Nonlinear breathing vibrations of a circular mesh antenna based on a equivalent model of a composite laminated circular cylindrical shell with membranes

摘要

This paper is focused on the nonlinear breathing vibrations of the circular mesh antenna based on a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix.The finite element model of the circular mesh antenna are established,we study the effects of different mesh stiffness on the first six orders frequencies.It is found that there is an approximate threefold relationship between the first-order frequency and the forth-order frequency.Based on the particular integer multiple relationship,we can conclude that there is the 1:3 resonance between the first-order and the forth-order vibrations of the circular mesh antenna.The method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation based on the two degree of freedom non-autonomous nonlinear equations of the equivalent model of circular mesh antenna and the 1:3 internal resonance is considered here.Then,based on the numerical method,the chaotic dynamics of the equivalent model of circular mesh antenna are studied by the bifurcation diagrams,the phase portraits,the waveforms,the power spectrums and the Poincare map.The temperature parameter excitation shows that the complex chaotic phenomena occur under the certain initial conditions.