We study the stability of breather solutions of a dissipative cubic discrete NLS with localized forcing. The breathers are similar to the ones found for the Hamiltonian limit of the system. In the case of linearly stable multi-peak breathers the combination of dissipation and localized forcing also leads to stability, and the apparent damping of internal modes that make the energy around multi-...

The homotopy analysis method HAM is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthe...

We investigate the dynamics of a delayed nonlinear Mathieu equation: ẍ + (δ + εα cos t)x + εγ x = εβx(t − T ) in the neighborhood of δ = 1/4. Three different phenomena are combined in this system: 2:1 parametric resonance, cubic nonlinearity, and delay. The method of averaging (valid for small ε) is used to obtain a slow flow that is analyzed for stability and bifurcations. We show that the 2:1...

We show that the nonlinear wave equation u + ut = 0 is globally well-posed in radially symmetric Sobolev spaces Hk rad(R 3) × Hk−1 rad (R 3) for all integers k > 2. This partially extends the well-posedness in Hk(R3) × Hk−1(R3) for all k ∈ [1, 2], established by Lions and Strauss [12]. As a consequence we obtain the global existence of C∞ solutions with radial C∞ 0 data. The regularity problem ...

We present a mathematical framework to provide general well-posedness and approximation results for a laminated curved beam. The layered beam consists of an elastic core layer, symmentric viscoelastic damping layers, symmetric constraining layers and bonded piezoceramic patch pairs on the outer surfaces. The model includes unbounded inputs from the piezoceramic patches, hysteresis and shear in ...

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit...

In order to build efficient reduced-order models (ROMs) for geometrically nonlinear vibrations of thin structures, a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities. The linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation. A special attention is focused on how al...

FeNi binary nanowires with gradient composition are fabricated by the electrodeposition method. The energy dispersive spec-trometer line-sweep results show that the composition changes gradually along the wire axis. The gradient FeNi nanowires exhibit polycrystalline and crystal twinning at different areas along the nanowire axis, with a textured face-centered cubic structure. The static and dy...

This paper is devoted to study the stabilization of the linear wave equation in a bounded domain damped in a subdomain when the geometrical control condition (see [ BLR]) of the work of C. Bardos, G. Lebeau and J. Rauch is not fulfilled. In such case, they [ BLR] proved that the uniform exponential decay rate of the energy cannot be hoped due to the existence of a trapped ray that never reaches...

Abstract The diagonal inerter is integrated into a suspension vibration reduction system (SVRS). dynamic model of the SVRS with and damping established. strong geometric nonlinearity. retaining non-linearity up to cubic terms validated under impact excitation. conditions omitting static deformation are determined. effects on performance explored random excitations. proposed both better than tha...