A second-order modified rational harmonic balance method is used for approximately solve the nonlinear differential equation that governs the oscillations of a system typified as a mass attached to a stretched elastic wire for which the restoring force for this…

Obtaining holographic volume gratings with high diffraction efficiencies that can be used under white light has been a serious problem for the polyvinyl alcohol-acrylamide-based photopolymers developed by other researchers. In this paper we propose to eliminate the residual monomer in…

Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and…

An analytical approximate procedure for a class of conservative single degree-of-freedom nonlinear oscillators with odd non-linearity is proposed. This technique is based on the generalized harmonic balance method in which analytical approximate solutions have rational forms. Unlike the classical harmonic…

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 dynamically shifted oscillator. This nonlinear oscillator is described by an equation of motion…

We report for the first time the results of a comparative performance study of silver-halide sensitized gelatin (SHSG) holograms recorded in the familiar Agfa 8E75 HD plates and the new BB-640 plates manufactured by Holographic Recording Technologies. High diffraction efficiency…

A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analyzed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force and this allows us to approximate the original nonlinear differential equation…

In their comment, Qing-Yin and Pei derived another analytical approximate expression for the large-angle pendulum period, which they compare with other expressions previously published. Most of these approximate formulas are based on the approximation of the original nonlinear differential equation…

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…

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analyzed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid…