| Summary: | 碩士 === 國立成功大學 === 機械工程研究所 === 84 === Based on the Bernoulli-Euler beam theory, the governing
equations and associated boundary conditions for the coupled
bending-bending vibration of nonuniform pretwisted cantilever
beams of rectangular cross-section are derived. The explicit
relations between the two flexural displacements are
established. The two coupled differential equations are
decoupled into two complete integral-differential equations
expressed in two flexural displacements, respectively. While
taking the limiting studies for the beam without pretwisting,
the integral-differential equation is reduced to a fourth-order
differential equation. Finally, we can get the closed-form
solutions of the governing equations through the decoupled
differential equations and boundary conditions. The frequency
equation is expressed in terms of the eight fundamental
solutions of the system. Finally, a semi-exact solution method
is used to find natural frequencies of the system.
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