| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 86 ===
An analytical method is submitted for solving the forced in-plane and out-of-plane vibration problem of non-uniform circular beams with typical boundary conditions. To enable in-plane and out-of-plane vibrations to be independent mutually, it must be assumed that (1) no warping effect (2) the dimensions of the cross-section are small in comparison with the radius (3) double symmetric cross-section. Besides, the shear effect is also neglected here for simplification. Therefore, external forces only pass through the shear center (also neutral axis) of the cross-section the four decoupled sixth order governing equations, with arbitrary variation coefficients, about this problem will be exactly derived. then, each frequency equation can be expressed in terms of the six normalized fundamental solutions of the corresponding sixth order governing equation. When the non-uniform circular beam with polynomial varying material constants, cross-sectional area and radiuses of gyration along arc length are conside-red, the fundamental solutions can be exactly set up by utilizing the method of Frobenius.
Then we find out Green's Function for the system, static Dimensionless Deflection Chart of Cantilever Circular beam and dynamic Dimensionless Deflection Chart of Cantilever Circular beam by Method of Variation of Parameters and Green's Function Method to verify each other.
|
|---|
