Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

Abstract

A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff-Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam, whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied. Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified model. Limitations on the simplified model application are specified.

Monoharmonic approximation in the vibration analysis of a sandwich beam containing piezoelectric layers under mechanical or electrical loading

“…The model stems from the earlier works [18,24,28]. This paper generalizes the results previously obtained by the authors [29,30] as well as provides the following new contribution to the field: it takes into account the inelastic response of the metal layer; provides a new mathematical interpretation of the approximate problem statement in the case of harmonic loading; and presents the computations and analysis for a particular configuration, namely, for a sandwich beam. Specifically, the new results on the variation of main mechanical variables are obtained and analysed; the electric current generated by piezoactive layers acting as sensors is calculated for different loading levels; amplitude-frequency characteristics are refined in the vicinity of the first bending mode resonance.…”

“…Electric potentials j z are specified on the surfaces of piezoactive layers. Based on the concept of complex moduli, the constitutive equations for piezoactive layers can be written as [18,30] s x ¼c D 11ẽ x þc D 12ẽ y þc D 13ẽ z Àh 31Dz ,s xy ¼ ðc D 11 Àc D 12 Þẽ xy =2,s y ¼c D 12ẽ x þc D 11ẽ y þc D 13ẽ z Àh 31Dz , s yz ¼c D 44ẽ yz Àh 15Dy ,s z ¼c D 13ẽ x þc D 13ẽ y þc D 33ẽ z Àh 33Dz ,s xz ¼c D 44ẽ xz Àh 15Dx ,…”

“…The running time of the code is approximately 100 times faster, see Refs. [29,30] for example. This is because there is no need to calculate the total time history from the very beginning to the steady-state vibration stage.…”

“…Henceforth, as in Refs. [29,30], the ''complete'' means the analysis is based on the time-dependent inelastic model (i.e. on the constitutive equations of one of the unified flow theories), and the ''approximate'' means the analysis relies on its harmonically linearised modification.…”

Vibration analysis of thin-wall structures containing piezoactive layers

“…In this paper, based on the electromechanical model [1,11], the simplified monoharmonic approach is considered to describe the coupled dynamic behaviour of thin wall structures consisting of elastic piezoactive and inelastic metal layers under cyclic electric or mechanical loading. As an example, a three-layer sandwich beam (aluminium alloy core covered with piezoelectric layers) with hinged ends is studied.…”