弹性地基上夹紧圆板加热后的非线性轴对称自由振动

摘要

Based on the non-dimensional ordinary differential control equations of the non-linear axial symmetry free vibration of a heated circular plate on elastic foundation,combining with clamped boundary condition,the numerical solution is obtained by using shooting method.The first-order thermal buckling mode with different stiffness coefficient k of foundation is analyzed,the front three order non-dimensional frequency with the non-dimensional heating valueμ is obtained,and the front three order vibration mode with the different stiffness coefficient k of foundation is obtained simultaneously.%根据弹性地基上的加热圆板非线性轴对称自由振动的无量纲常微分控制方程，结合周边夹紧的边界条件，采用打靶法得到了数值解答。分析了不同无量纲地基刚度系数 k 对应的1阶热屈曲模态，给出了无量纲升温μ对应的前3阶无量纲自然频率，同时得出了不同无量纲地基刚度所对应的前3阶振动模态。