Based on the research results of Plate-Beam theory and Saint-Venant torsion theory,the longitudinal displacement was assumed to be an expression containing a coefficient to be determined,and the total strain en-ergy equation of rectangular section rod of functionally graded materials was derived by geometrical equations.The coefficient to be determined was confirmed by using the principle of minimum strain energy,and the theoret-ical formula of free torsional stiffness was obtained.On this basis,the kinetic energy of the free vibration of the rectangular section rod was investigated when a pure torsional mode occurred.The kinetic energy expression,the expression of the total potential energy and the frequency expression were derived for the torsional vibration un-der the clamped support condition.The finite element software ANSYS was used to establish the finite element model of the torsional vibration of the rectangular section rod with functionally graded materials properties,and the vibration frequency corresponding to the boundary conditions was viewed through the post-processing com-mand.The verification by finite element software shows that the theoretical solution derived based on Plate-Beam theory agrees well with the finite element solution,and that the maximum error is within 4％.
关键词
功能梯度/矩形截面杆/扭转振动/板-梁理论/有限元
Key words
functional gradient/rectangular section rod/torsional vibration/Plate-Beam theory/finite element
维普
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