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Free vibrations of a non-uniform beam with general elastically restrained boundary conditions. (English) Zbl 1235.74175
Summary: A simple and efficient method is presented to study the problem of free vibration of a non-uniform Bernoulli-Euler beam with general elastic restraints at boundary points. With one set of particularly chosen fundamental solutions of the system, the frequency equation is derived and expressed in concise form. If the closed form fundamental solutions of the system are not available, the approximate fundamental solutions can be obtained through a newly developed algorithm which is shown to be efficient, convenient and accurate. Finally, several limiting cases of the general system are examined and some examples are presented to illustrate the validity and accuracy of the proposed method.

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