A new method for analytical solution of inplane free vibration of rectangular orthotropic plates based on the analysis of infinite systems

2016 ◽  
Vol 369 ◽  
pp. 228-245 ◽  
Author(s):  
S.O. Papkov
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
New Method ◽  
Orthotropic Plates ◽  
Infinite Systems

A new method for free vibration and buckling analysis of rectangular orthotropic plates

2015 ◽  
Vol 339 ◽  
pp. 342-358 ◽  
Author(s):  
S.O. Papkov ◽  
J.R. Banerjee
Keyword(s):  
Free Vibration ◽  
Buckling Analysis ◽  
New Method ◽  
Orthotropic Plates

scholarly journals Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders

2017 ◽  
Vol 63 (1) ◽  
pp. 115-132
Author(s):  
Y. Song ◽  
X. Chai
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Synthesis Method ◽  
Variable Separation ◽  
Element Analysis ◽  
Plane Vibration ◽  
Curved Girders

Abstract In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence.

The R-function method for the free vibration analysis of thin orthotropic plates of arbitrary shape

2003 ◽  
Vol 261 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Lidia Kurpa ◽  
Vladimir Rvachev ◽  
Eduard Ventsel
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Arbitrary Shape ◽  
Function Method ◽  
Free Vibration Analysis ◽  
Orthotropic Plates

A new method for free vibration analysis of nanobeams: Introduction of equivalent lattice stiffness method

2019 ◽  
Vol 287 ◽  
pp. 35-42 ◽  
Author(s):  
R.D. Firouz-Abadi ◽  
Fahimeh Mehralian
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
New Method ◽  
Stiffness Method

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

scholarly journals A Discrete Method for Bending and Free Vibration Analysis of Orthotropic Plates with Non-uniform Thickness

2003 ◽  
Vol 6 ◽  
pp. 331-340
Author(s):  
M. Huang ◽  
X.Q. Ma ◽  
T. Sakiyama ◽  
H. Matsuda ◽  
C. Morita
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Uniform Thickness ◽  
Orthotropic Plates ◽  
Discrete Method
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