Large Amplitude Excitation Research Articles

Nonlinear thermo-electro-mechanical responses and active control of functionally graded piezoelectric plates subjected to strong electric fields

Functionally graded piezoelectric plates (FGPPs) are often exposed to extreme thermal environments and subjected to large amplitude excitation and strong electric fields. Accurately predicting the nonlinear behaviors of FGPPs under large thermo-electro-mechanical loads remains a considerable challenge. This paper proposes a comprehensive nonlinear coupled analysis model that considers geometric nonlinearity, piezoelectric nonlinearity, and the temperature dependence of piezoelectric parameters. The total Lagrangian incremental finite element equations for FGPPs under thermo-electro-mechanical loads are derived using Hamilton's principle, by employing the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship. The accuracy of the model is validated through comparative studies. Based on this multi-nonlinear model, we further investigate the effects of geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence on the nonlinear static bending, dynamic responses, and active control of FGPPs. This study demonstrates that considering these factors enables accurate prediction of the static, dynamic, and active control behaviors of FGPPs.

Nonlinear dynamic analysis of parked large wind turbine blade considering parametric excitation

In this study, the nonlinear dynamics of parked large wind turbine blades are investigated, with a focus on the consideration of parametric excitations induced by the combined effect of wind and support motion. A continuum mathematical model for the blade is adopted. The time-varying damping terms that may induce parametric excitation are derived in this study. Nonlinear dynamic responses of NREL 5-MW wind turbine blade are numerically investigated using the multiple-scale method. Results show that the primary resonance of the first flapwise mode can induce the super-harmonic resonance of the first edgewise mode, with considering parametric excitation. Notably, when the ratio between the first flapwise to first edgewise modal eigenfrequencies is tuned to 1:2, the super-harmonic resonance leads to internal resonance between the two modes. In this case, the effects of incident wind speed, excitation direction and amplitude on the blade response are discussed. Quasi-periodic motions can also be induced because of the Neimark-Snack bifurcation in the case of large excitation amplitude.

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam’s vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.

Phase control of escapes in the fractional damped Helmholtz oscillator

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of ϕOPT≈π, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference ϕ and the fractional parameter α as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal ϕ value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.

Research on a Novel CRSM for a Type of QZS Vibration Isolator

Quasi-zero stiffness is usually abbreviated as QZS. This kind of QZS isolator has a negative stiffness mechanism, which is usually a spring mechanism (NSSM), thus possessing excellent isolation performance. However, it is prone to instability under low-frequency and large amplitude excitation. In response to this situation, a novel type of cam and roller spring mechanism (CRSM) is designed. This mechanism is composed of an arc-shaped groove, a rolling element, a spring, and a sliding pair. Use the combination of CRSM and NSSM to improve the stability of QZS isolators and prevent instability. Under two typical excitations, simulation tests in SIMULINK are conducted to analyze the vibration attenuation performance of the improved isolator and the role of CRSM in improving stability. The conclusion is that CRSM can greatly improve stability without reducing vibration damping performance.

A combined vibration isolation system capable of isolating large amplitude excitation

A combined vibration isolation system capable of isolating large amplitude excitation

Vibration suppression and stability analysis of a beam at large amplitude excitation using a two-degree-of-freedom nonlinear energy sink

Vibration suppression and stability analysis of a beam at large amplitude excitation using a two-degree-of-freedom nonlinear energy sink

An asymptotic approach for large amplitude motions of generic nonlinear systems

Starting from the observation that classical asymptotic methods fail to correctly describe the resonance peak of the frequency response curve of a nonlinear oscillator under moderate and large excitation amplitudes, an alternative approach is proposed to overcome this problem. The differences between the multiple time scale method (one of the most performant classical methods) and numerical simulations are initially shown with reference to on the paradigmatic Duffing equation. They are also shown some characteristics of the near peak behavior. Then, the proposed asymptotic approach is illustrated. The basic idea is that of having the zero-order problem nonlinear, while in classical methods it is linear. Thanks to the energy conservation, the zero-order problem is solved exactly. Also, the exact solution of the higher-order problems is obtained in closed-form, thus providing a fully analytical approach. Although the proposed method is valid for any kind of motion, special attention is dedicated to periodic nonlinear oscillations, because of their interest in practical applications. A simple formula for determining the exact intersection of the frequency response and backbone curves is obtained, and it is shown that it can be computed without the need of solving explicitly not even the zero-order problem. Some illustrative examples are finally reported.

