Study on Buckling, Free Vibration and Parametric Resonance of Sandwich Shell Panels with Viscoelastic Material Core

Abstract

Vibration suppression of many aerospace and mechanical engineering structures subjected to periodic excitations is of paramount importance, as these kinds of loads often cause parametric instability of the structures. Parametric instability or parametric resonance may lead to more catastrophic consequence than simple resonance condition of the structural member. Vibration damping of structural elements using viscoelastic materials has been a trending area of research in recent years. The present work focuses on the study of buckling, free vibration and parametric instability characteristics of doubly curved sandwich shell panels with viscoelastic material (VEM) core/s constrained by stiffer elastic layer/s using finite element method (FEM). Achieving the desired damping of the parent structure or that of the system as a whole using constrained layer like VEM is often termed as passive constrained layer damping (PCLD) treatment. A modified eight noded isoparametric finite sandwich shell elements, based on first order shear deformation theory (FSDT) with consideration of independent transverse displacement of the elastic layers have been proposed to model the three layer and five-layer sandwich shell panels. Longitudinal and transverse deformations of the VEM core layer are taken into account along with the transverse shear deformation. A through the thickness linear variation of displacements of the VEM core/s are considered. Static stability analysis of the sandwich shell structure has been carried out considering full geometric nonlinearity in the Green-Lagrange sense. The governing equations of motion of the laminated single shell panel and sandwich shell panels are derived using finite element method in conjunction with Hamilton’s principle. The equations of motion of the single/sandwich shell panels are represented as Mathieu-Hill type equations. The regions of instabilities of the single and sandwich shell panels have been established using Floquet’s theory based Bolotin’s method and Hsu’s criteria based Saito-Otomi conditions respectively. Extensive numerical studies have been carried out to ascertain the effect of different system parameters such as constraining layer thickness, core layer thickness, VEM loss factor, aspect ratio, skewness, lamination scheme etc. on the critical buckling loads, natural frequencies and system loss factors, as well as on the dynamic stability of the single/sandwich shell panels. Multilayer sandwich shell panel exhibits better damping capacity than the traditional three layer sandwich panel for equal effective thickness of VEM layer and constraining layer. Increase in skewness of the shell panels increase the buckling loads and natural
frequencies. Increase of core layer thickness is found to ensure better dynamic stability. The reported findings are expected to contribute towards the improved understanding of buckling, free vibration and parametric resonance phenomena of single and sandwich shell panels.