| Summary: | 碩士 === 國立成功大學 === 系統及船舶機電工程學系碩博士班 === 94 === The purpose of this thesis is to extend the continuous-mass transfer matrix method (CTMM) to determine the natural frequencies and associated mode shapes of the uniform or non-uniform Timoshenko beams carrying any number of point masses, rotary inertias, translational springs and rotational springs with various classical or non-classical boundary conditions. To this end, a continuous Timoshenko beam is subdivided into several beam segments with any two adjacent beam segments connected by a node, and then each kind of concentrated elements is attached to each node. So, it is easy to establish the mathematical model of a uniform or non-uniform Timoshenko beam with various boundary conditions by only adjusting the cross-sectional area and length of each beam segment, and the associated physical quantity for each kind of concentrated elements. Thus, for a free-free beam, one requires only to set each of the stiffness constant of translational springs and rotational springs at its two ends to be equal to zero. In addition, the shear deformation and rotary inertia effects, the natural frequencies and associated mode shapes of the uniform or non-uniform beam carrying various concentrated elements are determined with Euler beam theory and Timoshenko beam theory.
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