摘要
为了求解悬臂矩形薄板振动问题的精确解,利用二维有限积分变换的方法将高阶偏微分方程问题转化为易于求解的线性代数问题,推导出了悬臂矩形薄板固有频率和振型的精确解,该方法不仅概念清晰、计算简便,而且较传统叠加法、傅立叶级数法等解析方法计算量有了明显减少。由于在求解过程中不需要预先人为选取挠度函数,而是直接从弹性薄板的基本方程出发,仅利用有限域积分变换的数学方法推导出完全满足边界条件的精确解,使得问题的求解更加直接、简便,所得到的解析解更加合理、数值解更加精确。最后,通过计算实例验证了本文所采用方法合理性和公式推导的正确性。
The double finite integral transform method was used to obtain accurate vibration theoretical solution of rectangular thin cantilever plate.Compared with the superposition method and the Fourier series method,the approach used in this paper is concise in form and calculation.It is not need prior to select the deformation function arbitrarily due to the basic elasticity equations of the thin Cantilever plate were only used,therefore,the solution method is reasonable,and theoretical and the numerical solution is accurate.In order to prove the correction of formulation,the numerical results are compared with that in the other references.
出处
《土木工程与管理学报》
2012年第4期6-10,共5页
Journal of Civil Engineering and Management
关键词
悬臂矩形薄板
固有频率
振动分析
有限积分变换
thin cantilever plate
natural frequency
vibration analytical
finite integral transform
