Abstract
Generators of mechanical vibrations with nonlinear stiffness of the elastic element in the conservative case are investigated. It is shown that the vibrator of this type generates several harmonic components and that the number of those multiple harmonics can be controlled. One period of motion is investigated. The presented analytical relationships and numerically obtained graphical relationships reveal the qualities of the system and enable to choose the desirable parameters of motions. The performed investigation of this system showed that eigenvibrations take place with linear spectrums when the system in separate intervals consists from two linear parts. This takes place in the case when the border of difference of coefficients of stiffness is located in the position of equilibrium of the system. In both intervals vibrations by separate partial frequencies take place and general motion depends on the eigenfrequency of the whole system. Of course the latter frequency depends on both partial frequencies. General motion of the whole system takes place according to the infinite linear spectrum of eigenfrequencies. All this enables to create enhanced vibrators by using those qualities and to use them in technologies.
Highlights
In a number of publications basis of the theory of nonlinear mechanical generators of vibrations were investigated as well as their multi valued steady state regimes
This paper is based on the investigations of essentially nonlinear systems and their dynamics presented in a book by Ragulskienė V
Dynamical characteristics of the system x, x, x, xx are expanded into the Fourier series with respect to the eigenfrequency
Summary
In a number of publications basis of the theory of nonlinear mechanical generators of vibrations were investigated as well as their multi valued steady state regimes. This paper is based on the investigations of essentially nonlinear systems and their dynamics presented in a book by Ragulskienė V. This quality was observed when exciting vibrations of vibromotors in a book by Ragulskis K., Bansevičius R., Barauskas R., Kulvietis G. Nonlinear vibrating systems and their resonances are analysed in [1]. Several systems were investigated in which subsystems with different nonlinearities have a point of transition and when this point in the static positions of both subsystems coincides, for example [14]. In this paper the investigation is presented when the quality of this type takes place and the independence of eigenfrequencies from the amplitudes of motions is determined and motion takes place with infinite spectrum of frequencies.
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