Higher Excitation Amplitudes Research Articles

An experimental study on three-port measurements for acoustic characterisation of the perforate reactance

The usage of perforated plates in passive noise-control systems in e.g. aircraft liners and mufflers involves the standard operating conditions of grazing flow and high-amplitude acoustic incidence. This study focuses on the usage of the three-port experiment technique for the experimental passive acoustic characterisation of a perforated plate. Expanding on the previous paper about the resistance of the perforate, the influence of operating conditions on the imaginary part of the transfer impedance, i.e., the reactance is discussed here. The relationship between the end correction in the linear range, without the presence of grazing flow, and the frequency of acoustic excitation is demonstrated. The reduction in the value of the mass end correction under the individual effects of grazing flow, and high-amplitude excitation is presented. Additionally, depending on the excitation wavelength, the partial recovery of the reduced value of the end correction under simultaneous exposure is also shown. Using the experimental results, models for the end correction, and by extension the reactance are proposed. These models take into account the geometrical parameters of the perforate, and the dimensionless Mach, Shear and Strouhal numbers.

A comparative study on the torsional vibration suppression of rotor system using variable steady state nonlinear energy sink

Current studies have shown that the introduction of bistable nonlinear energy sink (B-NES) and tristable nonlinear energy sink (T-NES) can reduce the effective threshold and alleviate the separation resonance curve compared with traditional NES under the low and higher external excitation respectively. However, there is a lack of comparative studies on the performance of B-NES, T-NES and monostable nonlinear energy sink (M-NES) in the field of torsional vibration engineering application. Aimed at this limitation, a variable steady state nonlinear energy sink (V-NES) is proposed to suppress the torsional vibration of shafting. Negative stiffness is generated by the pre-compression of the spring. The proposed V-NES can be easily switched between monostable, bistable and tristable cases by the moving position of the spring bases. Based on this, the governing equation of torsional vibration coupled with V-NES after proper orthogonal decomposition (POD) reduction is derived. The approximate analytical solution of the coupled system is obtained by using complex averaging method and verified numerically. Then, the vibration reduction effects of M-NES, B-NES and T-NES on the torsional vibration of shafting are compared. Throughout the study, the motion states of strongly modulated response (SMR), interwell oscillation, and chaotic strongly modulated response (CSMR) are observed in the V-NES. Excessively high external excitation amplitudes can make V-NES exhibit CSMR, diminishing the effectiveness of vibration reduction in comparison to inter-well oscillations.

Towards digitally programmed nonlinear electroacoustic resonators for low amplitude sound pressure levels: Modeling and experiments

Passive acoustic foams have limitations in efficiently reducing low-frequency noise below 800 Hz due to the associated wavelengths for reasonable material thickness. To address this challenge, passive or semi-active resonators are commonly employed solutions. Linear resonators are very efficient within a narrow frequency bandwidth. However, nonlinear oscillators can broaden this bandwidth, but activation of their nonlinear responses typically requires high excitation amplitudes, beyond human hearing tolerance amplitudes. Furthermore, the specific type of nonlinearity in such devices is often predetermined by the inherent properties of the resonator. In this study, we employ a novel digital control algorithm, allowing to activate the nonlinear response of the electroacoustic resonator at low excitation amplitudes. This algorithm, which relies on real-time integration, facilitates the creation of nonlinear resonators featuring polynomial or diverse non-polynomial nonlinearities within the range of low amplitudes. The nonlinear control is carried out on a loudspeaker equipped with a microphone. Our research highlights the potential to create nonlinear resonators with different, versatile and programmable behaviors. Unprecedented non-polynomial nonlinear behaviors are experimentally exhibited, we consider cubic, piece-wise linear, and logarithmic nonlinearities. These behaviors are implemented and compared to a semi-analytic model to control an acoustic mode of a tube under conditions of low excitation amplitudes and frequencies.

