| Summary: | 碩士 === 崑山科技大學 === 機械工程研究所 === 92 === This paper investigates the active damping vibration control and its stability of a uniform beam with time-dependent elastic boundary conditions, adhered with conjugated sensor and piezoelectric actuator. First the coupled governing equations with their boundary conditions were derived by the Kinetics of a vibrating beam. The characteristics of the Mathematic model and its relationship with the vibrating behaviors were discussed.
Because of the piezoelectric control in the system, the complex variable terms would appear in differential equations. This paper suggested a method, which can transform the differential equations with complex variables into coupled equations by real part and imaginary part. The transformed equations can be expressed by matrix forms. The semi analytical solutions of matrix from the differential equations were derived first, and then the eigenvalue equations of matrix solutions were derived. Furthermore, how the geometric features of piezoelectric actuator, properties of material, conditions of control, and boundary conditions affected the free frequency, mode state, and stability of the system were studied.
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