| Summary: | 博士 === 中原大學 === 機械工程研究所 === 93 === Abstract
This dissertation investigates the vibration and dynamic stability of a simply supported viscoelastic beam, a sandwich beam with an electrorheological core and a sandwich beam with a magnetorheological core. All of beams subject to an axial harmonic load. The dynamic stability of a viscoelastic beam with a complex elastic modulus that depends on the vibrating frequency, was considered. The governing equation of motion is theoretically derived using Euler-Bernoulli theory. Applying Galerkin’s method to simplify the governing equation of motion into a complex Mathieu equation with frequency-dependent coefficients. Then, the boundaries of region of dynamic stability are determined by coupling the numerical binary search procedure and the complex incremental harmonic balance method, both of which are developed in this dissertation. The effects of beam length and static load parameter factor are discussed. The electrorheological beams and magnetorheological beams were obtained by sandwiching electrorheological material and magnetorheological material between two elastic face plates, respectively. The complex shear modulus of electrorheological material is a function of the applied electric field. The complex shear modulus of magnetorheological material is a function of the applied magnetic field. The theoretical model is developed from Mead & Markus sandwich beam theory. Galerkin’s method is used to simplify the governing equation of motion to the complex Mathieu equation. The complex incremental harmonic balance method is employed to determine the dynamic stability of the sandwich beam with an electrorheological core and the sandwich beam with a magnetorheological core. The influences of the electric field in the case of the sandwich beam with electrorheological core, the magnetic field in the case of the sandwich beam with the magnetorheological core, the core thickness, the beam length and the static load parameter factor on the dynamic stability are addressed. The formulae for natural frequency and loss factor of these simply supported beams can be obtained in Galerkin’s procedure. These vibration characteristics of these beams are also elucidated.
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