Strain-based running-reliability characterisation in time-domain for risk monitoring under various load conditions

This aim of this paper is to characterise the strain-based fatigue life data in time-domain using the newly modelled running-reliability technique that considers the load sequence effect. Current established conventional strain life models do not consider dependence for fatigue life of low or high amplitudes, on which with occur first in the load history. Finite element analysis is carried out to ensure the strain signals are captured at the most critical region during road test at various conditions. Fatigue life of 2.74 × 104 to 6.07 × 105 cycle/block with mean cycle to failure of 4.32 × 106 to 7.00 × 106 cycle/block is predicted based on the cycle sequence effect using cycle-counting method. The newly modelled running-reliability technique is formulated to extract the features of high amplitude excitation obtained from the strain signals for characterising the fatigue reliability features under load sequence effect. Hence, the reliability-hazard relationship for fatigue reliability characterisation of strain-based approach in time-domain using running-reliability technique.

Bandgap enhancement of a piezoelectric metamaterial beam shunted with circuits incorporating fractional and cubic nonlinearities

Nonlinear metamaterials have been widely studied for their potential to broaden the bandgap for vibration suppression. However, the bandgap widening effect induced by nonlinearity vanishes when the excitation amplitude is insufficient to trigger the nonlinear behavior. In order to broaden the applicable range of excitation amplitude for nonlinear metamaterials, a novel design of a piezoelectric metamaterial beam shunted with combined nonlinear circuits is presented in this work, which incorporates fractional and cubic nonlinearities in circuits to achieve bandgap enhancement under both low and high excitation amplitudes. Theoretical and numerical models are established for predicting the nonlinear dynamics behaviors of the piezoelectric metamaterial beam, and their computational results are in good agreement. The amplitude-dependent bandgap of the metamaterial beam induced by combined nonlinearity is analyzed through the effective bending stiffness of a unit cell and validated through the frequency response of a piezoelectric metamaterial beam. It is found that based on the complementary nature of fractional and cubic nonlinearities in the amplitude-dependent characteristics, combined nonlinearity of the circuits can effectively improve the bandgap width of the beam under both low and high excitation amplitudes. In addition, the effects of the two nonlinearities on the amplitude-dependent characteristics of the bandgap are studied, and the interplay between the two nonlinearities within the combination is analyzed. The results show that the amplitude-dependent characteristics of the combined nonlinear design can be precisely tuned by adjusting the nonlinear coefficients of the circuits. Overall, a piezoelectric metamaterial beam with both fractional and cubic nonlinearities in circuits possesses superior vibration control performance than those with single nonlinear counterparts in circuits.

Localized modes in platinum aluminides

Platinum aluminides have the prospect of being used as both functional and structural materials for a range of scientific and technical tasks. They possess unique properties that make them effective catalysts. The dynamics of the crystal lattice play an important role in the manifestation of these properties. In this study, an analysis of the density of phonon states of crystals and the possibility of the existence of localized lattice vibrations in Al and Pt alloys is conducted using atomistic modeling. The following compounds are considered: AlPt, Al2Pt, Al3Pt, AlPt2, Al3Pt5, AlPt3 (four types of lattices). The calculated phonon spectra allow for the assessment of the possibility of the existence of nonlinear localized modes in the forbidden zone of the spectrum, if it is present. It is shown that a number of crystals within the framework of the considered formalism and interatomic potential can have a forbidden zone. This condition, together with the nonlinearity of the bonds, ensures the existence of highly-amplitude localized modes in the following compounds: AlPt3, AlPt3(1), AlPt3(2), AlPt3(3). It is also established that in the Al3Pt5 alloy, the existence of prolonged high-amplitude excitations on the Al atom is possible.

Low-Engine-Order Forced Response Analysis of a Turbine Stage with Damaged Stator Vane.

