带硬涂层圆盘构件的固有振动特性的精确解法

Exact solution on inherent vibration properties for hard-coating circular plate component

研究了在广义弹性简支边界条件下的具有硬涂层的圆盘构件的自由振动的量纲一固有频率的精确解.首先利用多铁性多层圆盘的解析分析的多层板弹性理论,导出带硬涂层的圆盘结构的状态方程,其中以位移、电势、磁势、应力、电位移和磁感应强度为状态变量.利用有限Hankel变换和传播矩阵法,得到考虑压电和压磁效应的带硬涂层的圆盘的量纲一固有频率的精确解.根据算例结果,比较了压电、压磁两类硬涂层材料在单面涂层、双面涂层和不同涂层厚度的结构配置下的固有频率变化规律.

Under the broad-elasticity simply-supported boundary conditions,the exact solution on dimensionless inherent frequency of hard-coating circular plates is investigated via the free vibration.Pertaining to the literatures of multi-layered plate elastic theory about the analytical analysis on multi-ferrous and multi-layered circular plates,the state equation of hard-coating circular plate is deduced.Amongst this equation,the displacement,electric potential,magnetic potential,stress,electric displacement and magnetic induction density are treated as state variables.By applying the limited Hankel transform and propagation matrix,the exact solution is obtained with consideration of the piezoelectric and piezomagnetic effects.Based on the computational example results,in comparison with two hard-coating materials as well as single-sided and double-sided coating structures,the changing principle of inherent frequency is detected regarding coating thickness.