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General analytic solution of dynamic response of beams with nonhomogeneity and variable cross-section. (English) Zbl 0779.73026

The authors introduce a step-reduction method to investigate the dynamic response of Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free and forced vibrations are studied. The method requires the space domain to be discretized into a finite number of elements. Each element is treated as a homogeneous body with uniform thickness. Hence, a general analytical solution for homogeneous beams with uniform cross-section can be used for each element. Then, the general analytic solution of the entire beam can be obtained in terms of the initial parameters by satisfying the physical and geometric continuity conditions at the adjacent elements.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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