In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connecte...In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connected by shape memory alloy （SMA） spring. Shape memory alloys have ability to change their material properties with temperature. A polynomial constitutive model is assumed to describe the behavior of the SMA spring. The non-ideal source of power adds one degree of freedom, so the system has four degrees of freedom. The equations of motion have been solved numerically and pseudoelastic effects associated with the martensitic phase transformation are studied. It is shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system＇s various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities, Poincare maps and exponents of Lyapunov may be used.展开更多
文摘In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connected by shape memory alloy （SMA） spring. Shape memory alloys have ability to change their material properties with temperature. A polynomial constitutive model is assumed to describe the behavior of the SMA spring. The non-ideal source of power adds one degree of freedom, so the system has four degrees of freedom. The equations of motion have been solved numerically and pseudoelastic effects associated with the martensitic phase transformation are studied. It is shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system＇s various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities, Poincare maps and exponents of Lyapunov may be used.
