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This report is a part of the larger project of non-linear dynamics investigation of three coupled physical pendulums with damping and with arbitrary situated barriers, and externally driven. The set of differential equations and the set of algebraic inequalities (representing a barrier) governing the motion of three coupled rods are presented in the non-dimensional form. The system of governing equations...
The paper deals with investigation of a self-excited vibrating system with dry friction. The system is composed of a mass connected by viscoelastic element with the referring frame and interacting with a moving belt by means of dry friction. An experimentally identified, multi-parametric dry friction model for the pair composed of soft and hard elements like steel–polyester pair, describing both the...
The purpose of the present paper is to solve an active control problem of nonlinear continuous system parametric vibrations excited by the fluctuating force. The problem is solved using the concept of distributed piezoelectric sensors and actuators with a sufficiently large value of velocity feedback. The direct Liapunov method is proposed to establish criteria for the almost sure stochastic stability...
The stability and vibration characteristics of turbo-rotors running in journal bearings depend strongly on the characteristics of journal bearing determined by the oil film pressure and negative pressure developed in journal bearings. This paper is concerned with clarifying the development of this negative pressure and its influences by taking into account air bubbles in oil film, especially the surface...
We present a study of localized transversal excitations in a system of weakly nonlinear oscillators coupled by linear bonds. The equations of motion are written in a complex form and then the multi-scale expansion is used. Short wave-length asymptotics have been considered. We have shown that in the case nonlinear Schrodinger equation (NSE) corresponds to the main approximation. This equation, in...
We present a design procedure for enhancing nonlinear energy pumping from a mode of a linear-damped substructure to a weakly coupled, essentially nonlinear oscillator. By this we denote the one way, irreversible passive transfer of vibrational energy from the mode to the nonlinear attachment. The design relies in the asymptotic expansion for large energies of a nonlinear normal mode of the underlying...
In this work periodic and chaotic dynamics of a bush being in a contact with a rotating shaft is analysed using the classical friction and abrasive wear models with the inclusion of the frictional heat generation. First, an analytical chaos prediction using the Melnikov method (without tribologic processes) is given, and then the analytical predictions are verified numerically. Then numerical analysis...
The nonlinear response of a three degree of freedom vibratory system with double pendulum in the neighbourhood internal and external resonances is investigated. The equations of motion have bean solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibration there may also appear chaotic vibration. To prove the character...
We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.
The paper is concerned with the problem of stability of a power transmitting thin-walled shaft made of the active laminate PFC (piezoelectric fiber composite). The shaft rotates with a given operational angular velocity, and is loaded by a static torque. Such a system is known to exhibit divergence or oscillating type of instability. On the one hand presence of internal friction in the material of...
Conventional control systems express control solutions by means of control expressions, usually mathematically based. To completely express the control solution, a vast amount of data is required. This is either difficult or virtually impossible to obtain. In contrast, knowledge-based solutions require far less plant data and mathematical expression. This reduces development time proportionately....
The dynamical system or flow ż = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance...
By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number ‘eight’ in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under...
The paper deals with vibrations of mechanical systems torsionally deformed. These problems can be discussed using two-dimensional or one-dimensional models. After the presentation of basic equations for two-dimensional problems, the study is focused on one-dimensional problems for discrete-continuous systems with a local nonlinearity and on the effect of the local nonlinearity on the behaviour of...
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