Document Type

Thesis

Date of Award

5-31-1984

Degree Name

Master of Science in Mechanical Engineering - (M.S.)

Department

Mechanical Engineering

First Advisor

Calman Pecker

Second Advisor

Aaron Deutschman

Third Advisor

John Vincent Droughton

Abstract

This thesis deals with the vibration of a beam whose flexural and centroidal axis are not coincident. The elementary bending- twisting theory is employed to derive the equations of motion, in which the effects of rotary inertia are added to the bending displacements and the effects of warping are added to the twist. Bending translation is restricted to one direction so that one bending equation is used instead of two. The equations of motion are solved by using the boundary value problem. The exact natural frequencies are found from the frequency equation , which is obtained from the condition that the homogeneous system of algebraic equations representing the spatial solution shall not yield a trivial solution. The orthogonality conditions are established, and the principal mode equations of forced vibration are derived. As an example, a cantilevered beam is chosen and the first five natural frequencies and their modal shapes are found. It is concluded that the first natural frequency is a subharmonic frequency.

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