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Journal of Sound and Vibration
Journal Prestige (SJR): 1.36
Citation Impact (citeScore): 3
Number of Followers: 163  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0022-460X - ISSN (Online) 1095-8568
Published by Elsevier Homepage  [3162 journals]
  • Non-iterative, stable analysis of surface acoustic waves in anisotropic
           piezoelectric multilayers using spectral collocation method
    • Abstract: Publication date: 27 October 2018Source: Journal of Sound and Vibration, Volume 433Author(s): Bo Lan Surface acoustic waves (SAWs) enjoy profound importance across many disciplines, and one of their most prominent applications are the vast ranges of SAW devices made of piezoelectric multilayers. Thus a stable and efficient algorithm of analysing key SAW parameters in arbitrary layered media is of wide interest. This paper introduces such an algorithm based on the spectral collocation method (SCM). It firstly explains the fundamental governing equations and their numerical calculations via the SCM in a self-contained way, and then demonstrates the technique on the well-studied ZnO/diamond/Si material system, where the key factors of phase velocity, electromechanical coupling coefficient and effective permittivity are evaluated and discussed in detail. Compared to the widely employed root-finding approach, it is shown that the SCM is intuitive to formulate and code, and is highly accurate; it delivers all modes at once, and does not suffer from numerical instabilities. The establishment of the method on this simple example also implies potential applications to more general material and geometry types that could be difficult for the conventional approaches.
       
  • Revealing the effects of damping on the flow-induced vibration of flexible
           cylinders
    • Abstract: Publication date: 27 October 2018Source: Journal of Sound and Vibration, Volume 433Author(s): J. Kim Vandiver, Leixin Ma, Zhibiao Rao This study reveals how damping shapes the global vortex-induced vibration (VIV) response of flexible cylinders. Global behavior may vary from full-length standing waves to traveling waves on infinite cylinders. Structural damping rules the standing wave case whereas radiation damping regulates VIV response on very long cylinders. A single scalar equation expresses the balance of power flowing through the structure. In that equation, Arms, which is the root-mean-square response in the VIV excitation region, is shown to be an excellent indicator of global response because of its relation to power flow. Under steady-state conditions, the net power flow must be zero, which directly leads to three independent dimensionless damping parameters, namely α,βR,andc*.βR indicates when radiation damping is important, α reveals the relative importance of structural versus radiation damping, and c∗ locates the global VIV behavior on the spectrum of lightly to strongly damped systems. Structural, hydrodynamic, and wave radiation damping are all taken into account. Plots of Arms∗ versus c∗ show the global effects of damping on response. Uncontrolled factors often reveal themselves as graphical anomalies, leading to new insights on VIV. Data from experiments and numerical simulations are presented to support the conclusions.
       
  • Impact of soil–structure interaction on structures with inerter
           system
    • Abstract: Publication date: 27 October 2018Source: Journal of Sound and Vibration, Volume 433Author(s): Qingjun Chen, Zhipeng Zhao, Ruifu Zhang, Chao Pan Until now, the influence of soil–structure interaction (SSI) on structures equipped with an inerter system has been neglected in research studies. This study aims at investigating the impact of SSI on the dynamic response of such structures and explores a rather effective method for designing structures equipped with an inerter system. First, the parameters of the inerter system were obtained using the improved fixed-point method, and the foundation characteristics were derived from the classical sub-structure model. Then, dynamic responses of the structure, both with and without the sub-structure model, were comparatively evaluated through frequency- and time-domain analyses. It was found that structures with an inerter system demonstrate an increased dynamic response under the influence of SSI. In addition, structures equipped with an inerter system and designed using conventional methods are potentially unsafe. Hence, the parameter optimization of the inerter system should be performed with due consideration of the SSI effects. The dynamic response of structures equipped with an inerter system is found to be reduced when new inerter parameters obtained from the simulated annealing algorithm are applied. The results of the analyses demonstrate that SSI effects must be considered in the case of structures equipped with an inerter system and standing on flexible soil. Considering the SSI effects, an optimization algorithm, such as the simulated annealing algorithm, can be used to obtain design parameters of the inerter system, thereby more effectively reducing the dynamic response of structures equipped with an inerter system.
       
