A semi-analytical approach for vibration analysis of orthotropic thin rectangular plates

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (14) : 13-18.

Miao Wang1, Yong-Qiang Chen2, Zhi-Min Li3

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Abstract

The semi-analytical multi-term Kantorovich method (MTKM) is adopted for vibration analysis of orthotropic thin rectangular plates with two opposite edges both simply- supported, both clamped and one clamped the other simply-supported. Multiple beam characteristic functions are used as trial functions, which can satisfy the boundary conditions on two opposite edges exactly. With the Galerkin integral, the partial differential equation of motion is turned into several ordinary differential equations, which are then rewritten in the form of a space-state equation. By enforcing the boundary conditions on the other two opposite edges, the transcendent frequency equation can be derived and non-dimensional frequencies can be determined. Good agreements are shown between the present results and those from the references. It is revealed that the results from present method are exact for thin plates with two opposite edges both simply-supported. Moreover, the effect of the term number of trail functions on the non-dimensional frequencies under different aspect ratios is also investigated.

Key words

Orthotropic thin rectangular plates / multi-term Kantorovich method / beam characteristic functions / orthogonal conditions / semi-analytical solution /

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Miao Wang1, Yong-Qiang Chen2, Zhi-Min Li3. A semi-analytical approach for vibration analysis of orthotropic thin rectangular plates[J]. Journal of Vibration and Shock, 2016, 35(14): 13-18

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