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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

“Overkill” is characterized by the finding of excessive wounds on the victim’s body. Despite the large use of this term, it does not have a definition in the literature yet. Our study aimed to analyze the information related to the dynamics of overkill cases, collecting objective variables, and producing a profile of the players involved in this type of homicides. Data on 71 overkill cases from reports of the autopsies performed in the Section of Legal Medicine of the University of Rome Tor Vergata from 1 January 2000 to 31 December 2020 were collected. The victims and the perpetrators of overkill shared similar characteristics: they were usually male aged between 20 and 50 years, more likely in the 20–35 years range; victims however also showed another age peak in the range 50–55 years. The type of damage can be linked to the sole action of a cold weapon or the simultaneous use of multiple harmful tools with no significant differences. The most common motive proved to be a dispute for futile reasons; however, in the case of a single perpetrator of the crime, the economic and passionate motives are as frequent as the previous one. Implications of the findings and avenues for future research are discussed.

The main aim of this study was to investigate the post-mortem proteolytic degradation process of selected tissue antigens and correlate it to the post-mortem interval. During the autopsy of 12 cadavers (time interval ranging 1 day–2 years after death) samples of skin, liver, kidney, and spleen were collected. All samples were formalin-fixed and paraffin-embedded. Four µm paraffin sections were used for hematoxylin–eosin staining and immunohistochemical analysis (Ki67, Vimentin, Pan cytokeratin, and CD20). Data reported here show that immunohistochemical reactivity preservation was related to the characteristics of the tissues. In particular, the most resistant tissue was the skin, where the autolysis phenomena were not appreciable before 5 days. On the contrary, the liver and the spleen underwent early autolysis, while the kidney displayed an early autolysis of the tubules and a late one of the glomeruli. As concerns specific antigens, immunoreactivity was lost earliest for nuclear antigens as compared to cytoplasmic ones. In conclusion, our results demonstrate that immunohistochemical detection of specific antigens may be useful in estimating the post-mortem interval, especially when we need to know whether the post-mortem interval is a few days or more than 7–10 days.

Summary Conventional well plug and abandonment (P&A) can sever and remove the tubing to access casing or leave it in situ when it does not interfere with providing a seal over an indefinite time frame. This paper assesses the viability of pushing rather than pulling severed production tubing to gain casing access. The P&A decision to push, pull, or leave the tubing in situ depends on confirming existing seals and then placing suitable sealants, such as cement, to keep the risks of future well leakages as low as reasonably practicable (ALARP). Pushing or compacting tubing into the liquid space of a well could be used with smaller rigless units, which cannot hoist the production tubing, but can use production intervention or decommissioning logistics with coiled tubing or wireline cutting and severance. Associated pumps could then drive an inflatable piston to compact split and severed tubing into a lower liquid space to access casing for logging and P&A plugging. Rigless tools and methods have provided dramatic cost savings where casing access was not needed, and thus the present study investigates the viability of accessing casing by means of pushing or compacting tubing to extend rigless P&A use and savings. The viability of pushing and compacting North Sea sizes and grades were confirmed in real-scale physical-compaction simulations of production-tubing joints pulled from offshore wells. Independent small-scale physical simulations and numerical modeling then confirmed that the real-scale results were predictable and repeatable to demonstrate an ability to design and provide a window or gap in a production-tubing string for use by other P&A methods.

Made available in DSpace on 2020-12-12T02:41:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 Conventional vibration isolators have been used for a long time to isolate a receiver from a source of disturbance. Probably, the most popular example of vibration isolators can be found in automotive suspensions. In vehicles, the spring and damper elements are used to damp road vibration and also to maintain drive handling stability. In this process, the mechanical energy is converted into heat and dissipated in the damper element. The idea of recovering part of the energy has become an attractive topic among researchers over the last three decades. In this context, this study investigates the possibility of replacing the damper element with an electrical circuit coupled to the mechanic system using a permanent magnet/coil transducer. Different electrical circuit configurations are analyzed to study the influence of damping on the mechanical system. Expressions to obtain critical damping and optimum damping to reduce the maximum peak in the frequency response are developed and presented in tabular form for ease of reference. The methodology is then applied to a two-degree-of-freedom system representing a quarter-vehicle suspension model. The results show that coupled electrical circuits can be used to replace fluid dampers in the design of vibration isolators without performance loss. School of Engineering São Paulo State University (UNESP) School of Engineering University of Glasgow School of Engineering São Paulo State University (UNESP)

