Analysis of Sandwich Plates with Viscoelastic Damping Using Two-Dimensional Plate Modes

Abstract

A higher-order assumed modes analysis for a sandwich plate is developed. The base plate is an isotropic plate with the parallel edges of its span clamped and with its remaining edges free. An isotropic constraining layer sandwiching a viscoelastic core is centrally located over one-third of the span across the plate's chord. Analysis of the base plate uses two-dimensionalplate bending and in-plane extension mode shapes based on the Kantorovich-Krylov method. Free-free one-dimensional rod modes are used to approximate in-plane motions in both x and y directions for the constraining plate, and bending displacement compatibility is assumed between base and constraining plates. The Golla-Hughes-McTavish method was used to account for the frequency-dependent complex shear modulus of the viscoelastic core. Natural frequencies, mode shape functions, loss factors, and frequency responses of the sandwich plate were calculated and compared to the results of our previous analysis using one-dimensional beam and rod modes. Fewer modes were needed in the current analysis to achieve the same accuracy as compared to the previous analysis. Experiments were conducted to validate predictions, and the experimental data substantially agree with our results.

Applications of the poincaré inequality to extended Kantorovich method

“…Consider the Dirichlet space H In this paper, we will use the Poincaré inequality to study the extended Kantorovich method, see [6]. This method has been used extensively in many engineering problems, for example, readers can consult papers [4,7,8,11,12], and the references therein. Let us start with a model problem, see [8].…”