Vibrations of Stepped One-Way Rectangular Plates
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摘要: 研究非单一材质的n级阶梯式单向矩形板的振动.用奇异函数建立板自由振动和强迫振动的微分方程并用初参数法求得其通解.阶梯梁静力和动力问题的传统解法是分离变量后分阶梯写出常微分方程并分别求解,不胜其烦.运用W算子,只用一个式子便将方程的解表述出来,并给出主振型函数的表达式及常见支承条件下板的频率方程.用广义函数给出板在不同形式载荷作用下的强迫响应.文中所给影响函数,是解决正文所述类型常微分方程的有力工具,亦可用于求解阶梯梁或阶梯式单向矩形板的静力弯曲与稳定性问题.Abstract: Vibrations of non-unitary materials n-step one-way rectangular plates are researched. Differential equations of free/forced vibrations for such plates are established by using singular functions, their general solutions solved with method of initial parameter. The traditional solvent of static and dynamic problems for stepped prismatic beams is to set up ordinary differential equation in each step and answer it respectively. That is so troublesome. With W operator, resolution of the former may be expressed with one equation only, and expression of vibration mode function/frequency equations of plate on usual supports derived. Forced responses of like that plates stated here under different-type loads discussed with generalized functions. Influence functions given here are strong tools to settle ordinary differential equations which described in the text. It can also be to deal with problems of static buckling and steadiness of stepped beams or one-way rectangular plates.
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Key words:
- cascade trays /
- free vibration /
- natural frequency /
- responses
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