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This paper presents a finite element solution for the static analysis of a multi-layers beam with and without piezoelectric layers. The beam is under large deformation. The virtual work principle and the Lagrangian update method (LUM) have been employed to study the static behavior of piezoelectric beams. Four-nodes element with two displacement degrees of freedom and one electrical degree of freedom has been used in this analysis. Finally, in order to prove the validity of the presented formulation and the solving process, the results are compared with the other available data.

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in this paper natural frequencies of a rectangular mindlin plate with surface bounded piezoelectric patches is obtained. Simply supported boundary condition is imposed at the plate edges. Ritz approach based on the principle of minimum potential energy is applied to obtain the frequency parameters of rectangular plate. Since displacement fields of the plate are postulated by trigonometric series function, solution is a semi analytical one. For verifying the accuracy of this method, results are for the isothropic and piezoelectric plates are compared with those reported in the literature. As we see a good conformance is derived from the obtained results and the exact solution. At the end, natural frequencies of a rectangular mindlin with surface bounded piezoelectric patches is obtained.

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In this report, we present a direct current piezoelectric nanogenerator based on ZnO nanosheets, which is driven by ultrasound waves propagating in water. ZnO nanosheets have been grown by hydrothermal method on Al layer as the bottom ohmic contact, while Ni layer serves as the top Schottky contact. Then, we have designed a 1D phononic crystal to realize localized standing wave at the position of nanogenerator, and consequently enhance the energy harvesting performance. The proposed phononic crystal consists of water/steel periodic slabs which are enclosing both sides of the nanogenerator, and the created mid-gap state is matched with the source frequency in the designed structure. Our simulation results confirm that the pressure difference exerted to the nanogenerator is enhanced by a factor of about 12.3, in comparison with the pristine ZnO nanogenerator.

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In this paper a two dimensional elasticity for free vibrations and the effect of elastic foundantion on a two-direction functionally graded beams with integrated surface piezoelectric layers with combination of differential quadrature method and space-state method is presented here. Differential quadrature method in axial direction and space-state method in transverse direction is used. It’s considered that two parameters model or winkler-pasternak for elastic foundation which has been considered two kinds of boundary conditions include simply support and clamped-clamped. Also, It is assumed that beam properties in thickness and axial direction varying exponentially and poison factor is constant which has been considered the effects of materials properties gradient index and number waves on free vibrations beams. The obtained results show that this method has good accuracy and high speed of convergence.

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Analytical solution for the dynamic stability analysis of functionally graded piezoelectric materials (FGPM) circular plates has been presented based on Love-Kirchhoff hypothesis and the Sander’s non-linear strain-displacement relation. The FGPM plate assumed to be gradded across the thickness. The material properties of the FGPM plate assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituent materials. The plates are subjected to a radial loading and electric field in the normal direction. Bolotin’s method has been employed to obtain the dynamic instability regions. The effect of plate parameters such as thickness–radius ratios, power index, as well as electric field and state loads on instability behavior of the plate is comprehensively investigated.The functionally graded composite material plays a significant role in changing the unstable regions and the buckling loads.

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Parallel piezo-flexural nanopositioning stages are extensively used in advanced nano-scale imaging and manipulation applications such as scanning probe microscopy systems. One of the major deficiencies of these devices is the coupled motion between their different axes. That is, the motion of stage in one direction interferes with motions in the other directions, leading to undesirable disturbances. In this paper, analytical, dynamic, experimental, and finite element analyses are carried out to investigate the major root cause of the cross-coupling effect. Using ABAQUS FEA software, a 3D model of the stage has been developed. Model consists of a central elastic body connected to the fixed frame through four flexural hinges. A cylindrical stack of multiple piezoelectric layers is placed between the moving central body and the fixed frame. Simulations are carried out for two different friction coefficients in the contact surfaces of the piezoelectric layers, and for different frame materials. It is observed that the main cause of the cross-coupling effect is the rotation of piezoelectric stack due to its friction with the stage moving in the tangential direction, concurrent with a change in the geometry of the stage.

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A two dimensional generalized plane strain micromechanical model is developed to study electro-elastic behavior of piezoelectric fiber reinforced composites (PFRC) with transverse polarization. A small repeating area of the composite, representing a quarter of fiber surrounded by matrix is considered as representative volume element (RVE). The composite system consists of long parallel piezoelectric fibers with transversely isotropic properties and perfectly bounded to the isotropic matrix in a square array arrangement. In addition, the constituents are assumed to have both linear elastic and electrical behavior, whereas, the matrix is piezoelectrically passive. The element free Galerkin method is employed to obtain solution for the governing system of partial differential of equations. In this method, the Moving Least Square shape functions are used to approximate the field variable at arbitrary point. Comparison of the presented results with other techniques available in the literature reveals good agreement. It is demonstrated that the piezoelectric coefficient “e31” in the transverse polarization is considerably improved in comparison with corresponding coefficient of pure piezoelectric material. Furthermore, as a result, it is found that fibers with elliptical cross section may enhance the amount of electrical sensitivity of PFRC several times than circular fibers in a specific direction.

