Vibration of plate on foundation with four edges free by finite cosine integral transform method

Abstract

The analytical solutions for the natural frequencies and mode shapes of the rectangular plate on foundation with four edges free is presented by using the finite cosine integral transform method. In the analysis procedure, the classical Kirchhoff rectangular plate is considered and the foundation is modelled as the Winkler elastic foundation. Because only are the basic dynamic elasticity equations of the thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.

Flexural analysis of rectangular kirchhoff plate on winkler foundation using galerkin-vlasov variational method

“…Some conventions adopt a negative sign for the bending and twisting moments given by Equations (17), (19) and (20).…”

“…Other researchers who have worked on the plate on elastic foundation problem are: Althobaiti and Prikazchikov [18]; Zhong, Zhao and Hu [19]; Li, Zhong and Li [20]; Li, Zhong and Tian [21]; Li et al [22]; Zhang, Shi and Wang [23]; Agarana, Gbadeyan and Ajayi [24]; Are, Idowu and Gbadeyin [25]; Agarana and Gbadeyin [26]; Tahuoneh and Yas [27]; and Ye et al [28].…”

Ritz Variational Method for the Flexural Analysis of Rectangular Kirchhoff Plate on Winkler Foundation

“…Other researchers who have studied the plate on elastic foundation problem are: Althobaiti and Prikazchikov [16]; Zhong, Zhao and Hu [17]; Li, Zhong and Li [18]; Li, Zhong and Tian [19]; Li et al [20]; Zhang, Shi and Wang [21]; Agarana, Gbadeyan and Ajayi [22]; Are, Idowu and Gbadeyin [23]; Agarana and Gbadeyin [24]; Tahuoneh and Yas [25]; and Ye et al [26].…”

Solution of free harmonic vibration equation of simply supported Kirchhoff plate by Galerkin-Vlasov method

“…Some of the approximate methods used in dynamic plate problems are Raleigh Method, Raleigh -Ritz Method, Finite Element Method, Finite Difference Method and Variational Methods of Galerkin [15] and modifications by Kantorovich and Bubnov [5,6,14]. Another method is the integral transform methods [16].…”