中面单向受拉(压)的阶梯式矩形薄板的振动

VIBRATIONS OF STEPPED THIN RECTANGULAR PLATES SUBJECTED TO IN-PLANE TENSILE/COMPRESSIVE FORCES IN X-DIRECTION

用奇异函数建立x=0与x=a两对边简支并受面内均布拉(压)力作用、另两边为任意支承、非单一材质的n级阶梯式矩形薄板自由振动和强迫振动的微分方程并求得其通解,用W算子给出振型函数的表达式及常见支承条件下板的频率方程。文中给出的固有频率表达式表明,面内均布拉(压)力对固有频率的数值有影响。此处导出的各种情况下的影响函数,对于求解相应情况下的阶梯式矩形薄板的静力弯曲和稳定性问题,也是适用的。

Differential equations of free/forced vibrations of n-step thin rectangular plates which are simply supported and subjected to in-plane tensile/compressive forces at edges of x = 0 and x = a, are established by using singular functions. Their general solutions are solved. Expression of vibration mode function and frequency equations on usual supports are derived from W operator. Expression of natural frequencies given here indicates that numerical values of natural frequencies will be influenced by uniform-distributed in-plane tensile/compressive forces. Influence functions for various cases derived here may also be used to solve static buckling and steadiness of stepped thin rectangular plates in corresponding circumstances of the former.