scholarly journals Thermal Effect on Free Vibration of Non-Homogeneous Orthotropic Visco-Elastic Rectangular Plate of Parabolically Varying Thickness

2010 ◽  
Vol 01 (06) ◽  
pp. 456-463 ◽  
Author(s):  
Arun Kumar Gupta ◽  
Pooja Singhal
Keyword(s):  
Free Vibration ◽  
Thermal Effect ◽  
Rectangular Plate ◽  
Varying Thickness ◽  
Elastic Rectangular Plate

scholarly journals Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations

2008 ◽  
Vol 15 (6) ◽  
pp. 713-723 ◽  
Author(s):  
A.K. Gupta ◽  
Anupam Khanna
Keyword(s):  
Rectangular Plate ◽  
Nuclear Reactor ◽  
Ritz Method ◽  
Cartesian Product ◽  
Frequency Equation ◽  
Elastic Behavior ◽  
Thickness Variation ◽  
Engineering Structures ◽  
Varying Thickness ◽  
Elastic Rectangular Plate

Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

scholarly journals Analysis of free vibration of non-homogenous trapezoidal plate with 2D varying thickness and thermal effect

2016 ◽  
Vol 4 (4) ◽  
pp. 201-208 ◽  
Author(s):  
Ashish Kumar Sharma ◽  
Amit Sharma ◽  
A. K. Raghav ◽  
Vijay Kumar
Keyword(s):  
Free Vibration ◽  
Thermal Effect ◽  
Varying Thickness ◽  
Trapezoidal Plate

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

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