| Summary: | 博士 === 國立中興大學 === 應用數學系 === 92 === The research is focused on dynamic response for a finite multi-span continuous beam. Two different formulations are presented. First, a formulation is using transformation of state vectors, which is defined as displacement, rotation, moment, and shear force at supports. The state vector variation across a support is represented by transformation matrix. This method is easy to relate the state vector of every span by using transformations. There are four unknown variables in the governing equation, which are the components of propagating and non-propagating waves traveling to the left and to the right directions. Imposing the boundary conditions yields the equation for the multi-span beam of which the entire beam’s dynamics is condensed in one selected span. The present method is employed to analyze vibration isolation of a finite multi-span beam. Secondly, a scattering matrix is introduced to describe the transmission and reflection phenomena of which two incident waves from two different directions impinge upon a support or multiple supports. Reflection matrices specify the boundary conditions of the beam. The waves generated at the position of applied force are two outgoing waves, which in turn generate two reflected waves caused by the boundaries. These two reflected waves are derived based on the scatter matrices of the supports and the reflection matrices of the boundaries. The proposed formulation is used to study the dynamic characteristics of a multi-span beam and to develop the associated modal analysis. In both formulations a Singular Value Decomposition (SVD) analysis is applied to the equation to study the dynamics of the beam in terms of the eigenvectors associated with the singular values. Numerical examples are provided to demonstrate the formulation and associated dynamic characteristics as represented by the SVD analysis.
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