Lamb wave based damage imaging under nonlinear chirp excitation

Considering a trade-off between temporal-spatial resolution and multi-mode nature of Lamb waves, tone bursts with short durations are usually used as excitations in Lamb wave based damage detection. A short-duration excitation usually requires a large amplitude to carry sufficient energy so as to obtain response signals with enough signal-to-noise ratio and cover a large inspection area. In this paper, an alternative Lamb wave damage imaging method using nonlinear chirp (nonlinear frequency modulation, NLFM) excitation with a long duration and a small amplitude is proposed. The signal processing techniques of pulse compression and dispersion compensation are adopted to compress the long-duration wave packets of response signals into short ones. Compared with conventional tone burst excitations with short durations and small amplitudes, due to the long duration of the nonlinear chirp excitation and the use of pulse compression, sufficient energy can be applied to transducers under small amplitude excitations so the image contrast in imaging will not degrade. Furthermore, as large amplitude excitations are no longer required, high voltage amplifiers are not necessary so the hardware of the Lamb wave testing system is simplified. Experiments on a carbon steel plate with an artificial crack are carried out and Lamb wave signals are collected using a linear array consisting of nine PZTs. Experimental results under the NLFM signal and conventional tone bursts are provided. Experimental results show that under the condition of the same excitation amplitude, the proposed method under the NLFM excitation can achieve better imaging quality compared with methods under conventional tone bursts.

Fuel sloshing-induced effects on the dynamic response of a scaled research wing demonstrator

Fuel sloshing inside aircraft wing tanks is not currently considered as a means of passive loads alleviation due to the lack of maturity of modelling tools and overall understanding of vertical sloshing. In this work, a scaled research wing demonstrator is presented, designed for the study of fuel sloshing inside an aircraft wing-representative model. An experimental campaign was conducted to examine the impact of fuel sloshing on the vertical dynamics of a scaled aircraft wing demonstrator, investigating the influence of excitation amplitude, filling level, baffle geometry, spanwise liquid position, and dihedral angle. It was found that the sloshing of the liquid in the fuel tank causes significant energy dissipation following step release excitation, maximized in the 40-60% filling range depending on the dihedral angle. The sloshing-induced damping also varies with the amplitude of excitation, with maximum added damping ratio of 0.038 achieved earlier in the motion at larger excitation amplitudes. The spanwise distribution of the liquid was found to have the strongest effect on the sloshing-induced damping, with the baffles' main impact being through the compartmentalization of the tank. Solid baffles that maintain favorable liquid distribution can increase the damping effect, while perforated baffles are not as effective. This work indicates that by considering the fuel dynamics rather than the fuel equivalent dry mass during the aircraft wing design, the net damping may be increased, leading to lighter wing structure designs.

Large-Amplitude Gusts on the NASA Common Research Model

To date, there is limited knowledge on the topic of unsteady nonlinear transonic flow caused by large-amplitude excitations. The Certification Specifications for Large Aeroplanes, however, demand loads computations for large-amplitude excitations, e.g., for gust encounters of an aircraft. In this paper, numerical solutions to the unsteady Reynolds-averaged Navier–Stokes equations will be used to analyze gust responses of a transport aircraft configuration for a variety of sinusoidal gusts with different lengths and amplitudes at different Mach numbers. On the one hand, it is shown that unsteady nonlinear responses can lead to lower maximum lift values compared to their time-linearized reference due to unsteady shock-induced flow separation. This nonlinear effect dominates for large gust lengths and higher Mach numbers. On the other hand, for the lowest Mach number considered, the coalescence of a double shock at medium gust lengths introduces nonlinear effects leading to an overprediction of the time-linearized maximum lift by the nonlinear computations. Though the turbulence model of Spalart and Allmaras shows completely different separation patterns than a differential Reynolds stress model, the variation of the turbulence model does not alter the overall qualitative findings, but has an effect on the quantitative values.

