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 paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyap...

This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to inve...

*Correspondence: [email protected] 2School of Mathematical Sciences, Soochow University, Suzhou, 215006, China Full list of author information is available at the end of the article Abstract The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic...