In this paper, the nonlinear dynamic analysis of the circular truss equivalent to the cylindrical shell under the influence of the thermal excitation and the damping coefficient are studied. The annular truss structure is equivalent to the cylindrical shell structure based on the previous equivalent process, and the nonlinear dynamic equations of the equivalent cylindrical shell considering the effect of thermal excitation are established by using the first-order shear deformation theory. The natural frequencies and modes of the equivalent cylindrical shell are analyzed by the finite element method, and the frequency ratio between modes is calculated. Considering the fixed boundary condition of the equivalent cylindrical shell in the generatrix direction, the torsional mode function and the bending mode function of the equivalent cylindrical shell are selected by the Chebyshev polynomial approximation method and are truncated by Galerkin method. Based on the nonlinear ordinary differential equations of two degrees of freedom, the amplitude-frequency responses, bifurcation, and chaotic characteristics of the system are analyzed. The results show that under the influence of thermal excitation, the motions of the system are complex, and when the excitation amplitude is large, the system appears chaotic motion. The damping coefficient limits the possibility of complex motions of the system. With the influence of the damping coefficient, the motion of the system tends to be stable.

本文研究了在热激励和阻尼系数的影响下，等效于圆柱壳的圆形桁架的非线性动力分析。环形桁架结构相当于基于先前等效过程的圆柱壳结构，并利用一阶剪切变形理论建立了考虑热激励影响的等效圆柱壳的非线性动力学方程。用有限元方法分析了等效圆柱壳的固有频率和模态，并计算了模态之间的频率比。考虑到等效圆柱壳在母线方向上的固定边界条件，等效圆柱壳的扭转模式函数和弯曲模式函数通过Chebyshev多项式逼近法选择，并通过Galerkin方法截断。基于两个自由度的非线性常微分方程，分析了系统的幅频响应，分叉和混沌特性。结果表明，在热激励的影响下，系统的运动较为复杂，当激励幅度较大时，系统呈现混沌运动。阻尼系数限制了系统复杂运动的可能性。在阻尼系数的影响下，系统的运动趋于稳定。基于两个自由度的非线性常微分方程，分析了系统的幅频响应，分叉和混沌特性。结果表明，在热激励的影响下，系统的运动较为复杂，当激励幅度较大时，系统呈现混沌运动。阻尼系数限制了系统复杂运动的可能性。在阻尼系数的影响下，系统的运动趋于稳定。基于两个自由度的非线性常微分方程，分析了系统的幅频响应，分叉和混沌特性。结果表明，在热激励的影响下，系统的运动较为复杂，当激励幅度较大时，系统呈现混沌运动。阻尼系数限制了系统复杂运动的可能性。在阻尼系数的影响下，系统的运动趋于稳定。系统出现混沌运动。阻尼系数限制了系统复杂运动的可能性。在阻尼系数的影响下，系统的运动趋于稳定。系统出现混沌运动。阻尼系数限制了系统复杂运动的可能性。在阻尼系数的影响下，系统的运动趋于稳定。