  • Internal resonances and modes interactions in non-linear vibrations of
           viscoelastic heterogeneous solids
    • Abstract: Publication date: 27 October 2018Source: Journal of Sound and Vibration, Volume 433Author(s): Igor V. Andrianov, Vladyslav V. Danishevskyy, Graham Rogerson The aim of the paper is to study how viscous damping influences mode coupling in non-linear vibrations of microstructured solids. As an illustrative example, natural longitudinal vibrations of a layered heterogeneous medium are considered. The macroscopic dynamic equation is obtained by asymptotic homogenisation. The input continuous problem is analysed using a spatial discretisation procedure. An asymptotic solution is developed by the method of multiple time scales and the fourth-order Runge-Kutta method is employed for numerical simulations. Internal resonances and energy transfers between the vibrating modes are predicted and analysed. The conditions for possible truncation of the original infinite system are discussed. The obtained numerical and analytical results are in good agreement.
       
  • Extension of Hencky bar-net model for vibration analysis of rectangular
           plates with rectangular cutouts
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Y.P. Zhang, C.M. Wang, D.M. Pedroso, H. Zhang Comprising rigid bars and spring systems at the joints and in the cells, the Hencky bar-net model (HBM) has been shown to be a physical structural representation of the finite difference plate model (FDM). In this paper, the HBM is extended for the vibration analysis of rectangular plates with rectangular cutouts. This extension addresses the rotationally elastic and transverse spring stiffnesses for the HBM at the cutout corners. After verifying the HBM model by comparing the vibration results with existing solutions for some plate problems, the model is used to obtain some new free vibration solutions for plates having various boundary conditions including cracked corners modelled by free small rectangular cutouts.
       
  • Amplitudes of characteristic frequencies for fault diagnosis of planetary
           gearbox
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Mian Zhang, KeSheng Wang, Dongdong Wei, Ming J. Zuo Frequency contents have been widely investigated to understand the vibration behaviors of planetary gearboxes. Appearances of certain sideband peaks in the frequency spectrum may indicate the occurrence of gear fault. However, analyzing too many sidebands will create problems and uncertainty of fault diagnoses. To this end, it is of vital importance to focus on those sidebands, as well as their amplitudes, which are directly induced by the gear faults. The Sideband Energy Ratio (SER) method, which synthesize the amplitudes of characteristic frequencies and meshing frequency, has shown its effectiveness in fault diagnosis of fixed-shaft gearboxes. However, for planetary gearboxes, the effectiveness and theoretical explanation behind this method still needs to be explored. In this paper, we first explored the amplitudes of characteristic frequencies based on a phenomenological model. Our investigation demonstrated that monitoring the amplitude of a single frequency component is inadequate for fault diagnosis of planetary gearbox. Second, the theoretical explanation of SER for a planetary gearbox is explored. Finally, a modified SER, namely the Modified Sideband Energy Ratio, is proposed to deal with the problem of rotating speed fluctuation. Experimental studies are provided to demonstrate the effectiveness of the proposed method.
       
  • Active vibration suppression of a novel airfoil model with fractional
           order viscoelastic constitutive relationship
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Qi Liu, Yong Xu, Jürgen Kurths This paper aims to investigate the active vibration suppression of a fractional two-degree-of-freedom viscoelastic airfoil (TDOFVA) model with a harmonic external force by means of the sliding mode control (SMC) scheme. The viscoelastic behavior is described as a fractional-order derivative, leading to a new fractional TDOFVA model. Subsequently, an averaging technique is extended to derive the amplitude-frequency relations, and its correctness is verified by Monte Carlo simulations. In addition, effects of the system parameters on the dynamics are explored. To achieve a vibration suppression, we convert the TDOFVA system into a series of fractional-order differential equations. Then, a SMC strategy is employed, in which a fractional-order integral sliding surface is presented and asymptotical stability analysis of the SMC is performed. Several numerical results are presented to illustrate the performances of the proposed SMC scheme, which indicate that the given SMC methodology is effective to realize a vibration suppression of the TDOFVA model.
       
