Nonlinear Vibrations of FGM Cylindrical Panel with Simply Supported Edges in Air Flow

Y X Hao,S B Li,W Zhang,J H Zhang

doi:10.1155/2015/246352

Abstract

Chaotic and periodic motions of an FGM cylindrical panel in hypersonic flow are investigated. The cylindrical panel is also subjected to in-plane external loads and a linear temperature variation in the thickness direction. The temperature dependent material properties of panel which are assumed to be changed through the thickness direction only can be determined by a simple power distribution in terms of the volume fractions. With Hamilton’s principle for an elastic body, a nonlinear dynamical model based on Reddy’s first-order shear deformation shell theory and von Karman type geometric nonlinear relationship is derived in the form of partial equations. A third-order piston theory is adopted to evaluate the hypersonic aerodynamic load. Here, Galerkin’s method is employed to discretize this continuous nonlinear dynamic system to ordinary differential governing equations involving two degrees of freedom. The chaotic and periodic response are studied by the direct numerical simulation method for influences of different Mach number and the value of in-plane load. The bifurcations, Poincare section, waveform, and phase plots are presented.

Highlights

With the continuous variation of the material properties along the thickness, functionally graded materials (FGM) can be used in high temperature gradient environments especially when they are made of metal and ceramic
In order to validate the numerical results presented in this study, a comparison is shown in Figure 2 for a supported intact aluminum-zirconia FGM square plate with length 0.2 m and thickness 0.01 m
The plate is subjected to the aerodynamic force in this study and not uniform transverse load, as external pressures, both of them play the same role on the plate

Summary

Introduction

With the continuous variation of the material properties along the thickness, functionally graded materials (FGM) can be used in high temperature gradient environments especially when they are made of metal and ceramic. They presented the results for different factors Accounting for both the geometric and aerodynamic nonlinearities, Prakash et al [9] studied the nonlinear flutter of FGM plates under high supersonic airflow in frequency domain and time domain, respectively. The flutter boundaries were obtained for the FGM conical shells with different semivertex cone angles, different temperature distributions, and different volume fraction indices When it comes to FGM cylindrical panel identification, damage detection, and the control of the dynamics, it is necessary to investigate their complex nonlinear flutter in hypersonic air flow in great detail [18]. The bifurcations and chaotic dynamics of the hypersonic FGM cylindrical panel subjected to thermal and mechanical loads are investigated by applying geometrical nonlinear and the third-order piston theory. The nonlinear dynamical equations are analyzed to find the nonlinear responses of the system

Theoretical Formulation

Numerical Results and Discussions

Conclusions