Banerjee, J. R. Explicit analytical expressions for frequency equation and mode shapes of composite beams. (English) Zbl 0996.74039 Int. J. Solids Struct. 38, No. 14, 2415-2426 (2001). 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. Reviewer: I.Ecsedi (Miskolc-Egyetemvaros) Cited in 3 Documents 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 Keywords:model analysis; symbolic computation; package REDUCE; frequency equation; bending-torsion; composite beam; rectangular cross-section; mode shape; free vibrations; characteristic equation; cubic equation Software:REDUCE PDFBibTeX XMLCite \textit{J. R. Banerjee}, Int. J. Solids Struct. 38, No. 14, 2415--2426 (2001; Zbl 0996.74039) Full Text: DOI