for the nonlinear initial boundary value problem of Kirchhoff equation $$ \displaylines{ u_{tt}+\Delta^2 u + M(\|\nabla u\|^2)(-\Delta u) u_{t}= \ln |u|^2,\text{ in }\Omega\times (0,T), \cr u(x,0) = u_0(x), \quad u_{t}(x,0)=u_1(x),\quad x \in \Omega, u(x,t) \frac{\partial u}{\partial \eta}(x,t)=0, \partial \Omega,\; t\geq 0, }$$ where (\Omega;\)is a bounded domain \(R^2\) with smooth \(\partial...

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In th...

We study the effects of temperature and sliding velocity on superlubricity in numerical simulations of the Frenkel-Kontorova model. We show that resonant excitations of the phonons in an incommensurate sliding body lead to an effective friction and to thermal equilibrium with energy distributed over the internal degrees of freedom. For finite temperature, the effective friction can be described...

In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the o...

Context. Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. Aims. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence...