Phenomenon Of Parametric Resonance Research Articles

Universe reheating after inflation.

We study the problem of scalar particle production after inflation by an inflaton field which is oscillating rapidly relative to the expansion of the universe. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particles produced are described by a quantum scalar field \ensuremath{\chi}, which is coupled to the inflaton via linear and quadratic couplings. The particle production effect is studied using the standard technique of Bogolyubov transformations. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first-order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential V(cphi)=\ensuremath{\lambda}${\mathit{cphi}}^{4}$, the particle production process is very efficient for either type of coupling between the inflaton field and the scalar field \ensuremath{\chi} even for small values of coupling constants. The energy density of the universe after the decay of the inflaton oscillations is in this case a factor [\ensuremath{\lambda} ln(1/\ensuremath{\lambda})${]}^{\mathrm{\ensuremath{-}}1}$ times larger than the corresponding estimates based on first-order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the scalar field \ensuremath{\chi} and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde, and Starobinsky, the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.

歯付ベルトのパラメータ励振

Timing belts are usually used as standard apparatus for power transmission and the timing device in the diesel engines of ships, the OHC engines of cars and the machine tools. In such cases, it is well known that the timing belt is subjected to the fluctuation of tension which is caused by the eccentricity of the pulley shaft, engagement of the belt and the pulley, and the fluctuation of torque given to the pulley shaft. As a basic research on this problem, this paper describes the results of analytical and experimental investigations of the parametric resonance phenomena of the timing belt stretched vertically. As the first step, the author regarded the timing belt as a system with string and applied Mathieu's equation to the behavior of the timing belt which is subjected to periodic tension, and then compared the experimental results with approximate stability chart for Mathieu's equation. As a result, the experimental results agreed almost with approximate stability chart for Mathieu's equation. Namely, the vibration characteristics of timing belt showed remarkable features of the parametric excitations.

Nucleation and amorphous and crystalline growth: A dynamical model in two dimensions.

A model of nucleation and growth in two dimensions is proposed, which can be applied to covalent or metallic solids. The short- and medium-range correlations are taken into account by finding the energy minimum for a typical local configuration with given coordination number, and by assuming that the energy cost of the local defect is roughly the same for excess or deficiency of neighbors. The growth process is then treated in a probabilistic way, which enables us to derive the system of ordinary differential equations describing the evolution of the probabilities of finding given local configurations. The singular points of this nonlinear differential system correspond to the stable regimes of growth and can give rise to stable or metastable crystalline or amorphous networks. The temperature dependence of the process is discussed. The possibility of obtaining modulated structures via the phenomenon of parametric resonance is suggested.

Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures

A purely numerical method for the treatment of instability problems of parametric resonance is presented. The proposed way of solution, which is applicable to all types of structures, is based on the finite element discretization of an incremental variational principle. After the derivation of the theoretical background linear and quadratic eigenvalue problems for the critical excitation-frequencies of undamped and damped systems are presented and numerical procedures for the computation of the instability charts are established. Finally the efficiency of the developed algorithms is demonstrated by means of several shell responses.

Nonlinear Response of Roller Chain to Combined Forcing and Parametric Excitations

This paper describes the results of analytical and experimental investigations of the nonlinear harmonic and parametric resonance phenomena of a roller chain stretched vertically which is regarded as a system with many degrees of freedom, when the elongation of the chain during vibration is taken into account. The resonance treated in this report is one of the resonances excited under combined forcing and parametric excitations in which the ratio of the forced lateral displacement acting at a lower end to that of the tension fluctuation is 1:2. Two chains with different frictional coefficients were used in experiments in order to examine the effect of friction upon the vibration characteristics. The experimental results showed remarkable features attributable to the combined excitations and agreed well with the analytical results.

Wave stochastic parametric resonance (wave intensity fluctuations in a one-dimensional randomly inhomogeneous medium)

UDC 538.56:519.25 We obtain a stochastic expression for the wave intensity in a one-dimensional randomly inhomogeneous absorbing medium. In the absence of absorption it is shown that both the one-point intensity moments and the multipoint correlation functions are described by expressions which contain one quadrature. The wave intensity moments inside the layer increase exponentially with the layer thickness which corresponds to the phenomenon of stochastic parametric resonance.

An investigation of the buckling behaviour and parametric resonance phenomenon of a tensioned sheet with a central opening

The results of an experimental study of the buckling behaviour and parametric resonance phenomenon of a tensioned sheet with a rectangular opening having elliptic ends are presented. The data from the static experiments indicate that the local buckling phenomena of the free edge of the opening are dependent on cutout parameters. The variations of critical buckling stress on opening parameters are discussed. The parametric excitation experiments show two distinct types of resonant behaviour. The response-excitation frequency ratio is observed to be half for the principal region and the ratio is one for the secondary region. The size and amplitude of oscillations of the principal regions are found to be substantially larger than that of the secondary region. Further, parametric resonance experiments for different opening parameters indicate that the dynamic instability effects are more significant for narrow openings than for wider openings.

Origin.methods of analysis and damping of non-linear vibrations in a “rectifier frequency convertor - asynchronous motor” system

Summary The paper describes the physical nature of the origin and maintenance of vibrations resulting from the parametric resonance phenomenon in the “rectifier frequency converter asynchronous motor” system. The paper describes the influence of individual parameters and operational regimes of the system on the origin of these vibrations. It substantiates the application of the method of harmonic linearization for the analysis of parameters of set vibrations. The paper also examines ways and means of controlling the above-wentioned vibrations.