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Vibration of a prestressed orthotropic rectangular thin plate via singular perturbation technique

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Summary

The method of matched asymptotic expansions is used in investigating the vibration of a highly prestressed rectangular thin plate exhibiting natural material orthotropy. When the bending rigidity is small compared to the applied in-plane loading, analytical results which are correct toO(ε2) (where ε2 denotes a normalised bending rigidity) are presented for various boundary conditions including the fully clamped case. To leading order solution in ε, the eigenvalues of an ideal orthotropic membrane are obtained. The first order solutions in ε show the influence of bending stiffness and material orthotropy on the eigenvalue, while torsional rigidity affects the eigenvalues to second order in ε. In particular, Hutter and Olunloyo's results are recovered for the special case of isotropic material properties.

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Abbreviations

M :

mass density per unit area of plate

w :

deflection

x, y :

outer variables

t :

time

X, Y :

inner variables

λ2 :

eigenvalue

φ0 :

outer solution

ψi :

inner solution

D xx :

flexural rigidity inx-direction

D xy :

effective torsional rigidity

D yy :

flexural rigidity iny-direction

L :

characteristic length

T :

characteristic time

N xx :

applied in-plane loading inx-direction

N yy :

applied in-plane loading iny-direction

N 0 :

prestress in a preferred direction

m, n :

wave numbers

References

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Ilorin, Ilorin, Nigeria

    A. A. Oyediran

  2. Department of Mathematics, University of Ilorin, Ilorin, Nigeria

    J. A. Gbadeyan

Authors
  1. A. A. Oyediran
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  2. J. A. Gbadeyan
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Oyediran, A.A., Gbadeyan, J.A. Vibration of a prestressed orthotropic rectangular thin plate via singular perturbation technique. Acta Mechanica 64, 165–178 (1986). https://doi.org/10.1007/BF01450392

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  • DOI: https://doi.org/10.1007/BF01450392

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