Vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation

Abstract The fundamental natural frequencies and buckling loads of a rectangular plate with nonlinearly rotational restraints are obtained by using the finite element technique. If the rotational springs are unsymmetric the iterative scheme must be employed to acquire the solutions of the nonlinear problem. The values which describe the free vibration and stability behaviour of the plate will increase when either the parameters of rotational spring or the initial rotational angles increase. Incidentally, it can be concluded that these results grown nonlinearly with respect to either the linear or nonlinear rotational spring constants. Finally, both the frequency and stability parameters are evaluated for several boundary conditions which are quite useful in engineering analysis and design.

[1]  G. Venkateswara Rao,et al.  Free Vibration And Stability Behaviour Of Uniform Beams And Columns With Non-linear Elastic End Rotational Restraints , 1994 .

[2]  D. Evensen.  Nonlinear vibrations of beams with various boundary conditions. , 1968 .

[3]  R. E. Rossi,et al.  Fundamental frequency of vibration of a Timoshenko beam of non-uniform thickness , 1991 .

[4]  M. A. Dokainish,et al.  Experimental and theoretical analysis of the transverse vibrations of a beam having bilinear support , 1971 .

[5]  W. H. Liu,et al.  Non-linear vibrations of beams with elastically restrained edges , 1988 .

[6]  Gangan Prathap,et al.  Galerkin finite element method for non-linear beam vibrations , 1980 .

[7]  R. E. Rossi,et al.  Free vibrations of uniform Timoshenko beams with ends elastically restrained against rotation and translation , 1990 .

[8]  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 .

[9]  R. E. Rossi,et al.  Natural frequencies of a timoshenko beam of non-uniform cross-section elastically restrained at one end and guided at the other , 1990 .

[10]  A. Picard,et al.  Rotational restraint of a simple column base connection , 1987 .

[11]  Sen-Yung Lee,et al.  Free vibrations of a non-uniform beam with general elastically restrained boundary conditions , 1990 .

[12]  T. K. Varadan,et al.  Lagrange-type formulation for finite element analysis of non-linear beam vibrations , 1983 .

[13]  M. J. Maurizi,et al.  General equation of frequencies for vibrating uniform one-span beams under compressive axial loads , 1991 .

[14]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

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

[16]  A. V. Srinivasan,et al.  Large amplitude-free oscillations of beams and plates. , 1965 .

[17]  J. Vossoughi,et al.  Transverse and torsional vibrations of an axially-loaded beam with elastically constrained ends , 1984 .

[18]  S. Woinowsky-krieger,et al.  The effect of an axial force on the vibration of hinged bars , 1950 .

[19]  R. White,et al.  The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam , 1984 .