Dynamic responses of Reissner–Mindlin plates with free edges resting on tensionless elastic foundations

Abstract Dynamic response analysis is presented for a Reissner–Mindlin plate with four free edges resting on a tensionless elastic foundation of the Winkler-type and Pasternak-type. The mechanical loads consist of transverse partially distributed impulsive loads and in-plane static edge loads while the temperature field is assumed to exhibit a linear variation through the thickness of the plate. The material properties are assumed to be independent of temperature. The two cases of initially compressed plates and of initially heated plates are considered. The formulations are based on Reissner–Mindlin first-order shear deformation plate theory and include the plate–foundation interaction and thermal effects. A set of admissible functions is developed for the dynamic response analysis of moderately thick plates with four free edges. The Galerkin method, the Gauss–Legendre quadrature procedure and the Runge–Kutta technique are employed in conjunction with this set of admissible functions to determine the deflection-time and bending moment–time curves, as well as shape mode curves. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. The numerical illustrations concern moderately thick plates with four free edges resting on tensionless elastic foundations of the Winkler-type and Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results confirm that the plate will have stronger dynamic behavior than its counterpart when it is supported by a tensionless elastic foundation.

[1]  Jie Yang,et al.  FREE AND FORCED VIBRATION OF REISSNER–MINDLIN PLATES WITH FREE EDGES RESTING ON ELASTIC FOUNDATIONS , 2001 .

[2]  Sekhar K. Chakrabarti,et al.  Shear and attachment effects on the behaviour of rectangular plates resting on tensionless elastic foundation , 1997 .

[3]  Y. Weitsman On the Unbonded Contact Between Plates and an Elastic Half Space , 1969 .

[4]  Surkay D. Akbarov,et al.  On the bending problems of anisotropic (orthotropic) plates resting on elastic foundations that react in compression only , 1997 .

[5]  Sekhar K. Chakrabarti,et al.  Rectangular Plates Resting on Tensionless Elastic Foundation: Some New Results , 1996 .

[6]  Z. Celep,et al.  Circular Plate on Tensionless Winkler Fundation , 1988 .

[7]  Kadir Güler,et al.  Static and dynamic responses of a circular plate on a tensionless elastic foundation , 1995 .

[8]  Hui Li,et al.  Unbonded Contact of a Square Plate on an Elastic Half-Space or a Winkler Foundation , 1988 .

[9]  Hui-Shen Shen,et al.  Postbuckling of free edge Reissner–Mindlin plates elastically supported on a two-parameter foundation and subjected to biaxial compression and transverse loads , 2001 .

[10]  Arnold D. Kerr,et al.  On the derivation of well posed boundary value problems in structural mechanics , 1976 .

[11]  A. A. Khathlan Large‐Deformation Analysis of Plates on Unilateral Elastic Foundation , 1994 .

[12]  Kadir Güler,et al.  Static and dynamic responses of a rigid circular plate on a tensionless Winkler foundation , 2004 .

[13]  Circular Plates Resting on Biomodulus and No-Tension Foundations , 1977 .

[14]  J. R. Xiao Boundary element analysis of unilateral supported Reissner plates on elastic foundations , 2001 .

[15]  Jin-Guang Teng,et al.  Axisymmetric shells and plates on tensionless elastic foundations , 1999 .

[16]  Hui-Shen Shen,et al.  Nonlinear bending behavior of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations , 2004 .

[17]  Kadir Güler Circular Elastic Plate Resting on Tensionless Pasternak Foundation , 2004 .

[18]  Piero Villaggio A Free Boundary Value Problem in Plate Theory , 1983 .

[19]  Z. Celep,et al.  Rectangular Plates Resting on Tensionless Elastic Foundation , 1988 .

[20]  Y. Weitsman,et al.  On Foundations That React in Compression Only , 1970 .

[21]  P. Gonçalves,et al.  Numerical methods for analysis of plates on tensionless elastic foundations , 2001 .

[22]  Z. Celep,et al.  Axisymmetric Vibrations of Circular Plates on Tensionless Elastic Foundations , 1990 .