Vibrations of Nonlinear Systems in Aerospace Structures

研究薄壁结构轻量化的非线性动力行为具有重要意义，如微重力条件下的大空间柔性结构和高温动压作用下的高速飞机。首先，研究了超声速/高超声速飞行范围内由于气动加热引起的板屈曲弯曲梁的非线性振荡，预测了在一定的强迫强度和梁的曲率条件下，由于在poind -care图中出现马蹄形而出现混沌运动，并通过数值分析实际显示了混沌运动的发生。对于作为轻型结构重要构件的叠合板，本文提出了满足界面横向剪应力连续性的高阶位移场理论，并与现有的精确近似分析方法进行了比较。本文还研究了复合材料层合板机翼在超声速下的颤振和散度，以阐明临界速度下层合板弯曲/扭转刚度比对机翼颤振和散度的影响。最后，对天线悬臂梁在卫星部署过程中的非线性振荡进行了分析和实验研究。采用伸长单元法进行有限元分析，结果与试验结果吻合较好。除了有限元数值分析外，还采用格林函数方法对两端支承的展开梁的运动进行了解析检验。

It is important to study nonlinear dynamic behaviors of light-weigted of thin-walled structures, such as very flexible large space structures under a micro-gravity condition and high-speed aeroplanes subjected to high temperature and dynamic pressure. First, we examinated the nonlinear oscillation of a curved beam which modelled buckling of a plate due to aerodynamic heating in supersonic/hypersonic flight ranges, predicted that chaotic motions would appear on certain conditions of the forced intensity and the curvature of the beam because of the appearance of the horseshoe in Poin-care's map, and showed actually the occurrence of the chaotic motion using a numerical analysis. As for laminated composite plates as important elements of the light-weighted structures, a higher-order displacement field theory in which the continuity of transverse shear stresses is satisfied at interfaces ha s next been proposed to compare with existing exact and approximate analysis. Flutter and divergence of laminated composite plate wings in a supersonic flow were also studied to clarify the effect of ratios of bending/torsional rigidity of the laminae of the critical speed. Finally, the nonlinear oscillation of a cantilever beam representing an antenna during deployment from a satellite was also studied analytically and experimentally. The FEM was applied using elongating elements, and a good agreement between the analysis and the experiment was obtained. In addition to the finite element numerical analysis, the motion of a deploying beam having both ends supported was analytically examined using a green function approach.