The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method

Abstract A Rayleigh-Ritz approach for the study of the free vibration of systems comprised of rectangular plates is presented. The choice of the deflection functions for the component plates is simplified through the use of the concept of artificial springs being introduced at the joints between the plates and at the system boundaries; the shape functions for each component are thus those for a fully free plate. The necessary continuity and boundary conditions are enforced through allowing the appropriate spring stiffnesses to become very high compared with the stiffness of the components or, if flexible joints exist, the stiffnesses of the connecting springs are taken to be their true value. The applicability and the accuracy of the approach are illustrated through the consideration of three different types of systems: a stepped thickness plate, plates with slits (which approximate cracks) and box-type structures.

[1]  G. B. Warburton,et al.  Comment on: Vibration of stepped thickness plates: By I. Chopra, Int. J. Mech. Sci.16, 337 (1974) , 1975 .

[2]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[3]  D. J. Gorman.  A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-Distributed Uniform Elastic Edge Supports , 1989 .

[4]  S. M. Dickinson,et al.  On the use of simply supported plate functions in the Rayleigh-Ritz method applied to the flexural vibration of rectangular plates , 1978 .

[5]  S. L. Edney,et al.  Vibrations of rectangular plates with elastically restrained edges , 1984 .

[6]  S. M. Dickinson,et al.  On the use of artificial springs in the study of the free vibrations of systems comprised of straight and curved beams , 1992 .

[7]  R. E. Rossi,et al.  Free vibrations of rectangular plates elastically restrained against rotation and translation simultaneously at the four edges , 1978 .

[8]  D Young,et al.  Vibration of rectangular plates by the Ritz method , 1950 .

[9]  M. Mukhopadhyay.  Vibration and buckling of rectangular plates with varying degrees of rotational restraint along the edges , 1989 .

[10]  T. E. Carmichael,et al.  THE VIBRATION OF A RECTANGULAR PLATE WITH EDGES ELASTICALLY RESTRAINED AGAINST ROTATION , 1959 .

[11]  Inderjit Chopra,et al.  Vibration of stepped thickness plates , 1974 .

[12]  G. B. Warburton,et al.  Vibration of Box-Type Structures: , 1967 .

[13]  S. M. Dickinson,et al.  On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates , 1986 .

[14]  Hideya Yamaguchi.  Vibrations of a polygonal plate having orthogonal straight edges by an extended rayleigh-ritz method , 1985 .

[15]  S. M. Dickinson,et al.  On the flexural vibration of rectangular plates approached by using simple polynomials in the Rayleigh-Ritz method , 1990 .

[16]  P.A.A. Laura,et al.  On the effect of different edge flexibility coefficients on transverse vibrations of thin, rectangular plates , 1978 .

[17]  P.A.A. Laura,et al.  Vibrations of rectangular plates elastically restrained against rotation along all edges and subjected to a bi-axial state of stress , 1974 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  Koichi Maruyama,et al.  Experimental Study of Free Vibration of Clamped Rectangular Plates with Straight Narrow Slits , 1989 .

[20]  M. Mukhopadhyay,et al.  Free vibration of rectangular plates with edges having different degrees of rotational restraint , 1979 .

[21]  W. Ritz,et al.  Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern , 1909 .

[22]  L. Keer,et al.  Vibration and stability of cracked rectangular plates , 1972 .

[23]  S. M. Dickinson.  Vibration of Box-Type Structures with Flexible Joints between Constituent Plates , 1968 .