非线性地基上正交异性矩形板的非线性热振动

研究了非线性地基上正交异性矩形板的非线性固有热振动.采用常规的L-P法分析非线性地基上正交异性矩形板的非线性热振动难以得到高精度的近似解,为此,先对该强非线性振动系统进行参数变换,将该强非线性振动系统转化为弱非线性振动系统.然后采用改进的L-P法进行求解,得到了强非线性振动系统的高精度近似解.此外,讨论了温度、地基特征参数、长宽比等因素对非线性地基上正交异性矩形板非线性热振动固有频率的影响,得到了非线性地基上正交异性矩形板热振动频率随温度下降、地基特征参数变大、长宽比变大而增大的结论.

Nonlinear thermal vibration of rectangular orthotropic plate on nonlinear foundation

The nonlinear natural thermal vibration of a rectangular orthotropic plate on a nonlinear foundation was studied. To get a high-accuracy approximate solution which can't be obtained with the normal L-P method, the strongly nonlinear vibration system of the nonlinear natural thermal vibration of the rectangular orthotropic plate on the nonlinear foundation was changed to a weakly nonlinear vibration system firstly by the parameter transformation, and then the high-accuracy approximate solution can be obtained with the improved L-P method. The effects of temperature, characteristic parameter of foundation, ratio of length and width etc. on the natural thermal vibration frequency were discussed. The results showed that the natural thermal vibration frequency decreased with the increase of temperature and increased with the increase of the characteristic parameter of foundation and ratio of length and width.