Effects of longitudinal excitation on liquid hydrogen sloshing in spacecraft storage tanks under microgravity conditions

Based on the real physical model and operating environment of the spacecraft tank, the numerical model of the tank is established and the sloshing behavior of liquid hydrogen in the tank under different longitudinal excitations is studied in this work. The Realizable k- ε model is used to predict the fluid turbulence, and the mixture model is used to analyze the phase transitions and flows. The harmonic external excitation is loaded by the user-defined function (UDF). Based on the CFD sloshing model verified through comparison with experimental results, the influences of different longitudinal external excitation frequencies and amplitudes on the liquid hydrogen volume fraction in the tank are firstly analyzed. On this basis, including pressure and other physical quantities of the monitoring points and whole internal fluid domain during the sloshing simulation process are studied quantitatively. In addition, the relationship between the carrier amplitude of the sloshing curves and the external excitation amplitude is discussed. The simulation results show that in microgravity environment, compared with large amplitude excitation, high-frequency longitudinal harmonic excitation has a significant effect on the variation of physical parameters in the tank, which may become a negative factor for the safety of liquid hydrogen storage and supply systems. Meanwhile, the traditional baffle design has a limited influence on the liquid hydrogen motion under the high-frequency longitudinal excitation which may occur during the spacecraft changing load process. The results provide valuable information for the understanding of sloshing behavior and safety evaluation of the tank under longitudinal excitation.

Comparative Study of Bistable Vibration Energy Harvester Using Different Elastic Boundary

This paper demonstrates a novel bistable energy harvester coupled with a nonlinear elastic boundary (NEB-BVEH). The nonlinear elastic boundary changes the dynamic response of the bistable vibration energy harvester and improves its performance by providing additional support for the inclined spring through coupled dynamics. This work considers the performance of bistable vibration energy harvesters using different elastic boundary under different excitation amplitudes, including bistable energy harvester with linear elastic boundary (LEB-BVEH) and NEB-BVEH with different horizontal spring stiffness. The comparative results show that the performance of NEB-BVEH and LEB-BVEH is approximately the same under small excitation amplitude. However, NEB-BVEH with adding horizontal springs can significantly improve performance compared to LEB-BVEH under larger excitation amplitude. Results of the investigated case show that the bandwidth of NEB-BVEH is increased by 89.31%. The output power is increased by more than 25%. A comparative study demonstrates the superiority of NEB-BVEH, which is very beneficial for energy harvesting.

A Numerical Investigation of Sloshing in a 3D Prismatic Tank with Various Baffle Types, Filling Rates, Input Amplitudes and Liquid Materials

Partially filled liquid-carrying tanks have been used in many engineering applications, such as ships, vehicle fuel tanks, rockets, and drink or petroleum tankers. Liquid sloshing is an exciting phenomenon that researchers are investigating because of its complex behavior specifications. In this study, the sloshing responses of a prismatic tank with the approximate volume of an automobile fuel tank under different laterally harmonic excitation amplitudes, baffle structures, filling rates, and different types of liquid were investigated numerically. The computational fluid dynamics method (CFD) was used to solve fluid dynamics equations, and the volume of fluid method was applied to simulate two-phase flow in the tank. A validation study was performed by a literature study. Later, the effect of large and small excitation amplitudes, filling rates and fluid types on sloshing behavior were investigated and comparatively analyzed in the tank system with various baffle types.

