The governing differential equations for the in-plane vibrations of curved non-uniform beams subjected to in-plane normal distributed forces are derived by using the Hamilton's principle. It is shown that, for harmonic excitations, the longitudinal displacement parameter and its first and second order derivatives can be explicitly expressed in terms of the flexural displacement parameter and the in-plane normal distributed forces. With these explicit relationships, the two coupled governing equations can be reduced to a complete sixth-order ordinary differential equation with variable coefficients in the flexural displacement. Subsequently, the exact forced response of the beam in power series form is derived. Finally, a limiting study from the curved beam theory to the straight beam theory is successfully revealed.
|Number of pages||8|
|Journal||Journal of the Chinese Society of Mechanical Engineers, Transactions of the Chinese Institute of Engineers, Series C/Chung-Kuo Chi Hsueh Kung Ch'eng Hsuebo Pao|
|Publication status||Published - 2002 Apr|
All Science Journal Classification (ASJC) codes
- Mechanical Engineering