On the Transverse Vibrations of Rectangular Orthotropic Plates

1958 ◽  
Vol 25 (3) ◽  
pp. 389-395
Author(s):  
N. J. Huffington ◽  
W. H. Hoppmann
Keyword(s):  
Boundary Value Problems ◽  
Orthotropic Material ◽  
Boundary Value ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Energy Functions ◽  
Transverse Vibrations ◽  
Flexural Vibrations ◽  
Kinetic And Potential Energies

Abstract Frequency equations and modal eigenfunctions have been determined for the flexural vibrations of rectangular plates of orthotropic material, for those cases which may be treated by the method of M. Lévy (1). In addition, for a broader class of boundary-value problems, an orthogonality criterion for the eigenfunctions has been established and relations for the kinetic and potential energies derived. The value of these energy functions in dealing with forced vibrations is demonstrated.

scholarly journals Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators

1995 ◽  
Vol 18 (4) ◽  
pp. 789-797 ◽  
Author(s):  
T. Gnana Bhaskar ◽  
M. Venkatesulu
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Transverse Vibrations ◽  
Ordinary Differential Operators ◽  
Acoustic Waveguides

An algorithm for the computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators is presented and two examples from the studies of acoustic waveguides in ocean and transverse vibrations in nonhomogeneous strings are discussed.

Transverse Vibrations of Clamped Rectangular Plates of Generalized Orthotropy Subjected To In-Plane Forces

1980 ◽  
Vol 102 (2) ◽  
pp. 399-404 ◽  
Author(s):  
P. A. A. Laura ◽  
L. E. Luisoni
Keyword(s):  
Exact Solution ◽  
Variational Method ◽  
Forced Vibrations ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Structural Element ◽  
Transverse Vibrations ◽  
Free And Forced Vibrations ◽  
Title Problem ◽  
Algorithmic Procedure

An exact solution of the title problem is probably out of the question. It is shown in the present study that a very simple solution can be obtained using simple polynomials and a variational method. Free and forced vibrations of the structural element are analyzed in a unified manner. The algorithmic procedure can be implemented in a microcomputer. The problem is of particular interest in certain filamentary plates as well as of obliquely stiffened plates.

Exact Solutions for Transverse Vibrations of Beams and Plates of Parabolic Thickness Variation

2004 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Thickness Variation ◽  
Singular Problems ◽  
Free Boundary Conditions ◽  
Transverse Vibrations

This paper presents the class of nonuniform beams and nonuniform axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations, respectively, have been identified to be eigenvalue singular problems of orthogonal polynomials. Recent published results regarding a fourth order differential equation and eigenvalue singular problem of classical orthogonal polynomials allowed this study, which extends the class of nonuniform beams and circular nonuniform plates having exact solutions for the problem of free transverse vibrations. The geometry of the elements belonging to the class presented in this paper consists of beams convex parabolic thickness variation and polynomial width variation with the axial coordinate, and plates of convex parabolic thickness variation with the radius. Two boundary value problems of transverse vibrations of beams are reported: 1) complete beam (sharp at either end) with free-free boundary conditions, and 2) half-beam, i.e. a half of the symmetric complete beam, with the large end hinged and sharp end free. The boundary value problem of circular complete plate (zero thickness at zero and outer radii) with free-free boundary conditions has been also reported. For all these boundary value problems the exact mode shapes were Jacobi polynomials and the exact dimensionless natural frequencies were found from the eigenvalues of the eigenvalue singular problems of orthogonal polynomials.

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