Free Vibration Analysis of Moderately Thick Rectangular Plates on Pasternak Foundation with Point Supports and Elastically Restrained Edges by Using the Rayleigh–Ritz Method

2016 ◽  
Vol 16 (6) ◽  
pp. 1006-1023 ◽  
Author(s):  
Ahmad Rahbar-Ranji ◽  
Arash Shahbaztabar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Pasternak Foundation ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

Free vibration analysis of laminated composite plates with elastically restrained edges using FEM

2013 ◽  
Vol 3 (2) ◽  
Author(s):  
Avadesh Sharma ◽  
N. Mittal
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Laminated Plates ◽  
Laminated Composite Plates ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

AbstractThe application of FEM is shown for free vibration analysis of moderately thick laminated composite plates with edges elastically restrained against translation and rotation. The governing equations employed are based on the first order shear deformation theory including the effects of rotary inertia. Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Angle-ply and cross-ply laminates with different thickness-to-length ratios are examined. Comparisons are made with results for thin as well as moderately thick laminated plates.

scholarly journals Free vibration analysis on axially graded beam resting on variable Pasternak foundation

2021 ◽  
Vol 1206 (1) ◽  
pp. 012016
Author(s):  
Saurabh Kumar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Material Gradation ◽  
Euler Bernoulli Beam

Abstract Free vibration analysis is conducted on axially functionally graded Euler-Bernoulli beam resting on variable Pasternak foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying linearly along the axial direction. Two types of boundary conditions namely; clamped and simply supported are used in the analysis. The problem is formulated using Rayleigh-Ritz method and governing equations are derived with the help of Hamilton’s principle. The numerical results are generated for different material gradation parameter, foundation parameter and boundary conditions and the effect of these parameters on the free vibration behaviour of the beam is discussed.

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