The SARS-CoV-2 spread is a threatening and challenging issue for correctional systems worldwide because of many factors, particularly overcrowding and of the intrinsic characteristics of the population. The prevention measures adopted by the Italian Government were aimed to protect and preserve both inmates’ and prison workers’ health. The present study aimed to evaluate the efficacy of the adopted strategies. Methods: Data regarding Italian prisons’ occupation and prisoners’ population from January 2019 to June 2021, as well as the cumulative weekly increase of confirmed cases and the number of doses of vaccine administered among the population of inmates, the prison workers, and Italian population from November 2020 to the end of June 2021, were collected. Results: Prisons’ occupation dropped from 120% to 106% after the beginning of the pandemics. The confirmed cases between inmates were consistently lower than among the Italian population and prison workers. A time-series chart showed a time lag of one week between the peaks of the different population. Conclusions: The containing strategies adopted by the Italian correctional system have proved their effectiveness in terms of the prevention and protection of both inmate and staff health.

Most of the optimisation studies of Vibration Energy Harvesters (VEHs) account for a single output quantity, e.g. frequency bandwidth or maximum power output, but this approach does not necessarily maximise the system efficiency. In those applications where VEHs are suitable sources of energy, to achieve optimal design it is important to consider all these performance indexes simultaneously. This paper proposes a robust and straightforward multi-objective optimisation framework for Vibration Piezoelectric Energy Harvesters (VPEHs), considering simultaneously the most crucial performance indexes, i.e., the maximum power output, efficiency, and frequency bandwidth. For the first time, a rigorous formulation of efficiency for Multi-Degree of Freedom (MDOF) VPEHs is here proposed, representing an extension of previous definitions. This formulation lends itself to the optimisation of FE and MDOF harvesters models. The optimisation procedure is demonstrated using a planar-shape harvester and validated against numerical results. The effects of changing some structural parameters on the harvester performance are investigated via sensitivity analysis. The results show that the proposed methodology can effectively optimise the global performance of the harvester, although this does not correspond to an improvement of every single index. Furthermore, the optimisation of each performance index individually results in a variety of design configurations that greatly differs from one another. It is here demonstrated that the design obtained with the multi-objective function here proposed is similar to the design obtained when optimising the efficiency.

This paper provides a recent legal case which calls into discussion the women’s safe access to voluntary termination of pregnancy (VTP) after the first 90 days. On 15 January 2021, the Italian Supreme Court sentenced a physician to damage compensation because he did not correctly inform the patient, in her 22nd week of pregnancy, about the risks to the fetus relating to an infection from cytomegalovirus (CMV). The option for VTP was not offered since, at the time of the woman’s request, medical investigations did not show the evidence of fetal malformations, neither there were concrete risks for the life of the mother, as Italian law requires. The baby was born with severe brain injuries. The case is noteworthy because it offers a new precedent to extend legal requirements for late VTP. The impact of this decision must be tested in the clinical practice. Further studies are necessary to evaluate possible law amendments extending access conditions for this practice and new policies promoting the strengthening of informative and assistance procedures, including psychological help, to the pregnant woman are needed, as well.

