Civil Engineering ETDs

Publication Date

12-16-1971

Abstract

A method is presented to obtain the natural frequencies and related mode shapes of certain types of stiffened plate systems. Dynamic stiffness matrices, based on ordinary assumptions in beam and plate theory, are derived to relate the displacements at the edges of a system element to the edge forces. Both in-plane and transverse forces and displacements are considered. Compatibility and equilibrium conditions at the intersections of plate panels and stiffening elements are employed to derive the governing equations of the system.

For general systems, the result is a set of linear homogeneous algebraic equations which must be solved by trial-and-error. For regular systems, the governing equations may be solved by the methods of the finite calculus to obtain frequency and modal equations. A particular advantage of the method for regular systems is that the number of panels or elements in the system appears only as a parameter. Neither the complexity of the frequency equation nor the number of modal equations is affected by the number of panels in the system. This greatly reduces the necessary numerical work.

A variety of applications, including plates continuous in one direction, plates stiffened by beams and plates stiffened by plates, is discussed. Where possible, results are compared with those from previous studies.

Two appendices are included. The first is an introduction to the field of dynamic discrete mechanics. The second consists of a series of graphs which can be used to determine, approximately, the fundamental frequencies of vibration of one-way continuous plate systems.

Document Type

Dissertation

Language

English

Degree Name

Civil Engineering

Level of Degree

Doctoral

Department Name

Civil Engineering

First Committee Member (Chair)

Illegible

Second Committee Member

Marion Marvin Cottrell

Third Committee Member

John Lawson Brown Jr.

Fourth Committee Member

Illegible

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