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Vibrational Behavior of Tapered Triangular Plate with Clamped Ends under Thermal Condition

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Abstract

In the present study, the effect of thermal gradient on the vibration of different types of triangular plates is discussed. Tapering in triangular plate is assumed bilinear. Variation in temperature of plate material is considered as linear in x-direction. The Rayleigh–Ritz technique is employed to evaluate the first two modes of frequency parameter for different values of thermal gradient, taper parameters and aspect ratios. The author reported frequency for both the modes of vibration for different types of clamped triangular plates, i.e., an isosceles triangular plate, right-angled isosceles triangular plate and scalene triangular plate. All numerical results are presented in tabular form.

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Abbreviations

\(\nu \) :

Poisson ratio of the plate material

\(\rho \) :

Mass density per unit volume of the plate material

h :

Thickness of the plate at \((\xi ,\eta )\)

\(h_{0}\) :

Thickness of the plate at \((\xi ,\eta )\equiv (0,0)\)

t :

Time

w(x, y, t):

Deflection of triangular plate

W(x, y):

Deflection function

T(t):

Time function of triangular plate

\(\omega ^2\) :

Frequency constant

\(\beta _1\) :

Taper parameter in x-direction

\(\beta _2\) :

Taper parameter in y-direction

\(\alpha \) :

Thermal gradient

Y :

Young’s modulus

\(Y_{0}\) :

Young’s modulus at reference temperature

\(\lambda ^2\) :

Frequency parameter

\({\tilde{D}}\) :

Viscoelastic operator

\(D_1\) :

Flexural rigidity

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  1. Department of Mathematics, Statistics and Physics, Punjab Agricultural University, Ludhiana, 141004, Punjab, India

    Narinder Kaur

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  1. Narinder Kaur
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Correspondence to Narinder Kaur.

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Kaur, N. Vibrational Behavior of Tapered Triangular Plate with Clamped Ends under Thermal Condition. J. Inst. Eng. India Ser. C 101, 391–399 (2020). https://doi.org/10.1007/s40032-019-00551-9

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