The large amplitude vibration of tapered clamped beams

The large amplitude free vibrations of a beam with immovable clamped ends, with the actual non-linear equilibrium equations (i.e., specification of loads in terms of the deformed configuration) and the exact non-linear expression for curvature, and with no assumption made as to the constancy of axial force, have been determined by a simple numerically exact successive integration and iterative technique. By application of this technique, together with the definition of an eigenvalue-like quantity arising from certain definitions of the time function, results have been produced showing the dependence of the hardening effect of non-linearity on amplitude of vibration, for selected values of several parameters such as taper ratio, slenderness ratio and axial force. © 1978 Academic Press Inc.