Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

Theoretical Analysis and General Characteristics for Nonlinear Vibration Energy Harvesters

In this paper, we present a systematic theoretical and numerical study of the output performance of nonlinear energy harvesters. The general analytical expression of output power for systems with different combinations of nonlinear stiffness and nonlinear damping, as well as symmetrical and asymmetrical systems, have been derived based on harmonic balance method, observing compliance with numerical results. We theoretically prove that there is a limit power for all nonlinear systems which is determined exclusively by the vibrator mass, excitation acceleration, and mechanical damping. The results also indicate that for symmetrical stiffness systems, the asymmetrical damping components have no effect on the output performance. Additionally, we derived semi-analytical solutions of the matching loads and numerically investigated the influence of nonlinear coefficients on the output power with matched load. When the load matches device parameters and is much larger than the internal resistance, the equivalent time-average damping is equal to the mechanical damping. Although the matching load and output power vary with the nonlinear coefficients, the normalized power and matching resistance ratio follow a power function, named matching power line, which is independent of the structural parameters. With the improvement of the equivalent time-average short-circuit damping in the vibration range, the normalized power moves to the right end of the matching power line, and the output power approach to the limit power. These conclusions provide general characteristics of nonlinear energy harvesters, which can be used to guide the design and optimization of energy harvesters.

Effects of Coriolis force, vorticity and divergence on nonlinear energy conversions during different phases of July 1979 monsoon

ABSTRACT. Kinetic energy (KE) of the rotational and divergent flows and the nonlinear energy conversion between them due to the action of Coriolis force, divergence and vorticity, partition) further into stationary and transient motions are computed in the Fourier spectral domain during different phases of July 1979 monsoon over the latitudinal belt 10° S - 30° at 850 and 200 hPa and studied. It is found that nonlinear divergent to rotational KE exchange due to the action of Coriolis force is the primary contributor for all categories of stationary and transient waves at both the levels over tropics. Our results indicate that in the transient scale dynamics the wave-wave interaction plays a dominant role at 850 hPa. Divergent to rotational KE conversion by zonal-wave interaction due to divergence and wave-wave interaction due to Coriolis force are identified as important mechanisms for maintenance of rotational stationary planetary and transient synoptic scale waves respectively at 200 hPa. It is inferred that nonlinear energy conversions due to Coriolis force and vorticity oppose each other at 200 hPa. The results support that the energy conversion phenomenon may not be entirely barotropic. The importance of ageostrophic effect at different stages of monsoon activities is also shown.