A GENERAL APPROXIMATE SOLUTION OF THE PROBLEM OF FREE VIBRATIONS OF ANNULAR PLATES OF STEPPED THICKNESS

1996 ◽  
Vol 196 (3) ◽  
pp. 275-283 ◽  
Author(s):  
D.R. Avalos ◽  
H.A. Larrondo ◽  
V. Sonzogni ◽  
P.A.A. Laura
Keyword(s):  
Approximate Solution ◽  
Free Vibrations ◽  
Annular Plates

FREE VIBRATIONS OF ANNULAR PLATES COUPLED WITH FLUIDS

1996 ◽  
Vol 191 (5) ◽  
pp. 825-846 ◽  
Author(s):  
M. Amabili ◽  
G. Frosali ◽  
M.K. Kwak
Keyword(s):  
Free Vibrations ◽  
Annular Plates

Forced Vibration of Systems With Nonlinear, Nonsymmetrical Characteristics

1957 ◽  
Vol 24 (3) ◽  
pp. 435-439
Author(s):  
S. Mahalingam
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Free Vibrations ◽  
Frequency Function ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Vibration Absorber ◽  
Single Degree

Abstract A one-term approximate solution is given for the amplitudes of steady forced vibration of a single-degree-of-freedom system with a nonlinear (nonsymmetrical) spring characteristic. The method is similar to that of Martienssen (1), but the construction uses a modified curve (or “frequency function”) in place of the actual spring characteristic, the curve being so chosen that it gives the correct frequency for free vibrations. The method is extended to deal with a nonlinear vibration absorber fitted to a linear system.

Free vibrations of annular plates of variable thickness

1980 ◽  
Vol 12 (4) ◽  
pp. 508-512
Author(s):  
A. D. Lizarev ◽  
V. P. Kuz'mentsov
Keyword(s):  
Variable Thickness ◽  
Free Vibrations ◽  
Annular Plates ◽  
Plates Of Variable Thickness

Approximate solution for free vibrations of thin orthotropic rectangular plates

2005 ◽  
Vol 288 (1-2) ◽  
pp. 321-344 ◽  
Author(s):  
M.E. Biancolini ◽  
C. Brutti ◽  
L. Reccia
Keyword(s):  
Approximate Solution ◽  
Free Vibrations ◽  
Rectangular Plates

Integral Equation Method for Free Vibration of Annular Plates with Elastic Supports

2011 ◽  
Vol 52-54 ◽  
pp. 573-577
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Quan Cheng
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Infinite Order ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Orthogonal Functions ◽  
Elastic Supports ◽  
Annular Plates

Annular plates are commonly found in the fields of engineering. The present study is concerned with the integral equation method for the free vibrations of annular plates with elastic supports. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first and the second kind is used to construct the Green's function of annular plates. The eigenvalue problem of free vibration of annular plates with Elastic Supports is transformed into the eigenvalue problem of integral equation. And then, the problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical example shows the significant advantages of the present method.

Dynamic Modelling of Annular Plates of Functionally Graded Structure Resting on Elastic Heterogeneous Foundation with Two Modules

2015 ◽  
Vol 31 (5) ◽  
pp. 493-504 ◽  
Author(s):  
A. Wirowski ◽  
B. Michalak ◽  
M. Gajdzicki
Keyword(s):  
Mathematical Model ◽  
Dynamic Behaviour ◽  
Effective Properties ◽  
Plate Thickness ◽  
Dynamic Modelling ◽  
Composite Plates ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Annular Plates ◽  
Heterogeneous Foundation

AbstractThe contribution is devoted to formulate an averaged mathematical model describing the dynamic behaviour of the composite annular plates resting on elastic heterogeneous foundation with two foundation modules. The plates are made of two-phased, functionally graded — type composites. In contrast to most of the papers in which material properties vary through the plate thickness, in the presented study we have dealt with the plate and foundation in which effective properties vary in a radial direction of the plate. The formulation of the macroscopic mathematical model for the analysis of the dynamic behaviour of these plates will be based on the tolerance averaging technique (Woźniak, Michalak, Jędrysiak, [ed]). This averaging method is an alternative to known asymptotic homogenization. The general results of the contribution will be illustrated by the analysis of free vibrations of the composite plates on heterogeneous foundation. The results obtained from the tolerance model were compared with the results obtained from FEM. There were compared the first four natural frequencies. A good consistency of the results from both methods was obtained.

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