The use of reduced-order models (ROMs) for nonlinear systems has received significant attention due to their potential to greatly reduce computational cost, compared to full nonlinear finite-element models. Here, we consider and compare two indirect methods; the applied modal force and enforced modal displacement techniques, paying particular attention to the effect of nonlinear cross-coupling terms. The analysis we present shows that the applied modal force technique is able to account for some effects arising from modes that are not retained in the ROMs, but the resulting accuracy of the ROM depends on the amplitudes selected for the set of forces used to estimate the coefficients of the ROMs. This analysis also shows that the enforced modal displacement technique does not compensate for the effect of modal interactions with modes that are not included in the ROM, but its accuracy is independent of the amplitude of the forces used to estimate the coefficients. The mechanisms that lead to the differences between these techniques is firstly demonstrated using a two conceptually-simple, discrete systems, before a nonlinear beam model is considered.

Some creatures, such as eels, snakes and slender fish use body undulations to move the fluid around them and create propulsion; similarly, travelling waves in structures can be used as an alternative propulsion system. Based on this bio-inspired mechanism, the application of travelling waves is widespread in engineering, e.g. motors, pump systems and transport devices. However, generating high amplitude travelling waves is not as easy as generating standing waves, since travelling waves are generally observed away from resonance. Also, the reflection of the waves at the boundaries can interact destructively further reducing their amplitude. This paper investigates the characteristics of the experimental rig built for emulating the propulsion mechanism used in undulatory locomotion, introducing the conceptual design, and investigating the features that promote travelling waves. Finally, an analysis of the influence of individual components in the design is carried out.

Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freedom oscillator. The DNF method includes an inherent detuning, which can be physically interpreted as a series expansion about the natural frequencies of the underlying linear system and has previously been shown to increase its accuracy. In contrast, there is no such inbuilt detuning for MS, although one may be, and usually is, included. This paper investigates the use of the DNF detuning as the chosen detuning in the MS method as a way of equating the two techniques, demonstrating that the two can be made to give identical results up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon ^2$$\end{document}ε2 order. For the examples considered here, the resulting predictions are more accurate than those provided by the standard MS technique. Wolfram Mathematica scripts implementing these methods have been provided to be used in conjunction with this paper to illustrate their practicality. Electronic supplementary material The online version of this article (10.1007/s11071-018-4534-1) contains supplementary material, which is available to authorized users.

Survival of entropy waves during their advection throughout a combustor is central to the generation of entropic sound and the subsequent effects upon thermoacoustic stability of the system. However, the decay and spatial non-uniformity of entropy waves are largely ignored by the existing models used for the calculation of entropy noise generation. Recent investigations have demonstrated the complex spatio-temporal dynamics of entropy waves and cast doubts on the sufficiency of the one-dimensional approach, conventionally used for the analysis of these waves. Hence, this paper proposes a novel approach to the low-order modelling of entropy wave evolution wherein the wave is described by the two states of position and amplitude in the streamwise direction. A high-order model is first developed through direct numerical simulation of the advection of entropy waves in a fully developed, heat transferring, compressible, turbulent channel flow. The data are then utilised to build and validate a series of nonlinear, low-order models that provide an unsteady two-dimensional representation of the decaying and partially annihilating entropy waves. It is shown that these models need, at most, approximately 12.5% of the total trace of entropy wave advection to predict the wave dynamics accurately. The results further reveal that the existing linear low-order models are truly predictive only for the entropy waves with less than 2% increase in the gas temperature compared to that of the surrounding flow. Yet, in agreement with the assumption of existing models, it is shown that entropy waves travel with the mean flow speed.

Made available in DSpace on 2020-12-12T02:47:33Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 Background: Viscoelasticity is a property of materials that present elastic and viscous behavior when they experience deformation. The simplest model that can represent the viscoelastic behavior is generally called the Standard Linear Solid model or Zener model. Purpose: Based on the Zener model, the objective of this paper is to present the concept and the design of equivalent electromechanical systems that permit the emulation of viscoelastic behavior. Besides, the possibility of harvesting the energy normally wasted as heat in viscoelastic materials is also considered. Methods: The methods applied in this paper are based on the analytic development of equations in time and frequency domain, including optimization and numerical simulations. Results: Equivalent equations were derived considering the mechanical and electromechanical analogy. These equations were verified by correlating known results from the literature. New results for white noise excitation were obtained and optimization of power harvesting was performed. Conclusions: The proposed electromechanical system is equivalent to the Zener system if its mechanical damping is small when compared to the equivalent electrical damping effect. Resulting in viscoelastic behavior without the need of viscoelastic materials, electromechanical equivalent Zener systems also allow energy recovery whilst maintaining vibration isolation. School of Engineering São Paulo State University (UNESP) School of Engineering University of Glasgow School of Engineering São Paulo State University (UNESP)

