Stability Of Forced Oscillations Research Articles

Устойчивость трансляционных колебаний зажатой капли маловязкой жидкости

The study investigates oscillatory dynamics of a drop of a low-viscosity liquid surrounded by another liquid under translational low-amplitude vibration influence. A drop of equilibrium cylindrical shape is sandwiched between parallel solid planes. The contact angles are straight and constant, the contact lines of the three media slide freely along the surface of the plates. At the droplet–surrounding liquid interface, a thin viscous boundary layer is taken into account. Natural and forced oscillations of the drop are considered. In the main order of expansion in terms of small amplitude of vibrations, the natural frequencies of oscillations of an inviscid cylindrical drop were obtained. In the first order of expansion, a correction to the frequency was found, caused by energy dissipation in the viscous boundary layer. The stability of forced oscillations with respect to small disturbances was studied. Parametric resonance occurred when the synchronism condition was met: the vibration frequency was equal to the sum of the frequencies of two adjacent modes of natural oscillations. An expression describing the resonant regions was found. It is shown that low viscosity leads to the appearance of a vibration amplitude threshold and a shift in the instability region when compared with zero viscosity.

On functional differential equations connected to Huygens synchronization under propagation

The structure represented by one or several oscillators couple to a one-dimensional transmission environment (e.g. a vibrating string in the mechanical case or a lossless transmission line in the electrical case) turned to be attractive for the research in the field of complex structures and/or complex behavior. This is due to the fact that such a structure represents some generalization of various interconnection modes with lumped parameters for the oscillators.On the other hand the lossless and distortionless propagation along transmission lines has generated several research in electrical, thermal, hydro and control engineering leading to the association of some functional differential equations to the basic initial boundary value problems.The present research is performed at the crossroad of the aforementioned directions. We shall associate to the starting models some functional differential equations - in most cases of neutral type - and make use of the general theorems for existence and stability of forced oscillations for functional differential equations. The challenges introduced by the analyzed problems for the general theory are emphasized, together with the implication of the results for various applications.

Delay-Integral-Quadratic Constraints and Stability Multipliers for Systems With MIMO Nonlinearities

The formula for stability multipliers for systems with MIMO nonlinearities is derived using the method of delay-integral-quadratic constraints. The results, applicable to both time-invariant and time-periodic systems, are then used to derive a solution for a special case of a nonlinear regulation problem and a criterion for stability of forced oscillations. A linear time-periodic system is considered to illustrate the difference between the delay-integral-quadratic constraints that yield stability criteria in multiplier form and those that do not.

Existence and stability of forced oscillations in non-linear systems with one degree of freedom

Forced oscillations of one degree of freedom systems are considered. The size of the external periodic force and the non-linearity are not limited while the non-conservative forces are supposed to be small. The qualitative analysis is carried out with the aim of establishing the existence, behavior and stability of harmonic and subharmonic oscillations depending on the position and external forces. Some of the stability criteria obtained justify and generalize the known results established via approximate analytical methods; at the same time, cases are indicated where the application of such methods to stability analysis may result in error.

Stability and forced oscillations

In this paper we derive a differential-difference equation for a circuit involving a lossless transmission line and we give conditions for global asymptotic stability of an equilibrium point, existence and stability of forced oscillations. Some of such problems have been investigated for an equation obtained by R. K. Brayton [ Quart. J. Appl. Math. 24 (1967) , 289–301; O. Lopes, SIAM J. Appl. Math., to appear; M. Slemrod, J. Math. Anal. Appl. 36 (1971) , 22–40] but, for ours (which governs the same physical problem), better results can be proved. By using suitable Liapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality.

Nonsmall liquid oscillations in a right circular cylinder

In this study we consider certain nonlinear effects which occur during oscillations of a liquid partially filling a right circular cylinder. The problem of nonlinear oscillations of a liquid in a circular cylinder has been considered in [1, 2]. The same problem has been solved in [3, 4] for arbitrary cavities by a somewhat different method. In the present paper we investigate the stability of forced oscillations of a liquid in a cylinder when the latter performs small harmonic oscillations in a plane passing through its axis.

Solutions periodiques des systemes quasilineaires non autonomes a deux degres de liberte

In the first part the periodic solutions of a fourth-order differential system of the form: dx dt = Ax + tf(t) + μF(t, x, μ) are discussed and sufficient conditions for their asymptotic stability are given. It is shown that, under certain hypotheses, this stability is equivalent to that of singular points of an associated autonomous system, which permits the study, in first approximation, of domains of attraction (for particular initial conditions) of the periodic solutions obtained. In the second part, the above results are applied to the discussion of the existence and the stability of forced oscillations, especially of harmonics and sub-harmonics of the third order, for a mechanical system, with two degrees of freedom.

Stability of forced oscillations in nonlinear feedback systems

It has been known for a considerable time that non-linear systems may exhibit multivalued response under external periodic excitation. The stability of these forced oscillations has been extensively investigated for second-order systems and a general criterion for their stability was found. Stability of higher order systems was investigated by means of the incremental describing function. This function must be calculated for every case of interest. In this paper the general criterion formerly derived for second-order systems is extended to higher order systems. Thus it is not necessary to make a special stability investigation in every case.