A NEW ANALYSIS ON FREE VIBRATION OF A RECTANGULAR PLATE WITH FOUR FREE EDGES AND FURE CORNER POINT SUPPORTS

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Journal of Vibration and Shock ›› 2013, Vol. 32 ›› Issue (3) : 83-86.

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A NEW ANALYSIS ON FREE VIBRATION OF A RECTANGULAR PLATE WITH FOUR FREE EDGES AND FURE CORNER POINT SUPPORTS

XU Qi-lou

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Abstract

The vibration mode expression of the rectangular plate with four free edges and four corner point supports is composed of the two parts: the first is the basic intrinsic mode of the plate with four free edges, the second is the addition mode aroused by the four corner forces. The vibration mode function must satisfy the vibration differential equation and the differential relation between the corner force and the bending deflection. For to indicate the bi-directional vibration, the basic mode has the alone expression along the two coordinate axis respectively, which accord with the load-deformation characteristic limited by the relevant edges.The character is the zero shear force and the non-zero amplitude at the relevant free edges and the zero corner forces at the four corners. The addition mode must satisfy the differential relation between the corner force and the bending deflection at the four corner points, and its shear force is zero and the amplitude is not zero at the four free edges. The new method surmounts the theory drawback in original method, and the compute idea is reasonable.

Key words

elastic vibration / rectangular plate / corner point support / basic mode / addition mode

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XU Qi-lou. A NEW ANALYSIS ON FREE VIBRATION OF A RECTANGULAR PLATE WITH FOUR FREE EDGES AND FURE CORNER POINT SUPPORTS[J]. Journal of Vibration and Shock, 2013, 32(3): 83-86