A Microstructure Theory for the Buckling and Vibration of a Laminated Beam
WATERVLIET ARSENAL NY
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A theory is derived for the flexural deformation of laminated beams subjected to initial stresses. Each layer is treated as a Timoshenko beam and smoothed expressions for the kinetic and strain energies and the work done by external forces are derived. A SYSTEM OF THREE COUPLED PARTIAL DIFFERENTIAL EQUATIONS, INCLUDING THE EFFECT OF BENDING, EXTENSION, ROTATION, AND INITIAL AXIAL STRESS ARE OBTAINED FROM Hamiltons principle. Specific buckling and free vibration problems are solved exactly for hinged-hinged and clamped-clamped beams. The numerical results reveal values of buckling coefficients and natural frequencies that are in agreement with the corresponding results obtained from the effective modulus theory for relatively long beams, but that are considerably lower than the effective modulus values for relatively short beams. In the high frequency range, with the effect becoming more pronounced in the higher modes, the present theory predicts much smaller values for the flexural and thickness-shear natural frequencies than does the effective modulus theory.
- Structural Engineering and Building Technology