The Stability and Non-Linear Vibrations of an Orthotropic Hinged-Hinged Beam.

摘要

The field equations for the general non-linear theory of elasticity are expressed in variational form. Under the assumption of infinitesimal strains and small rotations, Euler-Bernoulli and Timoshenko type theories for the non-linear flexural vibrations of hinged-hinged beams are derived with the aid of this generalized form of Hamilton's principle. It is assumed that the beam is subjected to a sinusoidal forcing function applied along the length of the beam, and attention is focused upon a determination of the steady state periodic motions of the system. Frequency-amplitude plots are given for various values of the parameter which measures the degree of anisotropy of the system. The stability of the periodic motions is then considered, and Hsu's method is employed for the purpose of establishing the zones of stability in a frequency-amplitude diagram. (Author)