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带裂纹矩形板自由振动解析解
Analytical study of free vibration for cracked rectangular plate
投稿时间:2018-10-29  修订日期:2018-12-29
DOI:
中文关键词:  带裂纹矩形板  双重正弦级数  自由振动  解析研究
英文关键词:cracked rectangular plate  double sine Fourier series  free vibration  analytical study
基金项目:国家自然科学基金
作者单位E-mail
王春玲 西安建筑科技大学 wangchunlingjd@sina.com 
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中文摘要:
      选取带有补充项的双重正弦傅里叶级数作为振型函数通解来解析研究带裂纹矩形板的自由振动特性。先将带裂纹矩形板分割成若干小矩形板,利用各小矩形板的边界条件,并结合振型函数中待定常数的物理意义,简化得到各小矩形板的振型函数,再结合各板的控制方程、未使用的边界条件、公共边协调条件及本文提出公共自由角点的协调条件,建立求解频率的代数方程组,然后将其转化为广义特征值问题来求解带裂纹矩形板的无量纲频率;最后选取具体参数进行计算并与文献结果对比,吻合良好,证明了本文采用的研究方法以及所提出公共角点协调条件的正确性和合理性。由于该振型函数能满足矩形板的任意边界约束,且其中的待定常数具有明确的物理意义,使得矩形板问题的求解统一化,简单化,规律化。
英文摘要:
      A double sine Fourier series with supplementary terms function is adopted to investigate the cracked rectangular plate. The cracked plate is decomposed into several sub-domains and simplified function for each sub-domain is derived. For each specific function, the boundary conditions and the physical meanings for constants in original function are considered. Equation system, which contains governing equations, remaining boundary conditions, compatibility conditions for public boundary and the proposed equilibrium condition for public free corner in this paper, is converted to generalized eigenvalue problem to compute the non-dimensional frequencies. A sample is calculated and the results in this paper are close to published datas, which verified the correctness of derivition. Moreover, the validity of the proposed equilibrium condition for public free corner is proved. The adopted function, whose canstants contains certain physical meanings, could conveniently investigates layered rectangular plate with aribitrary boundary condition. Therefore, the method in this paper could unify the solution and simplify the approach for the study of rectangular plate.
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