  • A wavenumber domain numerical analysis of rail noise including the surface
           impedance of the ground
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Jungsoo Ryue, Seungho Jang, David J. Thompson In most previous studies of sound radiation from railway rails, the rail has been regarded as located in free space, disregarding the influence of the ground. However, in order to predict the noise from the rail more precisely, the effect of the ground should be included in rolling noise predictions. In this study, the rail noise is investigated by means of a wavenumber domain numerical method, including the presence of the ground. For rails attached to a rigid ground or located at a certain distance above it, the influence of the ground is examined in terms of the radiation ratio and longitudinal directivity. From the prediction of radiated power, it is found that the vertical and lateral bending waves of the rail radiate most of the noise for the corresponding direction. Hence, a simplified calculation is proposed that only includes these waves, instead of a full three-dimensional analysis. An absorptive ground is also modelled by applying impedance boundary conditions at the ground surface to investigate the influence of the ground on the rail noise. Finally, for the vertical and lateral bending waves in the rail, the cross-sectional directivity of the noise is predicted for various surface impedances of the ground. It is found that the simplified calculation proposed in this study is valid for the prediction of noise from the rail. Also the presence of the ground and its impedance condition have considerable effects on the level and directivity patterns of the noise radiated from the rail.
       
  • Effect of static load on vibro-acoustic behaviour of clamped plates with
           geometric imperfections
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Di Wang, Qian Geng, Yueming Li The effect of static load on the vibro-acoustic behaviour of clamped rectangular plates with various geometric imperfections is further investigated in this paper. An effective method applying static load on the plate subjected to dynamic excitations is proposed in the experiment. The Von Karman nonlinear incremental strain-displacement relationship is utilized to describe the large deflection and initial geometric imperfection. Based on the assumed mode method and Hamilton's principle, the nonlinear vibration governing equations of an imperfect plate considering the added effect in the experimental implementation are formulated. Firstly, the nonlinear static deflection is solved iteratively. Then the tangent stiffness matrix is utilized to calculate the linear vibration at the equivalent static position. The acoustic radiation can be derived hereof by Rayleigh integral. The theoretical, numerical and experimental results coincide well. The results show that the natural frequencies of the imperfect plate are higher than those of the original flat one. Under static load, different from the flat plate which is stiffened, the imperfection may lead to either stiffening or softening of the plate depending on the imperfection shape and the static load direction. And the vibro-acoustic characteristics are affected accordingly. It is noted that when the imperfection gets larger, snap-through may occur under static pressure. Furthermore, comparison of vibration characteristics among different load locations with the same static load is also discussed.
       
  • Straightforward impedance eduction method for non-grazing incidence wave
           with multiple modes
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Xianghai Qiu, Bo Xin, Xiaodong Jing The control of modern aeroengine noise poses great challenge to the design of acoustic liners, due to the existence of multiple higher-order modes over a very wide frequency range in acoustic nacelles. In order to meet the pressing demand, the straightforward impedance eduction method is further developed such that it can be applied to more general acoustic environment where there are both plane mode and higher-order modes incident upon a test liner. A novelty of the present method is using a diagonally mounted microphone array on the opposite wall of the test liner in a flow duct, thus the measured wall sound pressure simultaneously contains the information of the modes in both the axial and transverse directions. Then, the employment of Prony's method enables the realization of the full modal decomposition to the acoustic field in the flow duct. Numerical experiments simulating acoustic fields with a finite element model are conducted to investigate and validate the feasibility of the present method for both a small-scale and a large-scale flow ducts. Two ceramic tubular liners and a perforated liner are tested as specimens, whose impedance values to be educed are known a priori by means of existing impedance models. Random perturbation is added into the acoustic field data to simulate realistic noisy acoustic environments. The results show that the present method can educe the imposed impedance with a good accuracy when the liner specimens are subjected to the sound field composing of multiple incident modes including several transverse modes in both ducts. The frequency scope of the impedance eduction is considerably extended when compared with the methods restricted by the assumption of plane incident mode, with the upper frequency reaching up to 6.0 kHz and 5.0 kHz for the ducts, respectively. A parametric study indicates that the accuracy of impedance eduction can be promoted by increasing the signal-to-noise ratio and the number of microphones.
       
