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Torsional oscillations in structures subject to ground motion. (English) Zbl 0561.73060
A multiple-scale technique has been employed to study nonlinear torsional oscillations in single-storey structures with cubic softening stiffness members subject to a single frequency ground excitation. The structures are studied under free oscillation conditions, primary resonance, and combination resonance. Time history analyses are employed to quantify the dynamic behaviour of a single-storey structure. The instabilities are related to the jump in response which exists in single degree-of-freedom softening oscillators subjected to harmonic excitation. It is shown that this jump can be quantified analytically, and appers as a cusp catastrophe in the bending mode. Time history analyses show that the bending mode can exhibit a limit cycle behaviour of constant amplitude.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74L05 Geophysical solid mechanics
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