A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equation...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...

The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along a curvilinear trajectory in inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to solving ordinary differential equations for the complex curvature of the wave front and for ...

A simple scheme to steer optical beams is proposed. The basic idea is to impose a sinusoidal phase modulation on the optical beam and then propagate it in a nonlinear Kerr medium. Spatial phase modulation splits the input beam into multiple subbeams, while the nonlinear medium shapes a particular subbeam into a spatial soliton in such a way that most of the beam power appears in a narrow beam w...

We have developed an e cacious algorithm for simulation of the beam-beam interaction in synchrotron colliders based on the nonlinear f method, where f is the much smaller deviation of the beam distribution from the slowly evolving main distribution f0. In the presence of damping and quantum uctuations of synchrotron radiation it has been shown that the slowly evolving part of the distribution f...

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tant...

General analytical procedure for determination of the transverse feedback system parameters with a nonlinear regime of injection oscillations damping in circular accelerators and colliders is described. For this feedback loop the dependence between the kick value in the deflector and the beam deviation at the pick-up location is a nonlinear function. The beam dynamic nonlinear equation of the t...