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In recent years,the need for low power electronic circuits like sensors and wireless systems, has been considered by many researchers.Excessive weight, limited lifetime of the batteries and also having problem in replacing them, are the main reasons for harvesting energy from ambient vibrations. Among the various sources of environmental energy, mechanical vibrations, has gained popularity due to the availability. Among the different methods of ambient vibration energy harvesting, piezoelectric method, is one of the good ways to harvest energy due to the favorable effects of electromechanical coupling. The most common means of harvesting energy from vibrations, is a unimorph or bimorph cantilevered beam. In the present paper, electrical energy harvesting from Euler-Bernoulli trapezoidal cantilevered unimorph beam with base excitation using distributed parameter method has been considered. First, equations of motion analytically obtained and then using Assumed modes method(for rectangular beam), system’s natural frequencies is calculated and output voltage, current and power diagrams are presented. For verifying results, presented voltage, current and power diagrams for trapezoidal configuration close to rectangular configuration that it’s results are published in references, will be compared. Then, functional parameters for trapezoidal energy harvester, with resistance value changes for energy consumer has been analyzed.

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In this article, the buckling of multilayer rectangular thick plate made of functionally graded, transversely isotropic and piezoelectric materials in both closed and open circuit conditions are investigated. Based on the shear and normal higher-order deformation theory, the governing equilibrium equations of plate are obtained using the principle of minimum total potential energy and Maxwell’s equation. Using an analytical approach, the governing stability equations of functionally graded rectangular plates with piezoelectric layers have been presented in terms of displacement components and electric potentials. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply support boundary condition along all edges. Finally after ensuring the validation of the results, the effects of different parameters such as different loading conditions, functionally graded power law index, thickness-to-length ratio and aspect ratio, on the critical buckling loads of plates are studied in details. Furthermore, the effect of piezoelectric thickness on the plate critical buckling loads has been studied. The results present better accuracy in comparison with the classic and third order shear theories.

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Piezo‌electric materials are used as sensor and actuator in order to control the vibrations of structures. Geometry and location of the piezoelectric sensors and actuators have a substantial effect on the consumed electric energy and performance of the control system, therefore, in this study by defining an appropriate cost function, an optimum length and location of the piezoelectric actuator was determined in order to achieve a desirable decrease on vibration amplitude of a cantilever beam by using appropriate control energy. The standard quadratic function of beam displacement and control energy was used as the cost function. Mathematical modeling was based on Euler Bernoulli beam theory and Hamilton's principle was used in order to achieve the equations of motion. In this approach, the control voltage of actuator layer is emerged in the boundary conditions of the problem, which turns it to a time varying boundary condition problem. By defining special displacement functions and homogenizing the boundary conditions, control voltage of the actuator is appeared as external excitement in the equations of motion. In the current study, optimum LQR and LQG controllers were investigated and Kalman filter theory was used in order to estimate the state variables. In numerical simulations, by investigating the performance of optimized limited or unlimited patches in comparison with complete one, the effective role of the objective function and optimization have been shown in decreasing applied control voltage.

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Accurate determination of the electro-elastic fields of quantum nanostructures within piezoelectric media is an important issue for realizing the electro-mechanical behavior of these nanostructures. In this paper, the governing partial differential equations corresponding to piezoelectric media containing quantum nanostructures are presented and subsequently, generalized analytical solutions based on Fourier series technique are developed for determination of the coupled electro-elastic fields in transversely isotropic piezoelectric barrier due to periodically distributed quantum nanostructures. The electro-elastic couplings of the piezoelectric barrier as well as the interactions between the quantum nanostructures are exhibited within the framework of the presented analytical solution. It is observed that no electric field and no electric potential will be induced anywhere in the medium for periodic distribution of quantum wires. The presented analytical solution is capable of treating different shapes and geometries of quantum wires/quantum dots. The electro-elastic fields of various shapes of sections of quantum wires and different geometries of quantum dots are studied and the effects of the geometry of periodically distributed quantum nanostructures are demonstrated. The results show that geometry of quantum nanostructures may highly affect the induced electro-elastic fields and therefore, accurate determination of the geometry of quantum nanostructures as well as the induced electro-elastic fields would be essential for employment of these nanostructures in different fields of research and technology.

