Dynamics of a single mass vibrating system impacting into a deformable support

The investigated system comprises a mass attached by a deformable link to a fixed foundation, and an elastic-dissipative limiter of motion of that mass. Such types of systems are widely used in different technological devices and machines. This paper is devoted for the improvement of dynamical qualities of such systems. Free and forced stationary harmonic vibrations as well as the qualitative parameters of motions of the system are analyzed in this paper. Characteristics of vibrations are determined using analytical and numerical techniques. It is determined that for the case of zero fastening the values of eigenfrequencies of the system do not depend on the amplitude of excitation. Then the system has an infinite number of multiple eigenfrequencies. In the case of forced harmonic excitation single valued stable motions exist in the vicinity of the resonance. This gives rise to some qualities of the system which are useful in practical applications

Slow translation and fast rotation motions of an unbalanced particle subjected to propagating wave

The analysed system has three degrees of freedom in a plane: translation motion in the direction of wave propagation, oscillatory motion in the direction orthogonal to the direction of wave propagation, and the rotation motion. The dynamical parameters of the system are approximated for steady state motions. It is shown that the particle can be translated by the velocity much lower that the velocity of wave propagation. At the same time it can experience high angular frequency rotation motion. The condition of existence of such type of regime of motion is determined. Such modes of motion can exist in gaseous of liquid environment whenever an unbalanced particle is subjected to propagating longitudinal wave

Wave displacement of rigid bodies and particles

The displacement of various particles and mechanical systems by waves finds wide use in technical devices, technological processes, takes place in non living and living nature. Here the system displaced by waves with four degrees of freedom is analyzed when one member of the system, while contacting with the working profile of the input member performing wave motion, provides motion to the output system.The obtained differential equations of motion of the system have been analyzed analytically and numerically. For the analytical investigation modification of the asymptotic method is used, which is based on the division of motion into the slow and quick motions. This method is justified when the frequencies of variation of slow motions are much smaller than the frequencies of quick motions.When the working surface of the input member moves according to the harmonic Rayleigh waves more detailed full investigations have been performed. The characteristics of transition to steady state and of stationary regimes of motions have been obtained, such as the conditions of existence and stability of the stationary regimes, curves of bifurcation, existing complicated motions

Wave Displacement

Here the system displaced by waves with two degrees of freedom is analyzed when one member of the system, while contacting with the working profile of the input member performing wave motion, provides motion to the output system. For the analytical investigation modification of the asymptotic method is used, which is based on the division of motion into the slow and quick motions. This method is justified when the frequencies of variation of slow motions are much smaller than the frequencies of quick motions. More complicated cases are investigated by numerical methods

Chain type system with wave excitation

Various systems based on waves and vibrations are used for displacing, grouping, classification of multidimensional media and bodies. This paper deals with such wave operation based systems augmented by self-stopping elements which ensure one-directional motion of the driven sub-systems. Such enhancements can improve some dynamical characteristics of the analysed systems. The objective of this paper is to develop models of systems and methods of analysis which would help to reveal nonlinear dynamical properties and phenomena of those systems. The conditions of solutions' existence and stability, basin boundaries are determined. Simpler cases are analysed analytically. The obtained relationships provide insight into nonlinear dynamics of complex systems which are analysed numerically

Constant magnet motors

Motors or actuators with autonomic source of energy, such as for example with constant magnets have scientific and practical value. The transformation of energy of magnets into mechanical motion is performed by using various mechanisms. In the analysed case the wave profile with the elastic member is used. Such systems can be noted by their small dimensions. The expression of the driving force and some characteristics are presente

Dynamical directivity and chaos in some systems with supplementary degrees of freedom

In systems with supplementary degrees of freedom dynamical directivity followed by chaos may exist. Deterministic systems of such types are analyzed in the paper. Their steady state regimes which take place according to dynamically self setting trajectories or vibration modes depending on the eigenfrequencies of the system itself and on the excitation frequencies and parameters are determined. The research is performed by applying approximate analytical methods and numerical one