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

Minimal models for disk brake squeal

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

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

Piezo–beam systems subjected to weak electric field: experiments and modelling of non-linearities

Considerable effort is spent in the design and testing of disk brakes of modern passenger cars. This effort can be reduced if refined mathematical-mechanical models and new experimental techniques are used for studying the dynamics of these brakes. The present paper is devoted to the modeling and experimental investigation of a floating caliper disk brake, special regard being given to the suppression of squeal using active elements. To actively suppress brake squeal, smart pads were designed and manufactured. These pads contain piezoceramic staple actuators, which can be independently driven at both pads and within the pads. In experiments they were successfully used for the active suppression of squeal via optimal control. As the piezoceramic elements can be used both as actuators as well as sensors, the smart pads are also useful in experimental investigations such as measuring transfer functions. In this manner, design modifications proposed for conventional disk brakes can easily be tested using this method. Active control of squeal using smart pads is presently not envisaged as a technique to suppress squeal in mass produced disk brakes, but rather as a possible tool to be used in industrial laboratories to shorten the time for optimizing new brake designs, with high potential saving benefits. The development and laboratory implementation of the active squeal control goes along with a more profound understanding of brake squeal and a better modeling of the phenomena, ultimately leading to improvements in the design of disk brakes.

Active Control of Brake Squeal Via “Smart Pads”

Typical non-linear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relationship between excitation voltage and vibration amplitude as well as jump phenomena are observed in experiments with piezoceramics excited at resonance by weak electric fields. These non-linear effects can be observed for both the piezoelectric 31- and the 33-effect. In contrast to the well-known non-linear effects exhibited by piezoceramics in the presence of strong electric fields, these effects are not described in detail in the literature. In this paper, we attempt to model these phenomena using an electric enthalpy density to capture the cubic-like effects observed in the experiments. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. The ‘non-linear’ parameters are identified and the numerical results are compared to those obtained experimentally. The effects described herein may have a significant influence in structures excited close to resonance frequencies via piezoelectric elements.

Non-linear longitudinal vibrations of piezoceramics excited by weak electric fields

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

In this paper, high-dimensional probability density functions of non-linear dynamical systems are calculated solving the corresponding Fokker–Planck equations. Zeroth approximations are derived from solutions of corresponding linear systems and analytical results for first- and second-order expected values. The zeroth approximations are used as weighting functions for the construction of generalized Hermite polynomials. The Fokker–Planck equation is expanded in terms of these polynomials and subsequently solved by a Galerkin method. As an example, models of a quarter car with non-linear damping subjected to white or colored noise excitation are considered. The damping is piecewise linear and asymmetric leading to a non-vanishing expected value of the displacement of the car. The excitation is realized by the roughness of the road and the car moves with constant velocity. Monte-Carlo simulations and analytical results are used for comparison.

On non-linear stochastic dynamics of quarter car models

There is a wide range of nonlinear effects which can be observed in piezoceramicsOne example is the well-known butterfly hysteresis behavior for large stresses and strongelectric fields For small stresses and weak electric fields, piezoceramics are usuallydescribed by linear constitutive equations around an operating point in the butterflyhysteresis curve Nevertheless, typical nonlinear effects can be observed whenpiezoceramic actuators and structures with embedded piezoceramics are excited inresonance, even if the stresses and the electric field remain small

Utz von Wagner

Papers

Active Control of Brake Squeal Via “Smart Pads”

Non-linear longitudinal vibrations of piezoceramics excited by weak electric fields

Non-linear shear vibrations of piezoceramic actuators

On non-linear stochastic dynamics of quarter car models

Nonlinear effects of piezoceramics excited by weak electric fields