Abstract Deep cantilever beams, modeled using Timoshenko beam kinematics, have numerous applications in engineering. This study deals with the nonlinear dynamic response a nonprismatic characterized by considering deformed configuration of axis. The mathematical model is derived extended Hamilton’s principle under condition finite deflections and angles rotation. discrete motion constructed bas...

In this paper we generalize the automated multi–level substructuring method to certain classes of nonlinear eigenvalue problems which can be partitioned into an essential linear and positive definite pencil and a small residual. The efficiency of the method is demonstrated by numerical examples modeling damped vibrations of a structure with nonproportional damping, a gyroscopic eigenproblem, an...

Unexpectedly high Raman scattering activity of carbon-carbon bond length vibrations was found in polyacetylene nanoparticles. For exciting photon energy in the transparency range of nanopolyacetylene we observed extremely high Raman scattering cross section and high intensity ratio of anti-Stokes to Stokes bands. Furthermore, the Raman activity in trans-nanopolyacetylene is characterized by int...

We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT) corresponding to complete energy exchange is introduced. In certain sense this is an alternative to the nonlinear normal mode (NNM) characterized by complete energ...

The q–deformation of harmonic oscillators is shown to lead to q–nonlinear vibrations. The examples of q–nonlinearized wave equation and Schrödinger equation are considered. The procedure is generalized to broader class of nonlinearities related to other types of deformations. The nonlinear noncanonical transforms used in the deformation procedure are shown to preserve in some cases the linear d...