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This paper investigates static behavior of multilayered functionally grated piezoelectric plates under thermal loads. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Considering the thermal coefficients of piezoelectric material in the constitutive equations (the terms that will couple temperature effects to the piezoelectric properties, named pyroelectric constants) and using the kinematic assumptions of first-order shear plate theory (FSDT), the constitutive equation of FGP plate is written. Then, by using principle of virtual work, the governing equations of a FGP plate is obtained. These equations are solved by finite element method using eight node shell element. Functionally graded piezoelectric plate under static loading, different layers and boundary conditions are considered and results in various thermal loadings have been obtained. Deflection and voltage results for different power law exponent and different boundary conditions are shown. In this paper, the influence of power law index on the static behavior of FGPM plate (including deflection and voltage) under thermal loading is investigated. These responses can be used as a criteria for design of FGP sensors and actuators in the thermal environment.

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In this paper, the nonlinear free vibrations of a bimorph piezoelectric nanoactuator is studied based on nonlocal elasticity. The Euler-Bernoulli beam theory and Hamilton’s principle are used to derive the equation of motion of the actuator. In order to obtain the reduced-order form of equations, the Galerkin method is used. The mode shapes of a multi-span beam are used for a faster convergence. The nonlinear natural frequencies are obtained by using He’s variational approach. Equations are solved for clamped-clamped boundary conditions, and the effects of values of DC voltage, actuator length and thickness, length of piezoelectric layers and nonlocal parameter on the nonlinear natural frequencies are studied. The results show that applying a DC voltage induces a static deflection and an increase in the stiffness of the actuator. Therefore, the natural frequency increases. Moreover, increasing the nonlocal parameter decreases the rate of change in frequency variation. An increase in the nonlocal parameter or the length of the actuator increases the nonlinear to nonlinear natural frequency ratio. Finally, the effect of the middle layer material of the actuator on the frequency ratio is studied.

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Harvesting energy by piezoelectric materials is nowadays an efficient way for powering low-power electric devices. Required energy for sensors which are used in condition and health monitoring of bridges and other civil infrastructures can be examples of the energy harvesters. This study aimed to improve the piezoelectric-based energy harvesting on civil infrastructures, especially on bridge structures. In this investigation, harvesting energy from the vibrations of a bridge under moving consecutivemasses is studied. Harvesting energy iscarried out through a cantilever beam with piezoelectric patch which is installed atthe middle of a simply supported bridge. Governing equations for vibration of an Euler-Bernoulli beam under moving consecutivemasses arederived. The effects of inertial, centrifugal and coriolis forces areconsidered. For verifying, the results of the numerical solution of the moving mass problem are compared to the experimental tests data of the litterature. The harvester is modelled by a cantilever beam with piezoelectric patch under base excitations which are calculated from vibrations of the bridge mid-point. The obtained equations are then solved in MATLAB environment by using the forth order Runge-Kutta method. The calculated induced voltages are compared with those obtained from experiment. A good degree of accuracy is observed.

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In this paper, the dynamic behavior of atomic force microscope (AFM) based on non-classical strain gradient theory was analyzed. For this aim atomic force microscope micro-beam with attached tip has been modeled as a lumped mass. Micro-beam has stimulated via a piezoelectric element attached to the end of clamped and non-linear partial differential equation of the system has extracted based on Euler-Bernoulli theory and to be converted into ordinary differential equation by using Galerkin and separation method. The classic continuum theory because of lack of consideration size effect that has been observed in many experimental studies, has little accuracy in predicting the mechanical behavior of Nano devices. In this study, the stability region of micro-beam are determined analytically and validated by comparison with numerical results. Difference between presented analysis in dynamic behavior of micro-beam by classic and non-classic theories has been shown with variety of diagrams. It is clear that consideration the size effect changes the dynamical behavior of the problem completely and it is possible while classical theory predicts stable behavior for microscope the size effect is caused bi-stability. The results in this paper are very useful for the design and analysis of atomic force microscope.

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In this paper, design, fabrication and test of piezoelectric fiber composite transducer for Lamb wave inspection of fluid loaded plates has been investigated. First, dispersion and wave structure analysis has been performed in order to select proper mode and frequency for fluid loaded plate inspection. The S1 mode with zero out of plane displacement in free boundaries of a plate with predefined thickness has been extracted, afterward a piezoelectric fiber composite comb transducer has been designed and fabricated. Having manufactured the transducer, necessary tests has been done in order to prove that the transducer generated Lamb mode at selected mode and frequency is not affected by the fluid loading, in both pitch-catch and pulse-echo techniques. The tests has been done successfully and then crack detection in fluid loaded plate by means of fabricated transducers has been examined again in both pulse-echo and pitch-catch arrangements. It has been shown that in pitch-catch test, the presence of a predefined crack leads to decrease in S1 mode related peak in receiver. Moreover, in pulse-echo test, due to the interference of crack reflected wave signal with the transducer resonance response, continues wavelet transform, as one of time-frequency signal processing methods, has been employed successfully for crack detection. Consequently, the fabricated signal has necessary efficiency for damage detection in fluid loaded plates using lamb waves.

