Abstract
The axial and transverse motion of asymmetrically laminated cross-ply beams is coupled due to (i) the non-coincidence of reference and mid-planes and (ii) finite amplitudes. To derive the equations that govern the nonlinear oscillatory behavior of these laminated beams, a spatial deformation satisfying geometric constraints is substituted in the kinetic potential and Hamilton's principle is employed. This leads to three coupled nonlinear second order ordinary differential equations. These equations have quadratic nonlinear terms in addition to usual linear and cubic terms. The existence of these terms does not allow a straight forward solution in the presence of axial and rotatory inertia for nonlinear frequencies/periods. The objective of the present paper is to propose two possible solution methods for computing nonlinear frequencies/periods of asymmetrically laminated cross-ply beams. In both the methods, energy of positive and negative deflection cycles is maintained equal. A few numerical examples are solved to validate the methods. The effect of axial and rotatory inertia on the large amplitude oscillatory behavior is investigated.
Published Version
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