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首页> 外文期刊>Mathematical Problems in Engineering >AUTOPARAMETRIC VIBRATIONS OF A NONLINEAR SYSTEM WITH PENDULUM
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AUTOPARAMETRIC VIBRATIONS OF A NONLINEAR SYSTEM WITH PENDULUM

机译：摆非线性系统的自参数振动。

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摘要

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.
机译：本文已经分析了带有摆锤的非线性振荡器的振动，该振动由其悬挂点的移动激发。推导的运动微分方程表明，该系统是强非线性的，并且两个子系统（钟摆和振荡器）的运动都通过惯性项强烈耦合，从而导致所谓的自参数振动。已经发现，由外部谐波力强迫的振荡器的运动已经被摆振动动态地消除了。解析分析了非线性弹簧对主参量共振区域附近的振动吸收的影响，而采用数值方法则表明了从规则振动到混沌振动的过渡。还介绍了基础上的规则振动和混沌振动的传递力。

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