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 ...

We consider flow along a finite-length collapsible channel driven by fixed upstream flux, where section of one wall planar rigid is replaced plane-strain elastic beam subject to uniform external pressure. A modified constitutive law used ensure that the energetically conservative. apply finite element method solve fully nonlinear steady and unsteady systems. In line with previous studies, we sh...

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 new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement w...

The paper presents the theoretical basis for the simulation of active helicopter blades. The analysis of active helicopter blades is based on models for the structure, aerodynamics, actuation and sensing. For simulation and analysis purposes, the blade structural model is discretized in space using a Galerkin approach. The effect of the integral actuation enters the beam model via an active bea...

We study nonlinear propagation of surface plasmon polaritons along an interface between metal and nonlinear Kerr dielectric. We demonstrate numerically self-focusing of a plasmon beam at large powers and the formation of slowly decaying spatial soliton in the presence of losses. We develop an analytical model for describing the evolution of spatial plasmon-solitons and observe a good agreement ...