Recently x-ray photoabsorption in KLL resonances of O VI was predicted @A. K. Pradhan, Astrophys. J. Lett. 545, L165 ~2000!#, and detected by the Chandra X-Xay Observatory @J. C. Lee et al., Astrophys. J. Lett. ~to be published!#. The required resonance oscillator strengths f̄ r are evaluated in terms of the differential oscillator strength d f /de that relates bound and continuum absorption. We...

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

Solving nonlinear oscillations is a challenging task due to the mathematical complexity of related differential equations. In many cases, determining oscillation’s period requires solution complicated integrals using numerical methods. To avoid complexity, there are empirical equations in literature that can be used instead rigorous analysis provide an acceptable approximation. this paper, rece...

In this study, both the ansatz and averaging methods are carried out for analyzing complex Duffing oscillators including undamped/conserved oscillator (CDO) damped/unconserved CDO to obtain some approximate analytical solutions. To analyze conserved CDO, it is reduced two decoupled oscillators. After that, exact solution of employed derive an approximation in terms Jacobi elliptic function. dam...

This paper presents a recent self-sampled-data control algorithm applied to nonlinear systems with actuator failures. Our approach uses the linear model of a given nonlinear system, and based on a granted actuator fault observer method, an asynchronous sampled-data fault compensator controller is then formulated. The proposed sampling rule is realized by using an event-detector monitoring signa...

This paper reports dynamical effects in one-dimensional locally resonant piezoelectric metastructures leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The electromechanical unit cell is built upon a linear host oscillator coupled to circuit via piezoelectricity. Semi-analytical harmonic balance (HB)-based dispersio...

We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He’s Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn u . We employed this method for higherorder approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...