Energy transfer in double plate system dynamics

Abstract

The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.Keywords Energy transfer between subsystems · Double plate system · Multifrequency transversal vibrations · Analytical solution · Rayleigh function of dissipation IntroductionPlates, beams and belts have been extensively used as structural elements in many industrial applications. Investigation of vibrations of plates dates back to the nineteenth century. The interest in the study of coupled systems [1-13] as newThe English text was polished

Multi-frequency analysis of the double circular plate system non-linear dynamics

“…1(a), it is clear that the mathematical model of such a system may be expressed by the system of two coupled partial differential equations (1) [4,5,7,21]. The partial differential non-linear equations in this case are formulated in terms of two unknowns: the transversal displacement w i (r, ϕ, t), i = 1, 2 in direction of the z-axis, of the upper plate middle surface for i = 1 and of the lower plate middle surface for i = 2.…”

“…[3,4,7]) denoted as hybrid systems, characterized by the interaction between subsystem dynamics, governed by coupled partial differential equations with boundary and initial conditions. The energy transfer between coupled subsystems was indicated in system with nonlinearity [2,4,7].…”

“…The list of the valuable research results in the connected area of the objects of the author's research is large, but in this introduction, we make some subjective choices. An analysis of system energy of the excited modes depending on amplitudes, phases and frequencies of different non-linear modes is obtained with averaging and asymptotic methods for obtaining the system of ordinary differential equations of amplitudes and phases in first approximations [2,4] and [7]. The energy analysis of mode interaction in the multifrequency free and forced vibration regimes of nonlinear elastic systems (beams, plates, and shells) excited by initial conditions of system deformation and velocities, was made and a series of resonant jumps as well as energy transfer features were identified.…”

Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system)

“…Based on the author's previous published results (see [21,22]) for free transversal vibrations of the axially moving sandwich double belt system described by the coupled partial differential equations derived and analytically solved, as well as the papers [23,11,[15][16][17][18][19], [25], in this paper, new results in area of the transfer energy between belts of the axially moving sandwich double belt system and a transformation of the mechanical energy, kinetic and potential, in the one mode and in two frequency like regime are analytically described and analyzed.…”

“…The study of the transfer energy between subsystems coupled in hybrid system [3,4,11], as well as between modes in continuous nonlinear systems [6,7,[15][16][17][18][19] with hybrid dynamics, in free and forced deterministic or stochastic regimes, is very important for different applications.…”