This paper presents a state-of-the-art review on a hot topic in the literature, i.e., vibration based energy harvesting techniques, including theory, modelling methods and the realizations of the piezoelectric, electromagnetic and electrostatic approaches. To minimize the requirement of external power source and maintenance for electric devices such as wireless sensor networks, the energy harvesting technique based on vibrations has been a dynamic field of studying interest over past years. One important limitation of existing energy harvesting techniques is that the power output performance is seriously subject to the resonant frequencies of ambient vibrations, which are often random and broadband. To solve this problem, researchers have concentrated on developing efficient energy harvesters by adopting new materials and optimising the harvesting devices. Particularly, among these approaches, different types of energy harvesters have been designed with consideration of nonlinear characteristics so that the frequency bandwidth for effective energy harvesting of energy harvesters can be broadened. This paper reviews three main and important vibration-to-electricity conversion mechanisms, their design theory or methods and potential applications in the literature. As one of important factors to estimate the power output performance, the energy conversion efficiency of different conversion mechanisms is also summarised. Finally, the challenging issues based on the existing methods and future requirement of energy harvesting are discussed.

A comprehensive review on vibration energy harvesting: Modelling and realization

Gabrio Piola’s scientific papers have been underestimated in mathematical physics literature. Indeed, a careful reading of them proves that they are original, deep and far-reaching. Actually, even ...

https://hal.archives-ouvertes.fr/hal-00869677/document

At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola

Gabrio Piola's scientific papers have been underestimated in the mathematical-physics literature. Indeed a careful reading of them proves that they are original, deep and far reaching. Actually -even if his contribution to mechanical sciences is not completely ignored- one can undoubtedly say that the greatest part of his novel contributions to mechanics, although having provided a great impetus and substantial influence on the work of many preminent mechanicians, is in fact generally ignored. It has to be remarked that authors [10] dedicated many efforts to the aim of unveiling the true value of Gabrio Piola as a scientist; however, some deep parts of his scientific results remain not yet sufficiently illustrated. Our aim is to prove that non-local and higher gradient continuum mechanics was conceived already in Piola's works and to try to explain the reasons of the unfortunate circumstance which caused the erasure of the memory of this aspect of Piola's contribution. Some relevant differential relationships obtained in Piola [Piola, 1845-6] are carefully discussed, as they are still nowadays too often ignored in the continuum mechanics literature and can be considered the starting point of Levi-Civita's theory of Connection for Riemannian manifolds.

At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola

The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0790

Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium

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Introduction To Perturbation Techniques

https://hal.archives-ouvertes.fr/hal-00788555/document

Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables

https://hal.archives-ouvertes.fr/hal-00788461/document

On the effect of twist angle on nonlinear galloping of suspended cables

A general, nonlinear, multi-d.o.f. structure, excited by harmonic external force in 1:1 resonance with one of the modes of the system, is considered. The structure is attached to an essentially nonlinear oscillator, with small mass and damping (Nonlinear Energy Sink, NES). The scope of the NES is to passively control the amplitude of vibrations of the main structure. A mixed Multiple Scale/Harmonic Balance Method (MSHBM) is proposed to get the differential equations describing the slow- and fast-flow dynamics of the whole structure. The main advantage of the procedure is that no complexification-averaging is required, so that the analysis is reconducted in the framework of the classical perturbation techniques.

/pdf/dynamic-analysis-of-externally-excited-nes-controlled-1mgf41nmbn.pdf

Dynamic analysis of externally excited NES-controlled systems via a mixed Multiple Scale/Harmonic Balance algorithm

The issue to passively control aeroelastic instability of general nonlinear multi-d.o.f. systems, suffer- ing Hopf bifurcation, is addressed. The passive device consists of an essentially nonlinear oscillator (Nonlinear Energy Sink), having the task to transfer energy from the main to the secondary structure. The mathematical problem is attacked by a new algorithm, based on a suitable combination of the Multiple Scale and the Harmonic Balance Methods. The procedure is able to furnish the codimension-2 invariant manifold on which the motion occurs, thus revealing the passive character of the oscillations of the NES. The algorithm also provides the bifur- cation equations, which govern the slow flow on the manifold, expressed in terms of the main structure amplitude and phase of motion. It is shown that NES, under suitable conditions, can shift forward the bifurcation point, and, moreover, it can reduce the amplitude of the limit cycles. Theory is applied to a sample structure already studied in literature, consisting of a two-d.o.f. rigid wing under steady wind. Relevant asymptotic results are compared, for validation purposes, with numerical simulations.

/pdf/aeroelastic-instability-analysis-of-nes-controlled-systems-3m6hczxj0s.pdf

Aeroelastic instability analysis of NES-controlled systems via a mixed multiple scale/harmonic balance method

https://hal.archives-ouvertes.fr/hal-00788260/document

Daniele Zulli

Papers

Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables

On the effect of twist angle on nonlinear galloping of suspended cables

Dynamic analysis of externally excited NES-controlled systems via a mixed Multiple Scale/Harmonic Balance algorithm

Aeroelastic instability analysis of NES-controlled systems via a mixed multiple scale/harmonic balance method

Parametric, external and self-excitation of a tower under turbulent wind flow