  • Frequency and mode change in the large deflection and post-buckling of
           compact and thin-walled beams
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): A. Pagani, R. Augello, E. Carrera This paper deals with the investigation of normal modes change of metallic structures, when subjected to geometrical nonlinearities in the large displacement/rotations field. Namely, a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach are employed to formulate higher order beam theories including geometric nonlinearities. Thus, a finite element approximation is used along with a path-following method to perform nonlinear analyses. Linearized vibration modes around equilibrium states and along the whole equilibrium path of structures subjected to bending and compression loadings are evaluated by solving a classical eigenvalue problem. In order to show the capabilities of the proposed methodology, both solid and thin-walled cross-section beams are considered. The analyses demonstrate that, with some differences depending on the geometry and both boundary and loading conditions, natural frequencies and modal shapes may change significantly as the structure is subjected to large displacements and rotations.
       
  • Vortex structures and aeroacoustic performance of the flow field of the
           pantograph
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Tan Xiao-Ming, Yang Zhi-Gang, Tan Xi-ming, Wu Xiao-long, Zhang Jie The object of study in this paper is the Faiveley CX-PG pantograph. We first used the large-eddy simulation (LES) model to simulate the surrounding fluctuating flow field. We then identified the vortex structures in the flow field of the pantograph via the Q criterion, and performed a Fourier transform on the fluctuating pressure. We finally used the Ffowcs Williams-Hawkings (FW-H) equation to predict the far-field radiation noise of the pantograph. Through these steps, we explored the vortex structures in the flow field of the pantograph, aeroacoustic performance of the pantograph's main components, and the relationship between them, and proposed corresponding acoustic optimization countermeasures. The results showed that the vortex structures in the flow field of the pantograph varied with time and had a certain periodicity, and that the sound source intensity of the pantograph was mainly distributed in the bottom frame, three insulators, balance beam, upper arm frame, and lower arm. The sound source energy of these components accounted for approximately 92% of the total energy; the influencing factors for the aerodynamic sound source intensity of the pantograph included the shedding positions and vorticities of the vortex structures as well as whether it was located in the wake of the vortex structures. The aerodynamic noise of the pantograph could be effectively controlled by adjusting the vortex shedding position, reducing the vorticities of the vortex structures, increasing the distance between the mutually interfering components, setting the diversion structure to control the discharge area of the vortex structures. The sound source energy of the bottom frame area accounted for more than 50% of the total energy; a settlement platform or shroud could be installed to effectively control the noise in the area, thereby effectively reducing the noise radiated by the pantograph. The simulation results in this paper were in good agreement with the wind tunnel test results and theoretical results, and can provide a reference for the optimal design of future acoustics for the pantograph.
       
  • Characterization and modeling of the acoustic field generated by a curved
           ultrasound transducer for non-contact structural excitation
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Songmao Chen, Alessandro Sabato, Christopher Niezrecki, Peter Avitabile, Thomas Huber Conventional excitation techniques typically use an impact hammer, piezoelectric actuator, or mechanical shaker excitation for experimental modal testing. However, the use of these devices may be challenging if accurate high-frequency dynamic measurements on small or lightweight structural parts have to be performed. To overcome these problems, the high-frequency radiation force generated by focused ultrasonic transducers (FUTs) can be used. This approach has shown potential to be used as a non-contact method for modal excitation of small-sized or flexible structures such as MEMS devices, small turbine blades, integral blade rotors (IBR), and biological structures. However, the sound radiation in the air of these ultrasonic transducers and the resulting radiation force imparted onto a structure is not well understood and critically crucial for performing accurate modal analysis and system identification. In this research, the technical development of ultrasound radiation pressure mapping and simulation is presented. Starting from the calibrated sound pressure fields generated by the spherically FUT, driven by amplitude modulated signals, the dynamic focused ultrasound radiation force is modeled and estimated. The acoustic pressure field of a FUT operating in the air is measured and used for validating the accuracy of a new numerical boundary element method (BEM) model in predicting the direct acoustic force generated in the high-frequency range (i.e., 300–400 kHz). The results show that an excellent agreement is found regarding both the pressure profile and amplitude. Pressure fields up to 1200 Pa can be generated as the transducer is driven at 400 kHz. Experiments also prove that the FUT is capable of creating a focal spot size of nearly 3 mm in diameter. To finish, the FUT's dynamic focused ultrasound radiation force is quantified and could be used to quantify a force-response relationship for experimental modal analysis purposes.
       
