Nonlinear Dynamic Responses of a Honeycomb Sandwich Plate Subject to Transverse Excitations

Dongmei Wang,Minghui Yao,Wei Zhang,Yinli Liu,O Adiguzel,I Mcandrew,Y Yokoi,V Koryanov

doi:10.1051/matecconf/201815101003

Abstract

Nonlinear dynamic behaviors of a simply supported honeycomb sandwich plate subjected to the transverse excitations are investigated in this paper. Based on the classical thin plate theory and Von Karman large deformation theory, the governing equation of motion for the honeycomb sandwich plate is established by using the Hamilton principle. The nonlinear governing partial differential equation is discretized to the ordinary differential equations by differential quadrature method and then solved by Runge-Kutta-Fehlberg method. Based on the numerical simulations, combined with nonlinear dynamic theory, the influences of the frequency and amplitude of the transverse excitation are investigated respectively by using the bifurcation diagrams, Poincare maps and phase portraits. The results exhibit the existence of the period-1, period-2 and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.

Highlights

As a kind of special composite structural material, sandwich beam and plates are widely used in a variety of aircraft structures and satellite launch vehicles
In order to illustrate in detail the bifurcation behaviors, the Poincare maps which consists of the displacements w and the velocity dw, and the dt phase portraits which consists of the displacement w and the velocity dw are respectively depicted
Two types of bifurcation diagrams are presented to show the displacement and velocity projections of the Poincare maps changing with the frequency and the amplitude of the transverse excitation

Summary

Introduction

As a kind of special composite structural material, sandwich beam and plates are widely used in a variety of aircraft structures and satellite launch vehicles. Zenkour [1,2] performed a comprehensive analysis of functionally grade sandwich plates, including buckling, free vibration and stability analyzes. Li et al [3] applied the three dimensional Ritz method based on the use of the Chebyshev polynomials for the free vibration analysis of functionally graded material sandwich plates. Dozio[4] studied the free vibration behavior of sandwich plates with FGM core via variable-kinematic 2-D Ritz models using Chebyshev polynomials. The differential quadrature (DQ) method, which was introduced by Bellman [11] et al in 1972, is a highly efficient approach to directly solving a partial differential equation for a finite domain with a set of given boundary conditions. Since the DQ method has lots of merits, such as simple principle, high precision, less computation and

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Numerical results

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Summary