THE FUNDAMENTAL FREQUENCY OF TRANSVERSE VIBRATIONS OF RECTANGULARLY ORTHOTROPIC, CIRCULAR, ANNULAR PLATES WITH SEVERAL COMBINATIONS OF BOUNDARY CONDITIONS

1998 ◽  
Vol 216 (3) ◽  
pp. 543-551 ◽  
Author(s):  
D.V. Bambill ◽  
P.A.A. Laura ◽  
R.E. Rossi
Keyword(s):  
Boundary Conditions ◽  
Fundamental Frequency ◽  
Annular Plates ◽  
Transverse Vibrations

TRANSVERSE VIBRATIONS OF CIRCULAR, ANNULAR PLATES WITH SEVERAL COMBINATIONS OF BOUNDARY CONDITIONS

1998 ◽  
Vol 213 (4) ◽  
pp. 757-762 ◽  
Author(s):  
S.A. Vera ◽  
M.D. Sánchez ◽  
P.A.A. Laura ◽  
D.A. Vega
Keyword(s):  
Boundary Conditions ◽  
Annular Plates ◽  
Transverse Vibrations

Natural Frequencies of Transversely Vibrating Uniform Annular Plates

1965 ◽  
Vol 32 (4) ◽  
pp. 926-931 ◽  
Author(s):  
S. M. Vogel ◽  
D. W. Skinner
Keyword(s):  
Experimental Investigation ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Resonant Frequencies ◽  
Annular Plates ◽  
Transverse Vibrations ◽  
Predicted Values

Frequency determinants are derived for various combinations of boundary conditions associated with the transverse vibrations of uniform annular plates. From these equations, the values of the resonant frequencies of the various normal modes are calculated. Graphs and selected tables are included to facilitate the use of this material for design purposes. The results of an experimental investigation of two of the cases are also presented, and the agreement between these findings and the theoretically predicted values is remarkably good.

The Transverse Vibration of a Doubly Tapered Beam

1977 ◽  
Vol 44 (1) ◽  
pp. 123-126 ◽  
Author(s):  
D. O. Banks ◽  
G. J. Kurowski
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Eigenvalues And Eigenfunctions ◽  
Free Boundary Conditions ◽  
Tapered Beam ◽  
Transverse Vibrations ◽  
The Cross ◽  
Homogeneous Beam

We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form D(x)={(x,y,z)|x∈[0,1],y=xαy1,z=xβz1,(y1,z1)∈D1} where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.

scholarly journals In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianjie Shi ◽  
Dongyan Shi ◽  
Zhengrong Qin ◽  
Qingshan Wang
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Arbitrary Boundary ◽  
Different Boundary Conditions ◽  
Plane Vibration ◽  
Arbitrary Boundary Conditions ◽  
Annular Plates ◽  
Generalized Fourier Series

In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

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