  • Aerodynamic noise reduction using dual-jet planar air curtains
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Kun Zhao, Sajad Alimohammadi, Patrick N. Okolo, John Kennedy, Gareth J. Bennett In this paper, dual-jet planar air curtains are demonstrated to be able to successfully remove aerodynamic noise radiated from tandem rods in a crossflow. Single-jet air curtains have shown significant promise as a low noise technology but can introduce additional noise sources such as lip and mixing noise. In this work, dual-jet air curtains are shown to address these obstacles, achieving the same shielding height with a significantly lower overall system noise. Providing high amplitude tonal and broadband noise, tandem rods are chosen as the test case and the fluid mechanics and acoustics associated with their shielding by air curtains are examined both experimentally and numerically. Particle image velocimetry and flow visualisation methods allow the flow fields to be examined, and a numerical analysis with computational fluid dynamics to be validated. Barely examined in the literature to date, the trajectory of planar jets in crossflow are studied here and compared to a basic semi-empirical model. The accurate identification of the trajectory allows a method for an optimum shielding height and dual jet velocity combination to be proposed and tested. Acoustic beamforming and 1/3 octave band analysis are performed for diagnostic noise source localisation and comparative evaluation. It is demonstrated that a judicious choice of flow parameters can result in the complete removal of the aerodynamic noise with almost no acoustic penalty.
       
  • Passive self-tuning inductor for piezoelectric shunt damping considering
           temperature variations
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): R. Darleux, B. Lossouarn, J.-F. Deü Piezoelectric shunt damping offers a passive solution to mitigate mechanical vibrations: the electromechanical coupling induced by piezoelectric patches bound to the vibrating structure allows the transfer of vibration energy to an electrical circuit, where it can be dissipated in a resistive component. Among the existing passive piezoelectric shunt circuits, the resonant shunt leads to significant vibration damping if it is tuned with enough precision. However, temperature may have a strong influence on electrical parameters such as the piezoelectric capacitance and the circuit inductance. As a consequence, a temperature variation can lead to a deterioration of vibration damping performance. This paper describes how inductive components can be chosen to minimize the mistuning of the resonant shunt when temperature evolves. More specifically, inductors are made of magnetic cores whose magnetic permeability varies with temperature, which counterbalances the variations with temperature of the mechanical resonance frequency and of the piezoelectric capacitance. Experiments show the benefits of adequately choosing the magnetic material of the inductor for vibration damping of a cantilever beam. The concept of a fully passive shunt adapting to temperature variations is hence validated.
       
  • The control of aerodynamic sound due to boundary layer pressure gust
           scattering by trailing edge serrations
    • Abstract: Publication date: 13 October 2018Source: Journal of Sound and Vibration, Volume 432Author(s): Alex Siu Hong Lau, Xun Huang A theoretical model is proposed in the current work to shed light on the noise-reduction mechanisms of trailing-edge serrations, which have been shown to suppress noise generated at the trailing edge due to the scattering of boundary layer pressure fluctuations. The current analytical model, which is developed by incorporating Fourier series expansions and the Wiener-Hopf method, can quickly predict noise reductions due to various types of trailing-edge serrations at low Mach numbers. The present model is validated by comparing its predictions with relevant published theoretical and experimental results. Moreover, from the Winer-Hopf analysis, an effective method based on Fourier series expansion is proposed to approximately evaluate the noise-reduction performance of different serrated geometries under various working conditions. The current work shows that trailing-edge serrations reduce noise by producing scattered waves with spanwise modes which could be evanescent, and explains why some serrated geometries are more effective than others in suppressing noise. The efficient noise prediction capability of the proposed model makes it very suitable to be used in the trailing-edge designs and evaluations of low-noise aircraft components such as wings and aero-engine fan, compressor and turbine cascades.
       