Vibration suppression of nonlinear laminated composite plates using internal oscillator-enhanced nonlinear energy sinks

This paper concerns an investigation into the excessive vibration control of laminated composite plates using a nonlinear energy sink with internal oscillator (NES-IO). The proposed NES-IO can suppress vibration more effectively than traditional NES measured by both energy dissipation and frequency responses. Based on the first-order shear deformation theory and the Galerkin method, the dynamic model of the nonlinear laminated composite plate with the NES-IO is established. Then, the mechanism of the NES-IO is analyzed, and the internal oscillator improves the vibration reduction performance of the absorber, especially with large amplitude excitations. Through comparing the NES-IO with the traditional NES, it is found that the effective vibration reduction range of the NES-IO under shock excitation is wider. Moreover, the slow flow equations of the system are derived by the complexification-averaging method, and the result is verified by the Runge-Kutta method. It is also found that the NES-IO has a great advantage in suppressing the occurrence of higher branch responses through the frequency-responses analysis. Furthermore, the influences of the parameters of the grounded and internal oscillators on the vibration suppression are also discussed to optimize the NES-IO structure.

Experiments on the localized interaction at the interface fuel rod/spacer grid in pressurized water reactors

The release of fissile material into the coolant caused by fretting of the fuel rods at the interface with spacer grids is a significant safety issue and cause of financial losses in the operation of Pressurized Water Reactors (PWRs). Each fuel rod is kept in position inside spacer grids through friction from the preload exerted by retaining elements (springs and dimples). Fretting of the fuel rods occurs at the contact with the springs and dimples. In severe fretting cases the integrity of the fuel rod cladding is compromised and fission byproducts enter the primary coolant circuit. The reciprocating motion at the contact interface of the fuel rods and spacer grids resulting in material fretting is due to the Flow-Induced Vibrations (FIV) of fuel rods, caused by the unstable surrounding coolant flow, which in PWRs is predominantly parallel to the length of fuel rods (axial flow). Under specific flow conditions, fretting develops rapidly. The vibrations of fuel rods, as well as the relationship of fretting wear mechanisms with several factors associated with the fission process and coolant flow dynamics and stability (vibration amplitude, preload, oscillating loads, irradiation, axial slip, spring relaxation, temperature, oxidation, material of spacer grids and fuel rods), have been considered in the literature. However, direct experimental measurements of the contact force and axial slip during FIV have not been treated in the literature, likely because of the absence of suitable measurement methods. This gap in experimental measurement techniques is addressed in this work, specifically for the analysis of PWR fuel assemblies, by installing a piezoelectric stack and aiming laser Doppler vibrometers on a one-meter-long fuel rod, supported by two full-scale spacer grids, in-air or immersed in quiescent water. In the presence of small- and large- amplitude forced vibrations, the signal of the piezoelectric force transducer increases with the amplitude of vibration, but it is also affected by vibrations perpendicular to the excitation, which appear for large-amplitude excitations. The axial motion of the fuel rod at the spacer grid has a complex evolution and is significant for large-amplitude vibrations only. At any rate, the time histories of contact force and axial motion display the effects of impacts and slips, particularly during the tests in water. The measurement system shows that the severity of the interaction at the spacer grid interfaces is influenced strongly by the amplitude of the forced fuel rod vibrations. Since fuel rods and fuel assemblies are prone to several nonlinear phenomena, as demonstrated by recent studies, it follows that the usage of nonlinear models will be essential to numerically estimating the severity of fretting.

Primary and super-harmonic simultaneous resonance of van der Pol oscillator

In this paper the stability and the dynamic behavior of primary and super-harmonic simultaneous resonance of van der Pol (VDP) oscillator are researched. At first, the first-order approximate analytical solution is obtained by the method of multiple scales, and the correctness and satisfactory precision of the approximate solution are verified by comparing with the numerical solution. Moreover, the amplitude–frequency and phase-frequency equations of steady-state solution is derived from the approximate analytical solution, and the stability condition is discussed based on Lyapunov theory. Then the stability region and the types of equilibrium points are qualitatively analyzed and the result shows that the amplitude of the super-harmonic excitation is the major contributor to the stability and the types of equilibrium points. Finally, the periodic motion and chaos of VDP oscillator are analyzed numerically. It is found the VDP oscillator with small primary excitation amplitude and large super-harmonic excitation amplitude will generate complex dynamic phenomena including periodic and chaotic motions, which are certified by bifurcation diagram, largest Lyapunov exponent and power spectrum. These results are helpful to the analysis and design of the similar systems.

