非惯性参考系下中厚板的非线性自由振动分析

Non-linearFreeVibrationAnalysisofModerate-thickness Plate in Non-inertial Reference System

基于 Hamilton原理 ,利用 Timoshenko-Mindlin板理论建立了非惯性参考系中弹性中厚板在单轴转动下的非线性运动方程 .并利用符号代数语言分析了其在多种弹性边界条件下的自由振动情况 ,结果发现当单轴转动速率小于极限速率时 ,板的自由振动表现为周期运动 ,而当单轴转动速率大于其极限速率时 ,板的自由振动不再为周期运动 .

The dynamical equations of the Timoshenko-Mindlin moderate-thickness plate in a non-inertial reference system are derived by Hamiton's principle.The free vibrations of plate in different elastic boundary conditions are analysised.And the system vibration will be periodic motion when the rotation speed is less than the critical speed;while it will be non-periodic motion when the rotation speed is more than the critical speed..