Nonlinear dynamics of large circular annular truss antenna structures subjected to boundary loads

Abstract

This paper investigates the bifurcation and chaos in breathing vibration of a circular truss antenna that has expanded subjected to heating load. The circular antenna is reducing to a continuum circular cylindrical shell, and considering the loads that come from cable net structure. By using the first order shear deformation theory, geometrical non-linearity strain-displacement relationship and Hamilton’s principle, the nonlinear partial differential equilibrium equation of the system are deduced. Galerkin method is utilized to obtain the nonlinear ordinary differential governing equations of the cylindrical shell under the specific boundary conditions that one generatrix of the cylindrical shell is clamped and both ends of the shell are free. Using Runge-Kutta method for numerical simulation of equivalent cylindrical shell under special boundary condition, the bifurcation diagram of system and the largest Lyapunov exponent curve, three-dimensional bifurcation diagram, time history diagram, phase map and Poincare section can be obtained. The influences of radial line load and in-plane load on vibration characteristics of the continuum circular cylindrical shell are studied.