Abstract：A method based on improved Fourier series method (IFSM) was proposed to solve free vibration characteristics of rectangular thin plates under arbitrary boundary conditions. The plate vibration displacement function was expressed as a linear combination of 2-D Fourier cosine series and auxiliary series to overcome the defect of vibration displacement function being dis-continuous at boundary using the traditional Fourier series method. A plate’s energy functional was established based on vibration displacement function. Using Hamilton principle, a rectangular thin plate’s natural frequencies and the corresponding displacement function’s coefficients were solved. The calculation results agreed well with those published in literature and using the finite element method to verify the correctness and reliability of the proposed method. Boundary restraint springs’ stiffness values were changed to simulate arbitrary boundary conditions. A lot of calculation results showed that in combination of fixed boundary conditions and elastic ones, dimensionless frequencies of a rectangular thin plate grow with increase in the range of fixed boundary conditions; in combination of simply supported and free boundary conditions and elastic ones, dimensionless frequencies of a rectangular thin plate grow with increase in the range of elastic boundary conditions.
杜圆1，李海超1，庞福振1，缪旭弘1,2. 任意边界条件下矩形板薄板自由振动特性分析[J]. 振动与冲击, 2019, 38(19): 70-76.
DU Yuan1, LI Haichao1, PANG Fuzhen1, MIAO Xuhong1,2. Free vibration characteristics of rectangular thin plates under arbitrary boundary conditions. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(19): 70-76.
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