BACKGROUND AND AIM Cardiovascular diseases (CVDs) are the most frequent causes of death in the world. Inflammation and oxidative damage contribute significantly to the development of atherosclerosis and CVDs. European Food Safety Authority scientific opinion has acknowledged that hydroxytyrosol (3,4-dihydroxyphenylethanol) and derivatives, contained in extra virgin olive oil (EVOO), typically used in Mediterranean diet may play a crucial role in the reduction of the inflammatory pathway and in the prevention of CVDs. The aim of the study was to determine the effect in healthy volunteers of 25 g of phenols-rich EVOO (p-EVOO). METHODS The clinical study was a randomized, controlled trial to determine the acute effect in the postprandial time of 25 g of p-EVOO. We evaluated nutritional status using anthropometric parameters, body composition, serum metabolites, oxidative stress biomarkers and gene expression of eight genes related to oxidative stress and human inflammasome pathways, lasting 2 h after p-EVOO administration. Twenty-two participants resulted as eligible for the study. RESULTS A significant reduction of oxidized LDL, malondialdehyde, triglycerides and visceral adiposity index was highlighted (P

It is possible to use numerical techniques to provide solutions to nonlinear dynamical systems that can be considered exact up to numerica ltolerances. However, often, this does not provide the user with sufficient information to fully understand the behaviour of these systems. To address this issue, it is common practice to find an approximate solution using an analytical method, which can be used to develop a more thorough appreciation of how the parameters of a system influence its response. This paper considers three such techniques – the harmonic balance, multiple scales, and direct normal form methods – in their ability to accurately capture the forced response of nonlinear structures. Using frequency detuning as a method of comparison, it is shown that it is possible for all three methods to give identical solutions, should particular conditions be used.

Introduction. Inflammation is associated with obesity condition and plays a pivotal role in the onset and progression of many chronic diseases. Among several nutraceutical foods, hazelnuts (Corylus avellana L.) are considered an excellent anti-inflammatory and hypolipidemic food being the second richest source of monounsaturated fatty acids among nuts and because they are rich in vitamins, minerals, and phenolic compounds. Materials and Methods. A prospective pilot clinical trial on 24 healthy volunteers who consumed daily, as a snack, 40 g of hazelnuts (261.99 kcal/1096.17 kJ) for six weeks was conducted. Anthropometric measurements, body composition analysis, and nutrigenomic analysis on 12 anti-inflammatory and antioxidant genes were evaluated at baseline (T0) and after hazelnut intervention (T1). Results. No significant changes were detected on body composition analysis after hazelnut consumption. Conversely, significant upregulation was detected for SOD1 (2−ΔΔCt=2.42), CAT (2−ΔΔCt=2.41), MIF (2−ΔΔCt=4.12), PPARγ (2−ΔΔCt=5.89), VDR (2−ΔΔCt=3.61), MTHFR (2−ΔΔCt=2.40), and ACE (2−ΔΔCt=2.16) at the end of the study. Conclusions. According to emerging evidences, hazelnut consumption does not lead to weight gain probably due to the improvement of the body’s antioxidant capacity by the upregulation of genes implied in oxidant reactions and inflammation.

The cochlea, in the mammalian inner ear, transduces acoustic waves into electrical signals that are transmitted to the brain. One of the critical functions of the cochlea is its biological nonlinear behavior that amplifies faint sounds and compresses high sound levels. Previously, authors mimicked the aforementioned nonlinear characteristics in piezoelectric augmented structural cantilevers through nonlinear feedback controllers. The present effort is a continuation of the previous studies in the development of micro-electro-mechanical system (MEMS) scale artificial hair cells (AHCs).

