We describe an integrated project that includes theoretical, numerical and experimental studies designed to facilitate teaching the non-linear post-buckling of a cantilever column to undergraduate mechanical engineering students. We present the differential equation governing the behaviour of this mechanical system…

The analytical approximate technique developed by Wu et al. for conservative oscillators with odd nonlinearity is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining Newton's method with the method of harmonic balance, analytical…

The harmonic balance method is used to construct approximate frequency–amplitude relations and periodic solutions to the relativistic oscillator. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic…

A more accurate analytical approximate expression for the slope at any point of the elastic curve of a slender cantilever column is obtained by using a heuristic but pedagogical derivation. This derivation is based on the linearization of the nonlinear…

In this paper we analyze a simple experiment to study the effects of polarized light. A simple optical system composed of a polarizer, a retarder (cellotape) and an analyzer is used to study the effect on the polarization state of…

The second-order harmonic balance method is used to construct three approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. Two procedures are used to solve the nonlinear differential…

Holographic data storage is a new optical technology, which allows an important number of bits to be stored in a recording material. In this paper, holographic data pages were stored in a polyvinyl alcohol/acrylamide (AA) photopolymer layer, using a peristrophic…

We have calculated the inelastic mean free path, stopping power, and energy-loss straggling of swift electron, proton, and α-particle beams in a broad incident energy range in four organic polymers: poly(methyl methacrylate) (PMMA), Kapton, polyacetylene (PA), and poly(2-vinylpyridine) (P2VP). These…

The effect of bulk and surface excitations to inelastic scattering in low-energy electron beam irradiation of multi-walled carbon nanotubes (MWNTs) is studied using the dielectric formalism. Calculations are based on a semiempirical dielectric response function for MWCNTs determined by means…

The asymptotic behaviours for small and large amplitudes, A, of the period for a nonlinear oscillator, where the square of the angular frequency depends quadratically on the velocity, are obtained. These asymptotic expressions are compared with the exact period, T(A),…