欢迎光临《计算力学学报》官方网站!
王春玲,赵鲁珂,王涵,李东波.带裂纹矩形板自由振动解析解
Analytical study of free vibration for cracked rectangular plate[J].计算力学学报,2019,36(6):757~762
带裂纹矩形板自由振动解析解
Analytical study of free vibration for cracked rectangular plate
Analytical study of free vibration for cracked rectangular plate
投稿时间:2018-10-29  修订日期:2018-12-11
DOI:10.7511/jslx20181029001
中文关键词:  带裂纹矩形板  双重正弦级数  协调条件  自由振动  解析研究
英文关键词:cracked rectangular plate  double sine Fourier series  equilibrium condition  free vibration  analytical study
基金项目:国家自然科学基金(51878547)资助项目.
作者单位E-mail
王春玲 西安建筑科技大学 理学院, 西安 710055 wangchunlingjd@sina.com 
赵鲁珂 西安建筑科技大学 理学院, 西安 710055  
王涵 西安建筑科技大学 理学院, 西安 710055  
李东波 西安建筑科技大学 理学院, 西安 710055  
摘要点击次数: 28
全文下载次数: 23
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,所以可使矩形板问题的求解统一化、简单化和规律化。
英文摘要:
      A double sine Fourier series with supplementary functions is adopted to investigate a cracked rectangular plate.It is decomposed into several sub-domains and a simplified function for each sub-domain is derived.For each specific function,the boundary conditions and the physical meanings for constants in the mode functions are considered.The equation system,which contains the governing equations,the remaining boundary conditions,compatibility conditions for shared boundaries and the proposed equilibrium condition for shared free corners in this paper,is converted to a generalized eigenvalue problem to compute the non-dimensional frequencies.An example is calculated and the results in this paper are close to published data,which verifies the correctness of derivaition.Moreover,the validity of the proposed equilibrium condition for shared free corners is proved.The adopted function,whose canstant contain certain physical meanings,could conveniently investigates layered rectangular plates with aribitrary boundary conditions.Therefore,the method in this paper could unify the solution and simplify the approach for the study of rectangular plates.
查看全文  查看/发表评论  下载PDF阅读器
您是第6190874位访问者
版权所有:《计算力学学报》编辑部
本系统由 北京勤云科技发展有限公司设计