The aim of this study was to evaluate the effect of resveratrol supplementation of semen extender on fertility parameters of frozen-thawed buffalo sperm. After the initial semen assessment, buffalo semen was cryopreserved in BioXcell containing 0 (control group), 0.5, 1, 10, and 50-μM resveratrol. After thawing, viability, motility, and capacitation status (assessed by localization of phosphotyrosine-containing proteins) were evaluated. Based on the results of the dose-response trial, the concentration of 50 μM was selected for further assessments, such as membrane integrity, total antioxidant capacity, reactive oxygen species, and lipid peroxidation (LPO) levels. Moreover, in vitro fertilizing ability by heterologous IVF and in vivo fertility were assessed. No differences among groups were recorded in sperm motility and viability (on average 52.3 ± 2.1% and 76.6 ± 1.3%, respectively). However, data showed a resveratrol dose-dependent effect on sperm capacitation status, with a significant reduction of the cryopreservation-induced capacitation with the higher concentrations tested. In particular, both 10- and 50-μM resveratrol increased (P

This paper considers isolated responses in nonlinear systems; both in terms of isolas in the forced responses, and isolated backbone curves (i.e. the unforced, undamped responses). As isolated responses are disconnected from other response branches, reliably predicting their existence poses a significant challenge. Firstly, it is shown that breaking the symmetry of a two-mass nonlinear oscillator can lead to the breaking of a bifurcation on the backbone curves, generating an isolated backbone. It is then shown how an energy-based, analytical method may be used to compute the points at which the forced responses cross the backbone curves at resonance, and how this may be used as a tool for finding isolas in the forced responses. This is firstly demonstrated for a symmetric system, where an isola envelops the secondary backbone curves, which emerge from a bifurcation. Next, an asymmetric configuration of the system is considered and it is shown how isolas may envelop a primary backbone curve, i.e. one that is connected directly to the zero-amplitude solution, as well as the isolated backbone curve. This is achieved by using the energy-based method to determine the relationship between the external forcing amplitude and the positions of the crossing points of the forced response. Along with predicting the existence of the isolas, this technique also reveals the nature of the responses, thus simplifying the process of finding isolas using numerical continuation.

After death, the corpse is subjected to many different post mortem phenomena that change the whole biochemical and physical structures of the vital body. Those phenomena have different evolutions depending on numerous factors typical of the death body and of the setting where the body lies. Mummification is one of the special transformative process that consist in the drying of the entire body structures and requires particular wheatear condition and timing.

The ability to accurately model the behaviour of a mechanical structure using a fraction of the original number of degrees of freedom is pursued throughout the study of dynamics and, in recent years, this has been key in the study of nonlinear systems. One of the first ways in which this was implemented was through the Galerkin method, and it has been continually used since its original derivation due to the fact that it does not require the use of any commercial finite element packages. In fact, the modeshapes of the system have been previously calculated analytically and the linear natural frequencies calculated numerically, leading to large reductions in the amount of time needed to develop the model.

Nonlinear normal modes, which describe the unforced, undamped responses of nonlinear systems, are often used for understanding the dynamic behaviour of nonlinear structures in engineering. As such, a key property of nonlinear normal modes (NNMs) is that they relate to the dynamic behaviour of the system when forcing and damping are applied. Previous work has shown that an extremely large number of NNMs may be predicted for relatively simple systems; however only a small number of these NNMs have a meaningful influence on the forced and damped dynamics. As such, a method for determining which NNMs are significant (i.e., strongly relate to the forced dynamics) and which are not is crucial for the use of NNMs as a tool for understanding nonlinear systems.