A damaged stator vane can disrupt the circumferential symmetry of the design flow for turbine assemblies, which can lead to a low-engine-order (LEO) forced response of rotor blades. To help engineers be able to better address sudden vane damage failures, this paper conducts a mechanism analysis of the LEO forced response of rotor blades induced by a single damaged vane using an in-house computational fluid dynamic code (Hybrid Grid Aeroelasticity Environment). Firstly, it is found that the damaged vane introduces a family of LEO aerodynamic excitations with high amplitudes by full-annulus unsteady aeroelastic simulations of a single-stage turbine. In particular, the LEO forced response of the rotor blades excited by 3EO is 2.01 times higher than the resonance response excited by vane passing frequency, and the LEO resonance risk of the rotor blades is greatly increased. Then, by analyzing the flow characteristics of the wake and potential field of the stator row with a damaged vane, the localized high transient pressure in the notch cavity and the radial redistribution of the secondary vortex at the stator exit are the main sources of the low-order harmonic components in the flow field. Importantly, the interaction mechanisms in two regions with high LEO excitation amplitude on the rotor blade surface are revealed separately. Finally, an evaluation and comparison of a single damaged vane in terms of aerodynamic performance and LEO forced response was carried out. The results of this paper provide a good theoretical basis for engineers to effectively control the resonance response of rotor blades caused by a damaged stator vane in turbine design.

Nonlinear dynamics of magnetic multilayers and low-dimensional magnets. i. easy-plane magnetic anisotropy

The nonlinear dynamics of two magnetic elements with easy-plane magnetic anisotropy and ferromagnetic exchange interaction is considered in the framework of discrete Landau–Lifshitz equations. In the absence of damping, exact solutions of these equations are obtained for the proposed integrable dynamical system. The dynamics of the system, its frequency characteristics, and essentially nonlinear high-amplitude excitations, in particular, with a non-equal distribution of excitation between magnetic elements, have been fully investigated. The results of a theoretical study can be used in the analysis of dynamics of magnetic multilayers excited by a polarized current or a high-frequency field.

A novel passive nonlinear two-DOF internal resonance-based tuned mass damper

This paper presents a novel passive nonlinear two-degree-of-freedom (DOF) tuned mass damper (TMD) for harmonic vibration suppression. Proposed TMD has two translational modes of vibration. Both of the modes can be active during the vibration because of existing the nonlinear terms in the motion equations and internal resonance phenomenon. The vibration modes of the TMD can become active due to 1:2 internal resonance occurrence. Activation of the both modes during the vibration, helps the nonlinear TMD to have a better performance. Proposed TMD can be designed even by using low damping ratios. Three plans are considered for the design and optimization of the novel TMD. In the first plan, the damping ratios of the TMD are relatively high. Moreover, the jump phenomenon does not take place. In two other plans, the nonlinear TMD system is capable of the jump phenomenon. The performance of the two-DOF nonlinear TMD depends on the excitation amplitude. In the higher excitation amplitudes, proposed TMD can outperform the optimal linear TMD. Finally, a novel mechanical design is presented for the proposed two-DOF TMD which allows it to experience large displacements without any problem. The novel design solves the problems of frequency mistuning in the proposed TMD, and the natural frequency of the TMD can be retuned.

Broadband quasi-perfect sound absorption by a metasurface with coupled resonators at both low- and high-amplitude excitations

This study presents an acoustic metasurface (AM) consisting of coupled Helmholtz resonators with extended necks (HRENs) to effectively absorb broadband sound waves at both low and high amplitudes. A nonlinear acoustic model is proposed to characterize the AM performance based on the equivalent medium theory and the transfer matrix method. The nonlinear effects due to the high-amplitude excitation are considered by a velocity-dependence equivalent density of the air in the neck. The acoustic characteristics of an AM with two coupled HREN units at the sound pressure level (SPL) ranging from 100dB to 140dB are analytically, numerically, and experimentally investigated. Results from the three approaches show good agreement. The AM achieves quasi-perfect absorption (absorption coefficient α>0.9) in a wide range of SPL, while each HREN unit alone only performs well at around 130dB. The superior absorption performance of the AM at relatively low-amplitude excitation originates from the coherent coupling effects between adjacent units. With the increase of the sound level, the coupling effects tend to deteriorate; fortunately, the sound-vortex conversions occur, contributing to additional acoustic dissipation and thereby sustaining the quasi-perfect absorption capability. Based on the absorption mechanisms, a broadband AM with multiple coupled resonators is designed and manufactured. The measured averaged absorption coefficient of the AM is larger than 0.91 at the SPL below 140 dB (α>0.97 at 100dB) within [700,1100]Hz, and the compact thickness is of 1/18 wavelength at the lowest operating frequency. The findings in this study offer a promising approach to achieve highly efficient broadband sound absorption in a wide-ranging noise level, which holds great potentials in practical applications for noise control.

Finite Element Simulation of a Passive Damper System Using Contact Algorithm

Impact dampers are passive devices wherein a moving mass impacts with the primary structure. The vibrations caused due to these impacts are random in nature. During these impacts, exchange of momentum occurs resulting in dissipation of energy. Here, theoretical model of an impact damper system is modelled as MDOF system using Hertzian contact algorithm. Numerical simulation of the above problem was created using ANSYS Finite Element Analysis (FEA) package. Augmented Lagrangian method with Newmark’s time integration scheme is used for simulations. The problem being studied is highly nonlinear in nature with contacts being established during impact. Normal contact force generated due to impact of ball are used to get the transient response of the system.
 Detailed study was carried out with various mass ratio at low frequency and high amplitudes of excitation. Not much studies have been carried out earlier using MDOF systems with contact algorithm. Above modelling and simulation study was helpful to visualise and accurately capture the transient movement of the impact mass within the confined space.

Numerical investigation on the coupled vibrations of piezoelectric energy harvester with a liquid-filled proof mass

Replacing the solid tip mass of a piezoelectric cantilever beam with a liquid-filled mass can increase its frequency bandwidth due to the effect of nonlinear liquid sloshing. To investigate the coupled vibrations of the piezoelectric beam and the sloshing liquid, as well as their contributions to the output power, a coupled two-dimensional finite element method-smoothed particle hydrodynamics model has been developed in this study. Using this model, the dynamic behavior of a piezoelectric beam with a liquid-filled rectangular container as the tip mass, subjected to vertical harmonic excitation, has been investigated. The effects of parametric sloshing, excitation level, and geometric nonlinearity on the output voltages have been studied in detail. The simulation results indicate that: (a) the parametric sloshing in the liquid container exhibits subharmonic characteristics, which can be triggered by matching the excitation frequency to twice the natural frequency of the sloshing mode; (b) the piezoelectric beam exhibits subharmonic or harmonic oscillations at parametric resonance; (c) due to the effect of coupled vibrations, the energy harvester with a liquid-filled proof mass has a broader bandwidth compared to the traditional harvester; (d) the frequency response diagram of the output voltage shows multiple peaks at high excitation amplitudes, and the bifurcations are caused by parametric sloshing.

Ultrasonic needle hydrophone calibration in air by a parabolic off-axis mirror focused beam using three-transducer reciprocity

An acoustic field distribution investigation in air requires a small receiving sensor. Needle hydrophones seem to be an attractive solution, and it has previously been demonstrated that needle hydrophones designed for use in water can be used in air. The metrology problem is that an absolute sensitivity calibration is needed, because needle hydrophones are not characterized in air, especially for frequencies below 1 MHz, which is of interest for air-coupled ultrasound. Conventional, three-transducer/microphone reciprocity calibration requires measurements to be done in the far field. However, when transducer diameter is large and the frequency is high, the required measurement distance becomes very large: 3 m for a 20 mm source, transmitting at 1 MHz. Large propagation distance leads to high attenuation and nonlinear effects in air propagation, and distortion and losses accumulate. Small needle hydrophones have low sensitivity, so that high excitation amplitudes would be required, which can lead to transducer heating and increase nonlinearity effects. A derivative of the three-transducer reciprocity calibration method is proposed, where a large aperture transducer is focused onto a hydrophone, using hybrid of plane wave and spherical wave reciprocity. Use of a focused source minimizes the frequency-dependent diffraction effects, and the spherical wave approximation is valid at the focal distance, and low level excitation signals can be used. Focusing is accomplished using a parabolic off-axis mirror. Calibration is in transmission, which reduces the complexity of the electrical measurements. The corresponding equations have been derived for this setup. Calibration of the transducer and needle hydrophone absolute sensitivity is obtained.

