Development of a finite dynamic element for free vibration analysis of two-dimensional structures

1978 ◽  
Vol 12 (8) ◽  
pp. 1311-1327 ◽  
Author(s):  
K. K. Gupta
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Two Dimensional ◽  
Dynamic Element

scholarly journals Free Vibration Analysis of a Thin-Walled Beam with Shear Sensitive Material

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
K. B. Bozdogan ◽  
D. Ozturk
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Torsional Motion ◽  
Transfer Matrices ◽  
Sensitive Material ◽  
Planar Shear ◽  
Thin Walled ◽  
Element Transfer ◽  
Dynamic Element

This paper presents a method for a free vibration analysis of a thin-walled beam of doubly asymmetric cross section filled with shear sensitive material. In the study, first of all, a dynamic transfer matrix method was obtained for planar shear flexure and torsional motion. Then, uncoupled angular frequencies were obtained by using dynamic element transfer matrices and boundary conditions. Coupled frequencies were obtained by the well-known two-dimensional approaches. At the end of the study, a sample taken from the literature was solved, and the results were evaluated in order to test the convenience of the method.

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

2012 ◽  
Vol 226 (12) ◽  
pp. 2860-2873 ◽  
Author(s):  
AR Setoodeh ◽  
M Ghorbanzadeh ◽  
P Malekzadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Thermal Environment ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

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