Modern finite element (FE) packages are capable of capturing nonlinear behaviour in extremely complex structures. However, due to the scale of these models, full dynamic analysis is often prohibitively expensive. An alternative approach is to use the FE models to derive reduced-order models (ROMs) which capture the dynamic behaviour of interest at a significantly lower computational cost. An automatic identification of the stated ROMs is powerful and desirable when parametric, sensitivity and uncertainty analysis is of interest. The authors implemented in Matlab a strategy to automatically compute the reduced order model and investigate the effects of parametric variation exchanging information with FEM software. In the strategy it is adopted the Applied Modal Force (AMF) approach, where a force is applied to the FE model and the resulting displacements are used to identify coefficients of the ROM, as is done in the ICE method. The developed techniques are presented in the paper and validated considering a crossed beam structure modelled in Abaqus.

This paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic Bayesian framework, employing a Markov chain Monte Carlo algorithm. This approach uses analytical models to describe the unforced, undamped dynamic responses of structures in the frequency–amplitude domain, known as the backbone curves. The analytical models describing these backbone curves are then fitted to measured responses, found using the resonant-decay method. To investigate the proposed identification method, a nonlinear two-degree-of-freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found. These expressions are then used, in conjunction with the backbone curve data found through simulated experiment, to estimate the system parameters. It is shown that the use of these computationally-cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour, providing an identification procedure that is both fast and accurate. Furthermore, for the example structure, it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well-away from the backbone curve data provided; specifically the existence of an isola is predicted.

In this paper the $$N-1$$ nonlinear modal interactions that occur in a nonlinear three-degree-of-freedom lumped mass system, where $$N=3$$ , are considered. The nonlinearity comes from springs with weakly nonlinear cubic terms. Here, the case where all the natural frequencies of the underlying linear system are close (i.e. $$\omega _{n1}: \omega _{n2}:\omega _{n3} \approx 1:1:1$$ ) is considered. However, due to the symmetries of the system under consideration, only $$N-1$$ modes interact. Depending on the sign and magnitude of the nonlinear stiffness parameters, the subsequent responses can be classified using backbone curves that represent the resonances of the underlying undamped, unforced system. These backbone curves, which we estimate analytically, are then related to the forced response of the system around resonance in the frequency domain. The forced responses are computed using the continuation software AUTO-07p. A comparison of the results gives insights into the multi-modal interactions and shows how the frequency response of the system is related to those branches of the backbone curves that represent such interactions.

Energy harvesters based upon resonant mass-spring-damper systems can only generate useful power over a narrow range of excitation frequencies. This is a significant limitation in applications where the vibration source frequency changes over time. In this paper, an active electrical load is presented which can overcome the bandwidth limitations by parametrically tuning the overall harvester system. The electrical tuning technique synthesizes an optimum reactive load with high-efficiency switch-mode electronics, which also provides rectification, feeding the energy harvested into a dc store. The method is shown to be effective at increasing the power frequency bandwidth of resonant type harvesters and offers the capability of autonomous operation. The theoretical basis for the technique is presented and verified with experiment results. The paper illustrates the challenges of implementing the power electronic converter for a low-quiescent power overhead and in choosing the control architecture and tuning algorithms.

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.

The exploitation of nonlinear behavior in vibration-based energy harvesters has received much attention over the last decade. One key motivation is that the presence of nonlinearities can potentially increase the bandwidth over which the excitation is amplified and therefore the efficiency of the device. In the literature, references to resonating energy harvesters featuring nonlinear oscillators are common. In the majority of the reported studies, the harvester powers purely resistive loads. Given the complex behavior of nonlinear energy harvesters, it is difficult to identify the optimum load for this kind of device. In this paper the aim is to find the optimal load for a nonlinear energy harvester in the case of purely resistive loads. This work considers the analysis of a nonlinear energy harvester with hardening compliance and electromagnetic transduction under the assumption of negligible inductance. It also introduces a methodology based on numerical continuation which can be used to find the optimum load for a fixed sinusoidal excitation.

