HARMONIJSKE VIBRACIJE PDF

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Full text not available from this repository. Clearance type non-linearity is modeled by a symmetric piecewise linear force-displacement relationship, which represents non-analytical and strong non-linearity in the system. Equations for calculating non-linear frequency response characteristics of multi-degree-of-freedom systems with any number of clearances in the system in the frequency domain are derived by using the incremental harmonic balance method, and the harmonic balance Newton-Raphson method with the application of a discrete Fourier transformation algorithm.

With respect to the methods which give response in a time domain, the advantage of these methods is that during the iteration, they do not accumulate numerical errors.

Systems with single-degree-of-freedom and two degrees-of-freedom with single and two clearances are analyzed. By the comparison of the results obtained in the time domain a piecewise linear technique, Runge-Kutta 4th-5th order numerical integration routine and in the frequency domain the method of harmonic balance, the incremental harmonic balance method it is shown that extremely non-linear response can appear even in the frequency ranges in which the method of harmonic balance predicts linear response non-impact case.

In this way, it is shown that in these frequency ranges significant disagreement of the results obtained by the harmonic balance method and the time integration methods are not caused by the numerical errors which can arise during the simulation in the time domain. Extreme non-linear response in these frequency ranges can be explained by the influence of higher harmonics, which arise during the transient part of the response.

This phenomenon is very important, because in these frequency ranges well below or behind the resonance a non-linear response which amplitudes are very often much greater than amplitudes of a linear one is not expected.

Based upon performed investigations, the procedure for numerically efficient calculating the complete non-linear frequency response characteristics is proposed. The procedure is based on combined use of the methods which give response in the time and in the frequency domain. Item Type:.

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