Abstract
The objective of the present paper is to analyze coupled bending and torsional vibrations of distributed-parameter beams. The governing coupled set of partial differential equations is solved by separating the dynamic response in a quasistatic and in a complementary dynamic response. The quasistatic portion that may also contain singularities or discontinuities due to sudden load changes is determined in a closed form. The remaining complementary dynamic part is non-singular and can be approximated by a truncated modal series of fast accelerated convergence. The solution of the resulting generalized decoupled single-degree-of-freedom oscillators is given by means of Duhamel's convolution integral, whereby the acceleration of the loads is the driving term. The proposed procedure is illustrated for a dynamically loaded simply supported beam with channel cross-section, and the improvement in comparison to the classical modal analysis is demonstrated.
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