Multi-parametric dynamic analysis of lightweight elastic laminates

J Kaplunov,A Nikonov,T Savšek,D A Prikazchikov,L A Prikazchikova

doi:10.1088/1757-899x/683/1/012014

Abstract

Multi-parametric asymptotic analysis of dynamic phenomena in lightweight three-layered structures is performed. The presence of high contrast in densities of skin and core layers may lead to the small value of the lowest shear thickness resonance frequency, allowing a two-mode long wave low-frequency approximation of the exact dispersion relation. The range of uniform asymptotic validity of the two-mode approximation with respect to relative thickness and density are established. The theoretical predictions are illustrated numerically.

Highlights

Multi-layered structures with a strong vertical heterogeneity are of major importance for numerous high-tech domains in aerospace, automotive and civil engineering, see e.g. [1, 2] and references therein
The presence of high contrast in densities of skin and core layers may lead to the small value of the lowest shear thickness resonance frequency, allowing a two-mode long wave low-frequency approximation of the exact dispersion relation
The key message of the cited papers is that due to contrast the lowest shear mode may be excited over the low frequency range, requiring substantial amendments to the established structural theories

Summary

Introduction

Multi-layered structures with a strong vertical heterogeneity are of major importance for numerous high-tech domains in aerospace, automotive and civil engineering, see e.g. [1, 2] and references therein. In particular, photovoltaic panels and laminated glass, see [3, 4, 5] Another important example originating from automotive industry, is concerned with design of a new generation of environment-friendly lightweight vehicles, see [6, 7]. Instead of the classical Kirchhoff theory governing the fundamental vibration mode of a thin plate, a variety of two-mode approximations, strongly affected by the contrast parameters were discovered in [8]. The latter, in addition to the fundamental mode, include the first low-frequency harmonic.

Statement of the problem

Fundamental mode

Numerical results

The composite expansion versus the exact solution is shown in