Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness

Li Long-yuan

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Article Navigation > Applied Mathematics and Mechanics > 1986 > 7(7): 655-662

Li Long-yuan. Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness[J]. Applied Mathematics and Mechanics, 1986, 7(7): 655-662.

Citation:

Li Long-yuan. Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness[J]. Applied Mathematics and Mechanics, 1986, 7(7): 655-662.

Citation:

Li Long-yuan. Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness[J]. Applied Mathematics and Mechanics, 1986, 7(7): 655-662.

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Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness

Li Long-yuan

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

Received Date: 1985-09-06
Publish Date: 1986-07-15

Abstract

Abstract

In this paper, the flexural vibration analysis of moderate-thick rectangular plates with slowly varying thickness using perturbation method is described, and the explict expressions of free vibration frequencies for arbitrary thickness functions are derived. Finally, several numerical examples have been given and comparisons have been made with other proposed solution techniques. This comparison shows that the method yields very good results, so that this method may be regarded as an alternative effective method for the vibration and buckling analysis of plates and shells.

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References(16)

References

[1]	钱伟长,《奇异摄动理论》,清华大学讲义(1980).
[2]	Mindlin.R.D.,Influence of rotary inertia and shear on flexural motions of isotropic,elastic plates.J.Appl.Mech.,18(1951),31-38.
[3]	Burton,T.D.,A perturbation method for certain non-liner oscillators,Int.J.Non-linear Mech.,19(1984).397-407.
[4]	Ha1e,J.K.,Periodic solutions of a class of hyperbolic equations containing a small parameter,Arch.Rat.Mech.Anal.23(1967),380-398.
[5]	Roufaeil,O.L.and D.J.Dawe,Vibration analysis of rectangular mindlin plates by the finite strip method,Comput.Structures.12(1980),833-842.
[6]	Mindlin,R.D.,A.Shacknow and H.Deresiewics.Flexural vibrations of rectangular plates,J.Appl.Mech.,23(1956),431-436.
[7]	Srinivas,S.and A.K.Rao,Bending,vibration and buckling of simply supported thick orthotropic rectangular plates and laminates,Int.J.Solids Structures,6(1970),1463-1481.
[8]	Dawe,D.J.,and O.L.Roufaeil,Rayleigh-Ritz vibration analysis of Mindlin plates,J.Sound Vib.,69(1980),345-359.
[9]	Greimann,L.F.and P.P.Lynn.Finite element analysis of plate bending with transverse shear deformation,Nucl.Engng.Des.14(1970),223-230.
[10]	Rock,T.A.and H.Hinton,Free vibration and transient response of thick and thin plates using the finite element method,Earthquake Engng.Struct.Dyn,3(1974),57-63.
[11]	Hinton E.and N.Bicanic,A Comparison of Lagrangian and serendipity Mindlin plate elements for free vibration analysis,Comput.Structures,10(1979),483-493.
[12]	Dawe,D.J.Finite strip models for vibration of Mindlin plates,J.Sound Vib.,59(1978),441-452.
[13]	Benson,P.R.and E.Hinton,A thick finite strip solution for static,free vibration and stability problems.Int.J.Num.Mech.Engng,10(1976),665-678.
[14]	Timoshenko,S.P.,On the correction for shear of the differential equation for transverse vibration of prismatic bars,Philosph.Mag.,41(1921),288-286.
[15]	Takashi Mikami and Jin Yoshimura,Application of the collocation method to vibration analysis of rectangular Mindlin plates.Comput.Structures,18(1984),425-431.
[16]	Apple,F.C.and N.R.Byers,Fundamental frequency of simply supported rectangular plates with linearly varying thickness,J.Appl.Mech.,31(1965),163-168.