The fastest insight into the large amplitude vibration of a string

This paper recommends a simple and excusive approach to a strongly nonlinear oscillator. Its frequency property can be immediately obtained by the simplest calculation. The results show that the method leads to an approximate solution with relatively high accuracy. Considering the simplest solution process, this paper provides a highly efficient tool for fast determination of the amplitude-frequency relationship of a nonlinear oscillator. The large amplitude vibration of a string is used as an example to illustrate the solution process.

A twisting vibration based energy harvester for ultra-low frequency excitations

Ultra-low frequency mechanical excitations are omnipresent in our surrounding environment, but the efficient exploitation of them is generally difficult because they normally drive the widely reported cantilevered harvesters to work under non-resonant conditions. Although the frequency up-conversion strategy has been proposed to mitigate this issue, it usually leads to complicated structures. This paper reports a novel energy harvesting approach based on the twisting vibration of a string-driven rotor. To examine the feasibility of this approach, an electromagnetic energy harvester is designed, which is composed of a lid, a rotor with embedded magnets, a pendant, and a tube with pick-up coils attached to the outer surface. The rotor is suspended between the lid and the pendant through a piece of string, and then actuated by the ambient excitations through the string. Under the excitations produced by a crank-slider mechanism, the designed harvester can generate useful electric outputs that are proportional to the excitation amplitude, the initial angle between the pendant and lid, and the excitation frequency. Moreover, the harvester can also provide 0.034 mW power when it is periodically pulled by the human hand at approximately 1 Hz. This study demonstrates the potential application of the string-driven rotor in collecting energy from ultra-low frequency excitations.

Generalized Multi-Symplectic Integrator for Vibration of a Damping String with the Driving Force

Based on multi-symplectic theory, a generalized multi-symplectic formulation is used to simulate the vibration of a string with damping and driving forces. First, by introducing the canonical momenta, the generalized multi-symplectic form for the governing equation of a damping string is derived. Then, two multi-symplectic Box schemes are developed to obtain the discretization schemes for the generalized multi-symplectic form. Finally, numerical examples are carried out to verify the effectiveness of proposed schemes. Numerical results show that the proposed schemes can directly preserve the dynamic characteristics of the system, especially the non-conservative properties caused by damping and driving forces. The research can give a different approach when dealing with the non-conservative dynamics problems.