Shear deformation and rotary inertia effects of vibrating composite beams

Free vibration of symmetrically laminated composite beams is studied based on Timoshenko type equations. Shear deformation and rotary inertia are included in the analysis, but with the term representing the joint action of these effects omitted in the Timoshenko equations. Detailed analytical analysis is performed for the natural frequencies of laminated beams with different boundary conditions at their ends, with numerical examples being calculated for a hinged-hinged beam.

[1]  S. Timoshenko,et al.  LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars , 1921 .

[2]  K. Chandrashekhara,et al.  Free vibration of composite beams including rotary inertia and shear deformation , 1990 .

[3]  J. Whitney,et al.  Shear Deformation in Heterogeneous Anisotropic Plates , 1970 .

[4]  E. Brunelle.  Elastic instability of transversely isotropic Timoshenko beams , 1970 .

[5]  A. W. Leissa,et al.  Literature Review: survey and analysis of the Shock and Vibration literature : Recent Studies in Plate Vibrations: 1981-85 Part II. Complicating Effects , 1987 .

[6]  L. S. Teoh,et al.  The vibration of beams of fibre reinforced material , 1977 .

[7]  I. Elishakoff,et al.  Influence of shear deformation and rotary inertia on vibration frequencies via Love's equations , 1990 .

[8]  A. W. Leissa,et al.  LITERATURE REVIEW: survey and analysis of the Shock and Vibration literature: Recent Studies in Plate Vibrations: 1981-85 Part I. Classical Theory , 1987 .

[9]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

[10]  Arthur W. Leissa,et al.  RECENT STUDIES IN PLATE VIBRATIONS, 1981-1985, PART I: CLASSICAL THEORY , 1987 .

[11]  T. Y. Yang,et al.  Static and Dynamic Formulation of a Symmetrically Laminated Beam Finite Element for a Microcomputer , 1985 .

[12]  C. Bert,et al.  The behavior of structures composed of composite materials , 1986 .

[13]  John C. Halpin,et al.  Primer on Composite Materials Analysis , 1984 .

[14]  I. Elishakoff,et al.  Application of the Krein's method for determination of natural frequencies of periodically supported beam based on simplified Bresse-Timoshenko equations , 1987 .