Resonant phenomena of elastic bodies that perform bending and torsion vibrations
Journal Title: Український журнал із машинобудування і матеріалознавства - Year 2018, Vol 4, Issue 1
Abstract
The method of study of the influence of torsional oscillations of one-dimensional models of nonlinear elastic bodies, along which moves with a constant velocity continuous flow of inelastic homogeneous medium, into bending, is developed. It is believed that information on torsional oscillations is known from empirical studies. Based on the latter, the refined model of the dynamics of the process of the investigated object is constructed. The latter is a boundary value problem for nonlinear nonautonomous differential equations with partial derivatives. The imposed restrictions on power factors and the main parameters of torsional oscillations allow for the analytical study of the dynamics of the process to use the basic ideas of the asymptotic integration of equations with partial derivatives. With their help, we obtain a two-parameter set of solutions that describe the determinant parameters of bending vibrations of an elastic body. It is established that for the considered elastic body there can be resonance oscillations, which are caused not only by external factors, but also by internal - torsional oscillations. Regarding the law of the change in the basic parameters of the dynamics of the bending motion of an elastic body, its rotation around the vertical axis reduces the frequency of its own flexural oscillations of the body, and even small torsional oscillations cause an additional periodic action on the transverse. In connection with the above bending vibrations of the elastic body, which performs complex oscillations (torsion and bending), resonances are possible both at the frequency of the external periodic perturbation and at the frequencies of the torsional oscillations (internal resonances). The amplitude of the transition through the resonance: a) at the basic frequency of external perturbation takes less value for elastic bodies of greater flexural rigidity and for higher values of the relative relative motion of the medium; b) at the frequency of torsional oscillations for larger valuesof the angular velocity takes more importance; c) with "fast" transition through resonance at the frequency of external or internal perturbation is less than with "slow". The obtained results can serve as the basis for the choice of operating parameters of elastic elements of machines that carry out complex oscillations.
Authors and Affiliations
Andrij Andrukhiv, Bohdan Sokil, Mariia Sokil
Keywords
Related Articles
- EP ID EP498163
- DOI 10.23939/ujmems2018.01.065
- Views 97
- Downloads 0
Study of Surface Microstrains by Electron Speckle-Interferometry Methods
Despite the fact that speckle interferometry methods began to develop more than 30 years ago, they still remain a rather exotic laboratory tool that has not received wide practical application in tensometry measurements...
Dynamics of two-mass mobile vibratory robot with electromagnetic drive and vibro-impact operation mode
The purpose of research. Substantiation of inertial, stiffness and excitation parameters of mechanical oscillatory system of mobile vibratory robot in order to maximize its motion speed. Methodology. The technique of the...
Operational Conditions of Vehicles Motion and Formation of Urban Driving Cycle in the City of Lviv
To the greatest extent, the indicators of the motor vehicles being in the normative technical state are influenced by the operational conditions, which, in turn, are characterized by road, relief (terrain) and transport...
Hydraulic pump based on the rolamite mechanism
When designing pumping equipment the question arises not only of the improvement of the existing types but also the search for a new principle of uniting the supporting elements with the elements of the formation of the...
Synthesis of Structure and Research of Operation of Resonance Two-mass Vibrating Table with Electromagnetic Drive
An industrial necessity of creation of 100-Hz vibratory tables is grounded. The prospect of researches of just resonance electromagnetic vibratory tables is conditioned. The existing vibrating tables on the basis of elec...