EXACT SOLUTIONS AND DYNAMIC RESPONSES OF SDOF BILINEAR ELASTOPLASTIC STRUCTURES

Abstract

The model of single degree of freedom bilinear elastoplastic structures under external loading is treated in this paper. Based on the model sufficient and necessary conditions for plastic irreversibility are derived. It is analyzed and pointed out that for the bilinear structure the equation of motion is nothing but a two-phase linear system with an on-off switch, which is operated in the pace of an intrinsic measure of plastic irreversibility. Then the exact solutions of the dynamic responses are derived for arbitrary external loading and, especially the explicit results are worked out for sinusoidal loading inputs. Comparison with the corresponding linear structure shows that the characteristics of the bilinear structure have three folds: longer natural period, larger damping ratio and non-smooth modified loading due to on-off switching. For harmonic loading the necessary condition for plastic resonance is derived, and the elastoplastic behavior is found to exhibit stable hysteresis loop and limit cycle. The inelastic response spectra are also given for harmonic loading, from which the influences of structural parameters, namely natural frequencies, yield strengths and kinematic stiffness, are analyzed and discussed.