We propose and experimentally validate a first-principles based model for the nonlinear piezoelectric response of an electroelastic energy harvester The analysis herein highlights the importance of modeling inherent piezoelectric nonlinearities that are not limited to higher order elastic effects but also include nonlinear coupling to a power harvesting circuit Furthermore, a nonlinear damping mechanism is shown to accurately restrict the amplitude and bandwidth of the frequency response The linear piezoelectric modeling framework widely accepted for theoretical investigations is demonstrated to be a weak presumption for near-resonant excitation amplitudes as low as 05 g in a prefabricated bimorph whose oscillation amplitudes remain geometrically linear for the full range of experimental tests performed (never exceeding 025% of the cantilever overhang length) Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obta

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Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

This paper investigates the static bending, free vibration, and dynamic response of monomorph, bimorph, and multimorph actuators made of functionally graded piezoelectric materials (FGPMs) under a combined thermal-electro-mechanical load by using the Timoshenko beam theory. It is assumed that all of the material properties of the actuator, except for Poisson's ratio, are position dependent due to a continuous variation in material composition through the thickness direction. Theoretical formulations are derived by employing Hamilton's principle and include the effect of transverse shear deformation and axial and rotary inertias. The governing differential equations are then solved using the differential quadrature method to determine the important performance indices, such as deflection, reaction force, natural frequencies, and dynamic response of various FGPM actuators. A comprehensive parametric study is conducted to show the influence of shear deformation, temperature rise, material composition, slenderness ratio, end support, and total number of layers on the thermo-electro-mechanical characteristics. It is found that FGPM monomorph actuators exhibit the so-called 'non-intermediate' behavior under an applied electric field.

https://iopscience.iop.org/article/10.1088/0964-1726/16/3/028/pdf

Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators

Now a days, sandwich beams and plates made of functionally graded (FG) materials are widely used in many engineering industries. Therefore, several modeling techniques and solution methods ...

Modeling and analysis of functionally graded sandwich beams: a review

Nonlinear piezoelectric effects in flexural energy harvesters have recently been demonstrated for drive amplitudes well within the scope of anticipated vibration environments for power generation. In addition to strong softening effects, steady-state oscillations are highly damped as well. Nonlinear fluid damping was previously employed to successfully model drive dependent decreases in frequency response due to the high-velocity oscillations, but this article instead harmonizes with a body of literature concerning weakly excited piezoelectric actuators by modeling nonlinear damping with nonconservative piezoelectric constitutive relations. Thus, material damping is presumed dominant over losses due to fluid-structure interactions. Cantilevers consisted of lead zirconate titanate (PZT)-5A and PZT-5H are studied, and the addition of successively larger proof masses is shown to precipitate nonlinear resonances at much lower base excitation thresholds while increasing the influence of higher-order nonlineari...

Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects

Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

A wide range of non-linear effects are observed in piezoceramic materials. For small stresses and weak electric fields, piezoceramics are usually described by linearized constitutive equations around an operating point. However, typical non-linear vibration behavior is observed at weak electric fields near resonance frequency excitations of the piezoceramics. This non-linear behavior is observed in terms of a softening behavior and the decrease of normalized amplitude response with increase in excitation voltage. In this paper the authors have attempted to model this behavior using higher order cubic conservative and non-conservative terms in the constitutive equations. Two-dimensional kinematic relations are assumed, which satisfy the considered reduced set of constitutive relations. Hamilton's principle for the piezoelectric material is applied to obtain the non-linear equation of motion of the piezoceramic rectangular parallelepiped specimen, and the Ritz method is used to discretize it. The resulting equation of motion is solved using a perturbation technique. Linear and non-linear parameters for the model are identified. The results from the theoretical model and the experiments are compared. The non-linear effects described in this paper may have strong influence on the design of the devices, e.g. ultrasonic motors, which utilize the piezoceramics near the resonance frequency excitation.

Non-linear shear vibrations of piezoceramic actuators

Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method

Summary In the past few decades the finite element modelling has been developed as an effective tool for modelling and simulation of the biomedical engineering system. Finite element modelling (FEM) is a computational technique which can be used to solve the biomedical engineering problems based on the theories of continuum mechanics. This paper presents the state of art review on finite element modelling application in the four areas of bone biomechanics, i.e., analysis of stress and strain, determination of mechanical properties, fracture fixation design (implants), and fracture load prediction. The aim of this review is to provide a comprehensive detail about the development in the area of application of FEM in bone biomechanics during the last decades. It will help the researchers and the clinicians alike for the better treatment of patients and future development of new fixation designs.

A review on application of finite element modelling in bone biomechanics

Nonlinear behavior of piezoceramics at strong electric fields is a well-known phenomenon and is described by various hysteresis curves. On the other hand, nonlinear vibration behavior of piezoceramics at weak electric fields has recently been attracting considerable attention. Ultrasonic motors (USM) utilize the piezoceramics at relatively weak electric fields near the resonance. The consistent efforts to improve the performance of these motors has led to a detailed investigation of their nonlinear behavior. Typical nonlinear dynamic effects can be observed, even if only the stator is experimentally investigated. At weak electric fields, the vibration behavior of piezoceramics is usually described by constitutive relations linearized around an operating point. However, in experiments at weak electric fields with longitudinal vibrations of piezoceramic rods, a typical nonlinear vibration behavior similar to that of the USM-stator is observed at near-resonance frequency excitations. The observed behavior is that of a softening Duffing-oscillator, including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage. Other observed phenomena are the decrease of normalized amplitude responses with increasing excitation voltage and the presence of superharmonics in spectra. In this paper, we have attempted to model the nonlinear behavior using higher order (quadratic and cubic) conservative and dissipative terms in the constitutive equations. Hamilton's principle and the Ritz method is used to obtain the equation of motion that is solved using perturbation techniques. Using this solution, nonlinear parameters can be fitted from the experimental data. As an alternative approach, the partial differential equation is directly solved using perturbation techniques. The results of these two different approaches are compared.

Sandeep Kumar Parashar

Papers

Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

Non-linear shear vibrations of piezoceramic actuators

Modal analysis of shear-induced flexural vibration of FGPM beam using Generalized Differential Quadrature method

A review on application of finite element modelling in bone biomechanics

Nonlinear Longitudinal Vibrations of Transversally Polarized Piezoceramics: Experiments and Modeling