缓变厚度中厚板的自由振动

李龙元

缓变厚度中厚板的自由振动

李龙元

上海市应用数学和力学研究所

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出版历程
- 收稿日期: 1985-09-06
- 刊出日期: 1986-07-15

Vibration Analysis of Moderate-Thick Plates with Slowly Varying Thickness

Li Long-yuan

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要

摘要: 本文将中厚板的厚度函数按一小参数展开,并采用奇异摄动方法,把原来变系数的微分方程组化成一系列常系数微分方程组求解.文中给出了任意变厚度中厚板的自振频率计算显式表达式,由此式,我们不仅可以方便地计算出各种变厚度的自振频率值,而且也可以根据频率的要求来优化板的厚度.文中的算例表明,本文的方法具有较好的精度、方法简便、有效等其他优点,可以考虑作为分析各种变厚度板壳的振动及稳定特征问题的有效方法之一.

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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参考文献(16)

[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.