Analysis for an N-stepped Rayleigh bar with sections of complex geometry

作者：Fedotov Igor; Gai Ying^*; Polyanin Andrei; Shatalov Michael

来源：Applied Mathematical Modelling, 2008, 32(1): 1-11.

DOI：10.1016/j.apm.2006.10.028

• Rayleigh bar
• green function
• lagrangian
• eigenfunctions
• eigenvalues
• orthogonality

In this paper we analyse the vibrations of an N-stepped Rayleigh bar with sections of complex geometry, supported by end lumped masses and springs. Equations of motion and boundary conditions are derived from the Hamilton's variational principal. The solutions for tapered and exponential sections are given. Two types of orthogonality for the eigen-functions are obtained. The analytic solution to the N-stepped Rayleigh model is constructed in terms of Green function.

• 出版日期2008-1