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On Mixed Forced and Self-oscillations with Delays in Elasticity and Friction

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Advances in Intelligent Systems, Computer Science and Digital Economics II (CSDEIS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1402))


We consider mixed forced and self-oscillation in the presence of a delay in the forces of elasticity and friction. The system receives energy from a limited power source. The method of direct linearization is used to solve a nonlinear system of differential equations describing the system’s motion. It differs from the known methods of analysis of nonlinear systems in its simplicity of application. It lacks the time-consuming and complex approximations of various orders inherent in known methods. It can be used to obtain final calculated ratios regardless of the specific type and degree of non-linearity. Compared with known methods, it reduces labor and time costs by several orders of magnitude. Equations of non-stationary and stationary movements and conditions of stability of stationary vibrations are derived. To obtain information on the effect of delays on the modes of oscillations, calculations were performed. The influence of delays on the amplitude and the location of the amplitude-frequency curve in the frequency range is shown. It turned out that in the frequency domain there is a displacement and deformation of the amplitude curve depending on the delay value, which also affects the stability of vibrations. And also at certain values of the delay, the form of the amplitude curves is similar to the form of the curves in the absence of delay and the presence of a nonlinear elastic force.

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Alifov, A.A. (2021). On Mixed Forced and Self-oscillations with Delays in Elasticity and Friction. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Intelligent Systems, Computer Science and Digital Economics II. CSDEIS 2020. Advances in Intelligent Systems and Computing, vol 1402. Springer, Cham.

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