NONLINEAR THIRD ORDER DAMPED FORCED VIBRATIONS

Oscillation of third-order nonlinear damped delay differential equations

This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral...

Forced Vibrations for a Nonlinear Wave Equation

Uniform stability of damped nonlinear vibrations of an elastic string

Abstract. Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the ...

Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures

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...

The Third Order Nonlinear Optical behavior of Poly Ether Urethane

Poly (ether) urethane close/open cell (PEUCC/PEUOC) has been prepared by using in situ polymerization approach. The third-order optical nonlinearities of dissolved samples in DMF were characterized by Z-scan technique at the measurement wavelength of 532 nm. The synthesized samples were also examined by optical microscopy and UV-Vis absorption spectroscopy. The nonlinear refractive (NLR) indice...