scholarly journals Free Vibrations of Thick Plates with Concentrated Masses on In-homogeneous Pasternak Foundation

2003 ◽  
Vol 13 (4) ◽  
pp. 281-289
Keyword(s):  
Free Vibrations ◽  
Pasternak Foundation ◽  
Thick Plates ◽  
Concentrated Masses

scholarly journals Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Liu ◽  
Fanming Liu ◽  
Xin Jing ◽  
Zhenpeng Wang ◽  
Linlin Xia
Keyword(s):  
Boundary Conditions ◽  
Admissible Function ◽  
Three Dimensional ◽  
Future Research ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Thick Plates ◽  
Arbitrary Boundary Conditions ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

Free Vibrations of Timoshenko Beams Carrying Elastically Mounted, Concentrated Masses

1993 ◽  
Vol 165 (2) ◽  
pp. 209-223 ◽  
Author(s):  
R.E. Rossi ◽  
P.A.A. Laura ◽  
D.R. Avalos ◽  
H. Larrondo
Keyword(s):  
Free Vibrations ◽  
Timoshenko Beams ◽  
Concentrated Masses

ANALYTICAL APPROXIMATE SOLUTIONS TO LARGE-AMPLITUDE FREE VIBRATIONS OF UNIFORM BEAMS ON PASTERNAK FOUNDATION

2014 ◽  
Vol 06 (06) ◽  
pp. 1450075 ◽  
Author(s):  
YONGPING YU ◽  
BAISHENG WU
Keyword(s):  
Large Amplitude ◽  
Approximate Solutions ◽  
Free Vibrations ◽  
Integration Scheme ◽  
Nonlinear Frequency ◽  
Pasternak Foundation ◽  
Analytical Approximations ◽  
Numerical Integration Scheme ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

This paper is concerned with the large-amplitude vibration behavior of simply supported and clamped uniform beams, with axially immovable ends, on Pasternak foundation. The combination of Newton's method and harmonic balance one is used to deal with these vibrations. Explicit and brief analytical approximations to nonlinear frequency and periodic solution of the beams for various values of the two stiffness parameters of the Pasternak foundation, small as well as large amplitudes of oscillation are presented. The analytical approximate results show excellent agreement with those from numerical integration scheme. Due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large-amplitude vibration response of the beams.

Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

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