Abstract
An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.
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Abbreviations
- x,y :
-
Coordinate in the plane of plate
- M x , M y :
-
Bending moments
- M yx :
-
Twisting moments
- E :
-
Young’s modulus
- G :
-
Shear modulus
- ν :
-
Poisson’s ratio
- h :
-
Thickness of plate
- ρ :
-
Mass density per unit length of plate material
- D 1 :
-
Flexural rigidity
- \(\tilde{D}\) :
-
Visco elastic operator
- t :
-
Time
- η :
-
Visco elastic constant
- w(x,y,t):
-
Transverse deflection of plate at point
- a, b :
-
Length and breath of the plate
- α, α 1, α 2 :
-
Temperature constants
- β :
-
Taper constant
- α 3 :
-
Non-homogeneity constant
- τ :
-
Temperature excess above a given reference
- Λ :
-
Logarithmic decrement
- K :
-
Time period
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Gupta, A.K., Kumar, L. Thermal effect on vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness. Meccanica 43, 47–54 (2008). https://doi.org/10.1007/s11012-007-9093-3
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DOI: https://doi.org/10.1007/s11012-007-9093-3