Quasi-Green’s Function Method for Free Vibration of Clamped Thin Plates on Winkler Foundation
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摘要:
将准Green函数方法应用于求解Winkler地基上固支薄板的自由振动问题．即利用问题的基本解和边界方程构造一个准Green函数，这个函数满足了问题的齐次边界条件．采用Green公式，将Winkler地基上固支薄板自由振动问题的振型控制微分方程化为第二类Fredholm积分方程．通过边界方程的适当选择，积分方程核的奇异性被克服了．数值算例表明，该方法具有较高的精度,是一种有效的数学方法．
Abstract:The quasi-Green's function method was employed to solve the free vibration problem of clamped thin plates on Winkler foundation.A quasi-Green's function was established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates on Winkler foundation was reduced to Fredholm integral equations of the second kind by Green formula.Irregularity of the kernel of integral equation was overcome by choosing a suitable form of the normalized boundary equation.Numerical results show high accuracy of the method given by the present paper,and it is an effective mathematical method.
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Key words:
- Green function /
- integral equation /
- clamped thin plates /
- Winkler foundation /
- free vibration
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