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Explicit analytical expressions for frequency equation and mode shapes of composite beams. (English) Zbl 0996.74039

By the use of symbolic computation package REDUCE, the author derives frequency equation and closed-form mode shapes of bending-torsion for a composite beam with rectangular cross-section. The boundary conditions are as follows: the left end is built in, the right end is free. The governing differential equations of the mode shape are solved for the bending displacement and torsional rotation in the case of free vibrations. The characteristic equation is reduced to a cubic equation which is shown to possess three real roots, one of which is positive and other two are negativ. The validity of the presented theory is demonstrated by numerical examples which are in good agreement with published results.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E30 Composite and mixture properties
68W30 Symbolic computation and algebraic computation

Software:

REDUCE
PDFBibTeX XMLCite
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