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Title:	Vibration and buckling of elastic plates with shear and rotatory inertia
Author:	Batiwalla, Bomi
View Online:	njit-etd1972-011 (xvii, 145 pages ~ 2.9 MB pdf)
Department:	Department of Mechanical Engineering
Degree:	Doctor of Engineering Science
Program:	Mechanical Engineering
Document Type:	Dissertation
Advisory Committee:	Sun, Benedict C. (Committee chair) Herman, Harry (Committee member) Martin, James L. (Committee member) Fox, P. A. (Committee member) Wilson, Charles E. (Committee member)
Date:	1972-05
Keywords:	Shear (Mechanics) Inertia (Mechanics)
Availability:	Unrestricted
Abstract:	The effects of shear, rotatory inertia and inplane forces on the transverse vibration of thin plates are studied. In addition, the effect of shear on the buckling of thin plates is examined. A general differential equation of motion is derived for an isotropic thin plate subjected to normal and inplane forces with the consideration of shear and rotatory inertia. The method of internal constraints and Hamilton's principle are utilized. The resulting fourth order differential equation is solved for simply supported plates of various shapes by employing a finite difference technique. The shapes examined are a square, a circle, a circular annulus, and an elliptic annulus. The differential equation is written in its finite difference form and finally as a matrix. The value of the matrix is determined using the lower and upper decomposition method. The first few natural frequencies and the critical buckling loads are obtained using an iterative technique. The numerical results for the several shapes examined show that the inclusion of shear, rotatory inertia, and inplane forces result in substantially lower natural frequencies. The inclusion of shear effect in the buckling analysis also results in significantly lowering the critical buckling load. As a check on the numerical technique employed in the study, natural frequencies and critical buckling loads neglecting the effects of shear and rotatory inertia were also determined. Excellent agreement between these numerical results and analytical data obtained from classical theories is obtained.