Bifurcation analysis of a vibro-impacting capsule robot in contact with a circular fold

The lining of the small intestine consists of a series of circular folds, which is the main source of intestinal resistance for capsule endoscopy. This paper presents an in-depth bifurcation analysis for a vibro-impacting self-propelled capsule robot encountering a circular fold. Using the GPU parallel computing and path-following techniques, one- and two-parameter bifurcation analyses are performed to reveal the capsule–fold dynamics of a newly proposed model. It is found that the excitation parameters of the capsule and the fold’s mechanical properties can significantly influence bifurcation scenarios. Then basin stability analysis is further conducted to uncover the capsule–fold dynamics from a probability perspective. Numerical results indicate that the period-one motion of the capsule–fold interaction and the crossing motion can dominate the global dynamics of the system in the small and large excitation amplitude regions, respectively. Once the mechanical properties of the circular fold are varied, a significant change in multistability is also observed and demonstrated via the basins of attraction. The results presented in this work are intended to provide a solid basis for the locomotion control of the capsule robot in the small intestine when encountering different types of circular folds.

A non-smooth quasi-zero-stiffness isolator with displacement constraints

Quasi-zero-stiffness (QZS) mechanism is one of the significant solutions with its distinct advantage to the low-frequency vibration isolation problems in mechanical vibration. However, subject to the limitation of its effective range of very narrow, the strong nonlinearity of the single QZS mechanism under large-amplitude excitation might induce an undesirable large-amplitude vibration or even damage some essential equipment. Therefore, this paper designs a double-layer QZS vibration isolator with displacement constraints to reduce the undesirable large-amplitude vibration. Firstly, the mechanical model of a double-layer QZS vibration isolator with displacement stops is established based on Hertz's contact model (DLQZS-HCM). Subsequently, the incremental harmonic balance method is employed to examine the vibration isolation performance theoretically. The system parameters are then analyzed to explore their influences on the isolation performance. Compared with the double-layer linear isolator (DLL) and double-layer QZS isolator (DLQZS), it is found that the DLQZS-HCM isolator can perform better in both extending the frequency range of vibration isolation and decreasing the peak transmissibility when undergoing large-amplitude excitation. Finally, in order to further enhance the isolation performance at low-frequency levels, feedback control is applied to the DLQZS-HCM isolator. The obtained results reveal that the increasing displacement feedback gain can significantly broaden the vibration-isolation range of the DLQZS-HCM isolator in the frequency area tending to zero.

Dynamics of a vibro-impact self-propelled capsule encountering a circular fold in the small intestine

Given the anatomy of the small intestine, this paper investigates the dynamics of a vibro-impact capsule moving on an intestinal substrate with the consideration of a circular fold which provides the main resistance for the capsule’s progression. To this end, a new mathematical model of the capsule-fold contact that can depict the entire procedure of fold crossing is proposed. Our bifurcation analyses suggest that the capsule always performs period-1 motion when the driving force is small, and fold crossing requires a large excitation amplitude, especially when the duty cycle ratio is small. By contrast, the excitation period of the capsule does not have a strong influence on fold crossing. It is found that the inner mass, capsule mass, frictional coefficient and fold’s height have a significant influence on capsule’s crossing motion. We also realise that Young’s modulus of the tissue has a critical influence on the bifurcation pattern of the capsule, where a stiffer tissue may lead to the co-existence of three stable attractors. On the contrary, the capsule’s length and stiffness of the impact springs have less influence on the capsule’s dynamics. The findings of this study can help with the optimisation and control of capsule’s locomotion in the small intestine.