Zhou Ding. Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges[J]. Applied Mathematics and Mechanics, 1989, 10(10): 929-938.
 Citation: Zhou Ding. Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges[J]. Applied Mathematics and Mechanics, 1989, 10(10): 929-938.

# Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges

• Received Date: 1988-08-04
• Publish Date: 1989-10-15
• This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points.The number and location of these points on free edges may be completely arbitrary.This paper uses impulse function to represent reaction and moment at points.Fourter series is used to expand the impulse function along the edges.Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.
•  [1] Cox,H.L.and J.Boxer,Vibration of rectangular plates point-supported at corners,Aeronautical Quaricrly,11(1960). [2] Reed,R.E.,Comparison of methods in calculating frequencies of corner-supported rectangular plates,NASA TN D-3030(1965). [3] Kirk,C.L.,A note on the lowest natural frequency of square plate point-supported at the corners,J.the Royal Aeronautical Society,66(1962). [4] Kerstens,L.G.M.,Vibration of a rectangular plate supported at an arbitrary number of points,J.Sound and Vibration,65(1979). [5] Gorman,D.J.,Free vibration analysis of rectangular plates with symmetrically distributed point supports along the edges,J.Sound and Vibration,73(1980). [6] Gorman,D.J.,An analytical solution for the free vibration analysis of rectangular platess resting on symmetric point supports,J.Sound and Vibration,79(1981). [7] Gorman,D.J.,Vibration of Rectangular Plates,New York,Elsevier North Holland(1982). [8] Bapat,A.V.and N.Venkatramani,A new approach for the representation of a point support in the analysis of plates,J.Sound and Vibration,120(1988). [9] Bapat,A.V.and N.Venkatramani,Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates,J.Sound and Vibration,120(1988).

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沈阳化工大学材料科学与工程学院 沈阳 110142

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