Experimental and Analytical Investigation into the Effect of Ballasted Track on the Dynamic Response of Railway Bridges under Moving Loads

Ballasted tracks are among the most widespread railway track typologies. The ballast possesses multiple functions. Among them, it significantly affects the dynamic interaction between a rail bridge and a moving load in terms of damping and load distribution. These effects entail accurate modeling of the track–ballast–bridge interaction. The paper presents a finite-difference formulation of the governing equations of the track and the bridge, modeled as Euler–Bernoulli (EB) beams, and coupled by a distributed layer of springs representing the ballast. The two equations are solved under a moving load excitation using a Runge–Kutta family algorithm and the finite-difference method for the temporal and spatial discretization, respectively. The authors validated the mathematical model against the displacement response of a rail bridge with a ballasted substructure. In a first step, the modal parameters of the bridge, obtained from ambient vibration measurements, are used to estimate the bending stiffness of an equivalent EB beam representative of the tested bridge. In a second step, the authors estimated the coupling effect of the ballast by assessing the model sensitivity to the modeling parameters and optimizing the agreement with the experimental data. Comparing the bridge’s experimental displacement responses highlights the ballast’s significant effect on the load distribution and damping. The considerable difference between the damping estimated from output-only identification and that determined from the displacement response under moving load proves the dominant role of the ballast in adsorbing the vibrations transmitted to the bridge under the train passage and the different damping sources under high-amplitude excitation. The authors discuss the tradeoff between model accuracy and computational effort for a reliable estimation of ballasted tracks response under moving loads.

The effect of dynamic normal force on the stick–slip vibration characteristics

In the experiment, we observed such a phenomenon: the alternating normal force changes the vibration state of a friction system. A single-degree-of-freedom mathematical model was used in this paper to discuss the effects of a constant and alternating normal force on the stick–slip vibration characteristics for different dynamic and static friction coefficients. Under the condition that the applied constant normal force continues to increase, the vibration amplitude of the system, the amplitude of the limit cycle, and the adhesion time of the system increase. When the difference between the dynamic and static friction coefficients (DSFCs) is small, the system has a complete and clear limit cycle. When the dynamic friction coefficient is reduced, the difference between DSFCs increases, and the limit cycle of the system is deformed. The friction system has more abundant dynamic vibration characteristics under an alternating normal force than a constant normal force. The vibration state of the system presents a single-cycle stick–slip vibration when the alternating normal force excites the multi-order harmonic response of the friction system, and the excitation frequency of the alternating normal force is the same as the main response frequency of the system with the highest energy or the low-order even-order main frequency. In contrast, the system exhibits various vibration modes when the excitation frequency of the alternating normal force is dissimilar to the main frequency of the system's highest energy response or is consistent with the odd-order main frequency. In addition, increasing the difference between DSFCs or using very high excitation frequencies and excitation amplitudes increases the likelihood of the system entering a chaotic vibration state.

Vibrational resonance and bifurcation in a fractional order quintic system with distributed time delay

In this paper, vibrational resonance and bifurcation phenomena are investigated in the fractional order quintic system with distributed time delay. The approximate theoretical expression for the response amplitude at low frequency is derived by using the method of fast and slow variable separation. In the presence of fractional order and distributed time delay, the vibrational resonance and bifurcation are explored in the single-well, double-well and triple-well potentials, respectively. It is found that the decay rate of the kernel function σ can cause bifurcation, which is closely related to the high frequency excitation amplitude F. It is worth noting that the range of in which resonance occurs twice, three and four times decreases with the increase of σ. Furthermore, appropriate values of the decay rate σ, fractional order α and high frequency excitation amplitude F will enable to improve the response amplitude Q. The high match of the numerical simulation and analytical results confirms the validity of the theoretical analysis.