Modelling the dynamics of nonlinear systems poses a much more challenging problem than for their linear counterparts; as such, analytical solutions are rarely achievable and numerical or analytical approximations are often necessary to understand the system’s behaviour. While numerical techniques are undoubtedly accurate, it is possible to gain a greater understanding of the processes underpinning the workings of the dynamics. Therefore, it is valuable to investigate the accuracy and practicality of the aforementioned analytical approximation techniques and compare the results with numerical which are known to be accurate. In this paper, the unforced, undamped dynamics (known as backbone curves) of a non-symmetric two-mass oscillator will be calculated using the second-order normals forms (SONF), harmonic balance, and multiple scales techniques. The results of these will then be compared to responses found using numerical continuation. Furthermore, the forced responses will be approximated using the SONF and harmonic balance techniques. In addition, recent work has reported the possibility of using such analytical expressions for parameter estimation from experimental data.

When a nonlinear system is expressed in terms of the modes of the equivalent\ud linear system, the nonlinearity often leads to modal coupling terms between\ud the linear modes. In this paper it is shown that, for a system to exhibit\ud an internal resonance between modes, a particular type of nonlinear coupling\ud term is required. Such terms impose a phase condition between linear\ud modes, and hence are denoted phase-locking terms. The effect of additional\ud modes that are not coupled via phase-locking terms is then investigated by\ud considering the backbone curves of the system. Using the example of a twomode\ud model of a taut horizontal cable, the backbone curves are derived for\ud both the case where phase-locked coupling terms exist, and where there are\ud no phase-locked coupling terms. Following this, an analytical method for\ud determining stability is used to show that phase-locking terms are required\ud for internal resonance to occur. Finally, the effect of non-phase-locked modes\ud is investigated and it is shown that they lead to a stiffening of the system.\ud Using the cable example, a physical interpretation of this is provided.

This article aims to explore the regulatory and medicolegal aspects of experimental drug trials. Firstly, the authors provide definitions of drug according to WHO, the European Community and our official Pharmacopoeia, and that of experimental studies. They then explain the distinction between pure or basic research and drug trials and explain the various phases of the latter. Besides providing definitions, and exploring doctrinal, theoretical but also practical aspects of drug trials, the authors also discuss and analyze legislative aspects, with particular reference to the Italian legislative framework, and medicolegal issues, including informed consent, effects on humans, and professional responsibility.

This paper presents a novel design for a vibrational energy harvester. The design uses high permeability magnetic materials which brings about two key advantages. First, it gives strong coupling between the mechanical and electrical domains, thus enabling effective energy conversion. Second, it gives the device a bi-stable compliance characteristic, which gives the harvester a broad-band frequency response. An explicit analytical model is developed using a combination of experimental data and finite element modelling in order to accurately incorporate the magnetic forces. The model is then validated using dynamic tests of the experimental rig. The main features of the dynamic response of the bi-stable oscillator are highlighted and benefits discussed in the context of energy harvesting. Finally, comments are made on the relationship between the complicated behaviour resulting from the bi-stable compliance characteristic and the benefits of increased electrical coupling.

Nonlinear structures exhibit complex behaviors that can be predicted and analyzed once a mathematical model of the structure is available. Obtaining such a model is a challenge. Several works in the literature suggest different methods for the identification of nonlinear structures. Some of the methods only address the question of whether the system is linear or not, others are more suitable for localizing the source of nonlinearity in the structure, only a few suggest some quantification of the nonlinear terms. Despite the effort made in this field, there are several limits in the identification methods suggested so far, especially when the identification of a multi-degree of freedom (MDOF) nonlinear structure is required. This work presents a novel method for the identification of nonlinear structures. The method is based on estimating backbone curves and the relation between backbone curves and the response of the system in the frequency domain. Using a Bayesian framework alongside Markov chain Monte Carlo (MCMC) methods, nonlinear model parameters were inferred from the backbone curves of the response and the Second Order Nonlinear Normal Forms which gives a relationship between the model and the backbone curve. The potential advantage of this method is that it is both efficient from a computation and from an experimental point of view.

