Vibrations in engineering and technology

Olshansky Vasiliy Pavlovich – Professor of the Department of Theoretical Mechanics and Machine Parts, Kharkiv National University of Agriculture, Dr. Sci. (Phys.-Math).

Olshansky Stanislav Vasilyevich – Candidate . Sci. (Phys.-Math), (E-mail: stasolsh77@gmail.com)

The motion of an oscillator with a soft elastic characteristic, which is proportional to the square root with the deformation of the spring, is considered under the action of a force pulse. An analytic solution of a second-order nonlinear differential equation is constructed to calculate the oscillations caused by an instantaneously applied force or a rectangular pulse of a limited extent. It is shown that the coefficient of dynamism of an oscillator with a chosen elasticity characteristic, with a stepped power load, is 2.25, that is, it is larger than for a linear system. In the case of disturbance of motion by a rectangular pulse, the dynamic coefficient depends on the duration of the load and does not exceed 2.25. The pulse duration is found when the maximum free oscillation amplitudes of the unloaded oscillator appear. Unlike linear systems, this duration depends not only on the proper parameters of the oscillator, but also on the magnitude of the applied force. The pulse duration at which the unloaded oscillator does not perform free oscillations is determined, but is at rest. In the analytic solutions of the Cauchy problem, in addition to elementary functions, periodic Ateb-functions are also involved. To simplify the calculation, a table of used special functions is compiled. Examples of calculations are given.

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