  • Discussion on: Function-weighted frequency response function sensitivity
           method for analytical model updating, by R. M. Lin
    • Abstract: Publication date: Available online 28 June 2018Source: Journal of Sound and VibrationAuthor(s): Aakbar Esfandiari, Masoud Sanayei
       
  • Commentary on “Discussion on ‘Function-weighted frequency response
           function sensitivity method for analytical model updating’ by A.
           Esfandiari and M. Sanayei”
    • Abstract: Publication date: Available online 21 June 2018Source: Journal of Sound and VibrationAuthor(s): R.M. Lin
       
  • Experiences with nonlinear modeling and acoustic fatigue
    • Abstract: Publication date: Available online 24 May 2018Source: Journal of Sound and VibrationAuthor(s): Joseph J. Hollkamp This article explores the evolution of the nonlinear reduced-order modeling concept and its application to the acoustic fatigue problem as guided by a course of experiments. Since the advent of the jet engine, military aircraft have been plagued by acoustic fatigue. For decades, the resulting cracking has been a nuisance affecting mostly secondary structure, which can be routinely replaced. These thin aircraft panels are excited by ever increasing acoustic energy, causing the vibration to become nonlinear. The nonlinear response had been attributed to nonlinear damping but has been shown to be caused by geometric nonlinearity which results in nonlinear stiffness. Regardless of the cause of the nonlinearity, acoustic fatigue in conventional military aircraft can be controlled via damping treatments. However for high speed vehicles, the availability of high temperature damping treatments is practically non-existent. Furthermore, fatigue cracking in any part of the outer mold line can have catastrophic effects on the aerodynamic heating of these vehicles. Research into the prediction of the nonlinear vibration with reduced-order models has become popular in the past decade to address these concerns. This paper will document some experiences with these concepts through experimental investigations.
       
  • Exact 3D scattering solutions for spherical symmetric scatterers
    • Abstract: Publication date: Available online 6 February 2018Source: Journal of Sound and VibrationAuthor(s): Jon Vegard Venås, Trond Jenserud In this paper, exact solutions to the problem of acoustic scattering by elastic spherical symmetric scatterers are developed. The scatterer may consist of an arbitrary number of fluid and solid layers, and scattering with single Neumann conditions (replacing Neumann-to-Neumann conditions) is added. The solution is obtained by separation of variables, resulting in an infinite series which must be truncated for numerical evaluation. The implemented numerical solution is exact in the sense that numerical error is solely due to round-off errors, which will be shown using the symbolic toolbox in MATLAB. A system of benchmark problems is proposed for future reference. Numerical examples are presented, including comparisons with reference solutions, far-field patterns and near-field plots of the benchmark problems, and time-dependent solutions obtained by Fourier transformation.Graphical abstractfx1
       
  • A novel hybrid surrogate model and its application on a mechanical system
           subjected to friction-induced vibration
    • Abstract: Publication date: Available online 1 February 2018Source: Journal of Sound and VibrationAuthor(s): E. Denimal, L. Nechak, J-J. Sinou, S. Nacivet A new hybrid meta-modeling approach is proposed and developed for the propagating and quantifying of uncertainties in friction-induced instabilities. According to the available knowledge about design parameters, the associated uncertainty can be described by using different models. Hence, hybrid meta-models prove to be necessary to simultaneously treat different uncertainty models. So, this study presents a novel hybrid meta-model issued from the associating of the kriging formalism together with the generalized polynomial chaos for the prediction of friction-induced instabilities submitted to interval and probabilistic uncertainties. Its assessing through the considering of a friction system, reveals suitable accuracy about the estimating of the dispersion of the occurrences of instabilities. Moreover, it offers a promising alternative to the prohibitive Monte-Carlo/scanning based methods that are usually used for the same task.
       
 
 
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