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In this article the vibration analysis of a viscoelastic cantilever beam with piezoelectric layers under aeroelastic force and base excitation is investigated. The beam viscoelastic material is assumed to obey the Kelvin-Voight model. Also the piezoelectric layers are located at the top and bottom beam surfaces with series connections. The aeroelastic force based on piston theory is considered to act as an external force on the beam and also the base excitation is assumed to be random. In this research the cantilever beam with two piezoelectric layers are considered as a mechanism to harvest the bending vibration energy. First, the Galerkin method is used to convert the governing partial differential equation into a set of ordinary differential equations. Then the resulted nonlinear ordinary differential equation coupled with electrical circuit equation of piezoelectric layer are solved numerically by Rung-Kutta method. Finally, by analyzing the response of the governing equations, the influence of the system parameters on the vibration behavior of beam and output voltage are discussed. Results show that the increase of fluid velocity increases vibrational energy system which leads to increase of both vibration amplitude and output voltage. In addition, it was shown that structural damping has a significant impact on the output voltage.

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In this paper, the nonlocal buckling behavior of a biaxially loaded graphene sheet with piezoelectric layers based on an isotropic smart nanoplate model is studied. The equilibrium equations are derived with the von Karman-type geometrical nonlinearity by considering the small scale effect. The buckling of multilayer smart nanoplate made of graphene and piezoelectric materials in open circuit conditions is investigated. Based on the nonlocal elasticity and shear and normal deformation theories, the governing equilibrium equations are obtained using the principle of minimum total potential energy and Maxwell’s equation.
Using an analytical approach, the governing stability equations of smart nanoplate have been presented in terms of displacement components and electrical potential. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling load values have been compared with available resources. Finally, following validation of the results, numerical results for intelligent nanoplate are presented.
Also, the effects of different parameters such as nanoplate length, different nonlocal parameter, piezoelectric layers thickness, the graphene thickness to length ratio, the piezoelectric layer thickness to graphene thickness ratio and type of Piezoelectric material on the critical buckling loads of intelligent nanoplate are studied in detail. Furthermore, the effect of the mentioned parameters on the critical buckling loads have been presented in some figures.

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in recent years, Variety of analytical methods have been used to calculate the output piezoelectric energy, but it is new something the use of finite element method and compared using analysis software with numerical methods. And also check the types of circuit connection of piezoelectric layers So in this article particular form of numerical analysis method is called separation of variables method compared with the finite element method, To take advantage of these methods is to be determined. The model is a Bimorph beam with two piezoelectric layers and a central elastic layer. This Bimorph beam starts vibrating at various frequencies as a result of base excitation. First, frequency behavior of the Bimorph beam is simulated using the separation of variables method. In this method, the equations of motion in parallel and series connection of piezoelectric layers are obtained as separate parameters. The coupled mechanical and electrical equations are derived using the solution of equations obtained from the separation of variables method. Finally, the output voltage, current and power are obtained in terms of frequency.
Then, the Bimorph beam is modeled based on finite element method using ABAQUS software. after the illustrating Output voltage, current and power diagrams is illustrated for a certain range of frequencies and the results of the finite element method and the steady state method are compared to validate the model.

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In this study, a galloping-based energy harvesting system is designed using a nonlinear energy harvesting sink (NES). In doing so, electromechanical equations of motion for the energy harvesting system are derived and the theoretical results are validated with experimental results. Then, three steps are presented to make system work efficiently. In the first step, several cross-section geometries for the bluff body are investigated and the results are verified by the Harmonic Balance Method. These results indicate that isosceles triangular section can harvest more energy than the other ones. In the second step, effect of changing the electrical load resistance on electromechanical behavior of the system is investigated and it is demonstrated that the maximum energy is harvested for load resistance values of more than 1 MΩ. In the third step, influence of changing the tip mass on the system is studied and it is shown that increasing the tip mass leads to increase the output voltage while the bluff body amplitudes remain constant. Consequently, the system is designed to work with the maximum possible tip mass which is about 35.3 gr. Finally, this system with a bluff body of isosceles triangular section can generate 700 mV using the load resistance value of 10 MΩ in the wind speed of 2.5 m/s. This system with the total mass of less than 500 gr and low-amplitude oscillations is designed to work properly in low wind speeds and presents an efficient application for low-power energy harvesting systems.