectrums in a broad frequency range for single-wall and hybrid double-wall sandwich shells at selected external and air gap Mach numbers. The proposed smart hybrid active/semi-active double-wall configuration is demonstrated to provide satisfactory overall acoustic insulation control performance with much lower operative energy requirements. Limiting cases are considered, and validity of the formulation is verified against the available data.

Conical shell vibration optimal control with distributed piezoelectric sensor and actuator layers

In this study, conical shell vibration with distributed piezoelectric layers on the shell surface is controlled by a distributed optimal controller. Two piezoelectric layers are distributed on the conical shell surface with the same geometry and they are segmented into the same numbers of patches. One piezoelectric layer is considered to be a sensor layer and the other one is considered to be an actuator layer. An optimal controller with various constants for each piezoelectric patch is determined with an optimal input voltage. The conical shell electromechanical equations of motions with piezoelectric layers are extracted. The Galerkin method is used for obtaining the time domain equations and after that optimal constants of the controller are determined. Various kinds of distribution for the piezoelectric layer are considered and their effects on the conical shell vibration control are evaluated. For a better assessment, free vibration response, forced vibration response with concentrated and distributed force, and the frequency response of the considered system are computed and compared with the uncontrolled response. The results show the high impact of the optimal controller on the vibration mitigation of the conical shell and also the actuator applied voltage amplitude is considerably low. The applicability of the piezoelectric layer in the conical shell vibration mitigation is vividly determined by using an optimal controller which decreases the actuator applied voltage amplitude dramatically.

Conical shell vibration control with distributed piezoelectric sensor and actuator layer

In this study, a simply supported conical shell with distributed piezoelectric sensor and actuator layers is considered and the shell’s vibration reduction is investigated. Four kinds of piezoelectric layer distribution which are upper circumferential, middle circumferential, lower circumferential, and longitudinal distribution are considered. The output voltage of each piezoelectric sensor patch which is proportional to the shell deformation is calculated. A PD controller is considered which magnifies sensor output voltage and applies it on the allocated piezoelectric actuator patch. By this method the amplitude of conical shell vibration reduced. The effect of a distributed sensor and actuator on the conical shell vibration is evaluated. Controller type, controller constant, sensor/actuator distributions effectiveness on the free vibration response, the frequency response is evaluated. The results show that derivative controllers can affect more on natural frequencies of conical shells and it can increase the damping of the structure. The circumferential distribution can change natural frequencies easily and it has more effects on the dynamic of the conical shell than longitudinal distribution, especially the lower circumferential distribution. The maximum voltage for the piezoelectric actuator patch is also calculated and better distribution with lower actuator voltage and higher vibration reduction is chosen.

An actively constrained viscoelastic layer with the inclusion of dispersed graphite particles for control of plate vibration

In this work, the damping characteristics of an actively constrained viscoelastic material layer are examined because of the inclusion of dispersed graphite particles within the viscoelastic material layer. The study is carried out by analysing the active–passive damping in a layered plate made of a substrate layer, a constrained viscoelastic particulate composite layer and a thin constraining piezoelectric actuator layer. The effective properties of the viscoelastic particulate composite are estimated using a differential scheme and the elastic–viscoelastic correspondence principle. The piezoelectric layer is activated according to the velocity feedback control law, and a closed-loop finite element model of the overall plate is derived for the analysis. The results reveal that the inclusion of graphite particles not only causes an improved transfer of active action from the piezoelectric layer to the substrate plate but also enhances the energy dissipation capability of the constrained viscoelastic layer. It is found that the maximum transfer of active action and the maximum passive damping capability of the viscoelastic particulate composite layer arise almost at the same volume fraction of inclusion. So, an optimal volume fraction of inclusion is obtained for significantly improved active–passive damping in the overall plate. The overall study presents a potential means of improved active–passive damping treatment of structural vibration.

An analytical approach for nonlinear thermo-electro-elastic forced vibration of piezoelectric penta – Graphene plates

This paper deals with the nonlinear forced vibration of imperfect penta – graphene plates integrated with piezoelectric actuator layers. The plate is subjected to combination of mechanical, thermal, and electrical loadings. Based on the first order shear deformation plate theory, the governing equations are established taken into account the effect of the von Kármán type of geometrical nonlinearity, the Pasternak type elastic foundations, the damping and the piezoelectric – thermal effects. Four edges of the hybrid plate are assumed to be simply supported and immovable in the in-plane directions. The solution forms that satisfy the boundary conditions are assumed to be trigonometric. The closed form expressions of natural frequency, the frequency ratio – amplitude and the deflection amplitude – time curves are obtained by using the Galerkin and Runge – Kutta methods. The numerical results show positive effects of elastic foundations, negative effect of temperature increment and initial imperfection, considerable effect of geometrical parameters as well as small effect of applied voltage on the nonlinear forced vibration of piezoelectric penta – graphene plate.

Study of the effects of shear piezoelectric actuators on the performance of laminated composite shells by an isogeometric approach

This paper presents an isogeometric approach based on the Non-Uniform Rational B-Splines (NURBS) to investigate static and free vibration responses of smart composite shells integrated with shear piezoelectric actuators. The degenerated shell formulation according to the Mindlin-Reissner shell theory is combined with the isogeometric approach. To model the laminated smart shells, the Equivalent Single Layer (ESL) theory is used. To consider the electric potential in the shear piezoelectric actuator layers, a sub-layer approach is adopted that assumes linear variation in the thickness direction of the sub-layer. The effect of different mechanical and electrical boundary conditions on transverse deformation and natural frequencies of laminated smart shells by applying the electric field have been investigated. In the case studies, two parallel edges of the considered shell structures are assumed simply supported and the other two with an arbitrary combination of boundary conditions including clamped, free or simply supports. Also, open-circuit and closed-circuit conditions are used as electric boundary conditions. Investigation of the effects of the shear piezoelectric actuator layers on various factors, including the simultaneous mechanical and electrical loadings as well as the radius of curvature of the shell are amongst the objects of this paper. Also, several numerical examples are presented to demonstrate the efficiency and accuracy of the isogeometric approach in the study of shear effects of the piezoelectric actuator layers. The obtained results indicate the reliability and desirability of the proposed approach.