Nonlocal nonlinear phononics

Nonlinear phononics relies on the resonant optical excitation of infrared-active lattice vibrations to induce targeted structural deformations in solids. This form of dynamical crystal structure design has been applied to control the functional properties of many complex solids, including magnetic materials, superconductors and ferroelectrics. However, phononics has so far been restricted to protocols in which structural deformations occur within the optically excited volume, sometimes resulting in unwanted heating. Here, we extend nonlinear phononics to propagating polaritons, spatially separating the functional response from the optical drive. We use mid-infrared optical pulses to resonantly drive a phonon at the surface of ferroelectric LiNbO3. Time-resolved stimulated Raman scattering reveals that the ferroelectric polarization is reduced over the entire 50 µm depth of the sample, far beyond the micrometre depth of the evanescent phonon field. We attribute this effect to the anharmonic coupling between the driven mode and a polariton that propagates into the material. For high excitation amplitudes, we reach a regime in which the ferroelectric polarization is reversed, as revealed by a sign change in the Raman tensor coefficients of all the polar modes.

Study on Energy Dissipation Mechanism of an Impact Damper System

Abstract The objective of this paper is to investigate how higher damping is achieved by energy dissipation as high-frequency vibration due to the addition of impact mass. In an impact damper system, collision between primary and impact masses cause an exchange of momentum resulting in dissipation of energy. A numerical model is developed to study the dynamic behavior of an impact damper system using a multi-degree-of-freedom (MDOF) system with augmented Lagrangian multiplier contact algorithm. Mathematical modeling and numerical simulations are carried out using ansysfea package. Studies are carried out for various mass ratios subjecting the system to low-frequency high amplitude excitation. Time responses obtained from numerical simulations at fundamental mode when the system is excited in the vicinity of its fundamental frequency are validated by comparing with experimental results. Magnification factor evaluated from numerical simulation results is comparable with those obtained from experimental data. The transient response obtained from numerical simulations is used to study the behavior of first three modes of the system excited in vicinity of its fundamental frequency. It is inferred that dissipation of energy is a main reason for achieving higher damping for an impact damper system in addition to being transformed to heat, sound, and/or those required to deform a body.

Nonlinear dynamics of bistable composite cantilever shells: An experimental and modelling study

The nonlinear dynamics of cantilever bistable shells with asymmetric stable configurations is investigated. The possibility of maximizing the kinetic energy associated with snap-through motion offered by the considered cantilevered shells is pursued to enhance the sought-after energy harvesting capabilities. Through an experimental campaign under harmonic forcing the resonance scenarios around the stable configurations are analysed. The resulting nonlinear behaviour observed for high amplitude excitation is adopted to guide a reduced order model derivation. By combining the experimental response with two double-well oscillators derived from FE simulations, a double-well quintic oscillator capturing the observed softening behaviour is proposed. It involves a parameter identification phase in which a nonlinear damping model is introduced. A numerical continuation approach is adopted to discuss the local periodic solutions around each stable configuration in terms of resonance curves, bifurcation diagrams and basins of attraction. The global dynamics involving regular and chaotic dynamic regimes as well as snap-through motion is eventually described.

Numerical Investigations Into Nonlinear Vibro-Ultrasonics and Surface Vibration Comparison Method for Detection of Defects in a Composite Laminate

Abstract This paper begins with a numerical study based on earlier experiments of nonlinear vibro-ultrasonic behavior of a composite laminate with a delamination defect upon sinusoidal linear sweep signal excitation. A methodology to model laminates with cross-ply layup is presented which can be extended to any layup if desired. In comparison to experiments where it is challenging to visualize the fine details of vibrations, simulations make it easier to visualize and help in optimizing the defect probing methods. The paper goes on to discuss with the help of numerical results that a separation gap between the delamination surfaces occurs to be a common cause for the failure of nonlinear vibro-ultrasonic methods to detect delamination defects. This constraint can often be overcome with application of higher excitation amplitudes as has been demonstrated in several experimental works. However, in this study, a new approach named surface vibration comparison method to probe delamination defects in the absence of contact acoustic nonlinearity is proposed as a proof-of-concept. The technique is then evaluated for detection of weak kissing bond defects in composite beam specimens. Both the experimental and simulation results show potential of the method as damage detection technique in thin composite structures.