In this paper, a three degree-of-freedom oscillator with cubic elastic nonlinearities is considered. For this system, the natural frequencies of its underlying linear modes are set to be approximately equal so that \(\omega _{n1}:\omega _{n2}:\omega _{n3} \approx 1:1:1\). As a result, the nonlinear normal modes in the system are able to potentially interact with each other. In this study, the underlying unforced and undamped system is considered. The second-order normal forms technique is used to estimate the backbone curves of the system, which give information on the frequency and modal response amplitudes and phases. Then, through choosing the activate modes and their specific phase differences, the single-, double- and triple-mode backbone curves are computed. The results show the effect of nonlinear multi-mode interactions on the dynamic response of nonlinear oscillators. These insights will be beneficial when considering how a structure will respond and for the system identification of nonlinear multi-degree-of-freedom systems.

Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.

The majority of work in the literature on modal interaction is based on two degree-of-freedom nonlinear systems with cubic nonlinearities. In this paper we consider a three degree-of-freedom system with nonlinear springs containing cubic nonlinear terms. First the undamped, unforced case is considered. Specifically the modal interaction case that occurs when all the underlying linear modal frequencies are close is considered (i.e. \(\omega _{n1}:\omega _{n2}:\omega _{n3} \simeq 1: 1: 1\)). In the case considered, due to the symmetry of the system, the first mode is linear and not coupled with the other two modes. The analysis is carried out by using a normal form transformation to obtain the nonlinear backbone curves of the undamped, unforced response. In addition, the frequency response function (FRF) of the corresponding lightly damped and harmonically forced system obtained from the continuation software AUTO-07p is compared with the backbone curves to show its validity for predicting the nonlinear resonant frequency and amplitude. A comparison of the results gives an insight into how modal interactions in the forced-damped response can be predicted using just the backbone curves, and how this might be applied to predict resonant responses of multi-modal nonlinear systems more generally.

In nonlinear systems the constituent linear modes may interact due to internal resonance. In this paper we classify two distinct classes of modal interactions: phase-locked interactions, in which there is a specific phase between the interacting modes; and phase-unlocked interactions, in which the modes may interact regardless of their phase. This discussion is accompanied by the study of an example structure in which both classes of interaction may be observed. The structure is used to demonstrate the differences between phase-locked and phase-unlocked interactions, both in terms of their individual influence on the response, and in terms of their influence on each other when both classes of interactions are present.

This paper considers the dynamic response of coupled, forced and lightly damped nonlinear oscillators with two degree-of-freedom. For these systems, backbone curves define the resonant peaks in the frequency-displacement plane and give valuable information on the prediction of the frequency response of the system. Previously, it has been shown that bifurcations can occur in the backbone curves. In this paper, we present an analytical method enabling the identification of the conditions under which such bifurcations occur. The method, based on second-order nonlinear normal forms, is also able to provide information on the nature of the bifurcations and how they affect the characteristics of the response. This approach is applied to a two-degree-of-freedom mass, spring, damper system with cubic hardening springs. We use the second-order normal form method to transform the system coordinates and identify which parameter values will lead to resonant interactions and bifurcations of the backbone curves. Furthermore, the relationship between the backbone curves and the complex dynamics of the forced system is shown.

In this paper we discuss an analytical method to enable modal reduction of weakly nonlinear systems with multiple degrees-of-freedom. This is achieved through the analysis of backbone curves—the response of the Hamiltonian equivalent of a system—which can help identify internal resonance within systems. An example system, with two interacting modes, is introduced and the method of second-order normal forms is used to describe its backbone curves with simple, analytical expressions. These expressions allow us to highlight which particular interactions are significant, as well as specify the conditions under which they are important. The descriptions of the backbone curves are validated against the results of continuation analysis, and a comparison is also made with the response of the system under various levels of forcing and damping. Finally, we discuss how this technique may be expanded to systems with a greater number of modes.