Continuous Dynamic Model for Tapered Beam‐Like Structures

Abstract

Distributed parameter modeling may offer a viable alternative to the finite‐element approach for modeling large flexible space structures. In addition, the introduction of the transfer matrix method to the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to more complex configurations. This paper proposes a piecewise continuous Timoshenko beam model, which was used for the dynamic analysis of a tapered beam‐like structure. Instead of the arbitrarily assumed shape functions used in a finite‐element analysis, the closed‐form solution of the Timoshenko beam equation was used. Application of the transfer matrix method was used to relate all elements as a whole. Using the corresponding boundary conditions and compatibility equations, a characteristic equation for the global tapered beam was produced and natural frequencies derived. The results from this analysis were compared to those obtained from a conventional finite‐element analysis. While comparable results are obtained, the piecewise continuous Timoshenko beam model significantly decreased the number of modal elements required.