Accepted Manuscripts

Expert View  
Dane Sequeira, Xue-She Wang and Brian Mann
J. Vib. Acoust   doi: 10.1115/1.4040046
Parameter sweeps are commonly used to explore the behavior of dynamical systems. This paper derives exact solutions for the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. This work will enable more accurate bifurcation diagrams and Poincare sections in parameter regimes where numerical approaches may lead to incorrect behavior characterization. The simplest case of a linear frequency sweep is first considered before generalizing the results to include more complex functions with nonlinear sweep rates and arbitrary phase shifts.
TOPICS: Phase shift, Dynamic systems, Bifurcation, Excitation
Chuan-Xing Bi, Yong-Chang Li, Rong Zhou and Yong-Bin Zhang
J. Vib. Acoust   doi: 10.1115/1.4040047
The equivalent source method (ESM) and monopole time reversal method (MTRM) are two popular techniques for noise source localization. These two methods have some similar characteristics such as using the pressure field measured by a microphone array as the input and using similar propagation matrices obtained from the Green's function. However, the spatial resolutions of results obtained by these two methods are different. The aim of this paper is to reveal the reason resulting in this difference from a theoretical analysis and compare the performance of these two methods using results from numerical simulations and experiments. Using the singular value decomposition technique, the difference between the two methods is found to be only the diagonal matrices of singular values, and the two methods are equivalent after simply replacing the diagonal matrix in the MTRM with its inverse. Comparison of the results demonstrate that the ESM can calculate the real source strength and obtain a high spatial resolution due to the significant amplification of evanescent waves in the inverse process. However, it doesn't work when the signal-to-noise ratio is low or the measurement distance is large. The performance of ESM under these situations can be significantly improved by introducing a regularization procedure. Whilst the MTRM fails to calculate the real source strength and locate the source at low frequencies due to the loss of information of evanescent waves, it works well at high frequencies even with a low signal-to-noise ratio and a large measurement distance.
TOPICS: Time reversal, Noise (Sound), Signal to noise ratio, Waves, Resolution (Optics), Pressure, Computer simulation, Microphone arrays, Theoretical analysis
Keiyu Kadoi, Tsuyoshi Inoue, Junichi Kawano and Masahiko Kondo
J. Vib. Acoust   doi: 10.1115/1.4040042
Centrifugal pendulum vibration absorber (CPVA) has been used as a vibration suppression method of torsional vibration. Recently, downsizing turbo technology is widespread and it causes a torsional vibration in the drive-train shaft of automotive, and CPVA is used for the mean of its vibration suppression. In such cases of vibration suppression of the drive-train shaft, it should be modeled as a multi degree of freedom system, and considered the suppression of its multiple modes. However, most of researches of CPVA so far has focused on a one degree of freedom system, and the vibration analysis and its suppression of the torsional vibration caused in the multi degree of freedom system has been hardly investigated. In this paper, the dynamical characteristics of the torsional vibration of the multi degree of freedom system with CPVA is investigated both theoretically and experimentally. Vibration suppression mechanism of CPVA on the torsional vibration of the multi degree of freedom system is studied by the eigenvalue analysis. The vibration suppression effect of CPVA on the harmonic resonances, and the occurrence of super harmonic resonances in multiple modes are observed by the numerical simulation. Then, nonlinear theoretical analyses are demonstrated for them and the vibration suppression effect of CPVA are explained. These obtained theoretical results are confirmed by experiments.
TOPICS: Vibration, Vibration absorbers, Pendulums, Vibration suppression, Degrees of freedom, Trains, Resonance, Computer simulation, Turbochargers, Theoretical analysis, Eigenvalues, Vibration analysis
Turki Haj Mohamad, Mohsen Samadani and C. Nataraj
J. Vib. Acoust   doi: 10.1115/1.4040041
This paper introduces a novel method called Extended Phase Space Topology (EPST) for machinery diagnostics and pattern recognition. In particular, the research focuses on fault detection and diagnostics of rolling element bearings. The proposed method is based on mapping the vibrational response onto the density space and approximating the density using orthogonal functions. The method has been applied to vibration data of a rotating machine where the data was measured by proximity probes. The method was applied to two operating conditions: constant operating speed and variable operating speed. As will be shown, the proposed feature extraction method has an outstanding capability in characterizing the system response and diagnosing the system. The method is evidently robust to noise, does not depend on expert knowledge about the system, requires no feature ranking or selection, and can easily be applied in an automated process. Finally, a comparison with utilization of statistical features is performed for each operating condition which demonstrates that the proposed method performs better than the traditional statistical methods.
TOPICS: Phase space, Rolling bearings, Topology, Density, Machinery, Noise (Sound), Vibration, Feature extraction, Flaw detection, Pattern recognition, Probes
Abdollah Javidialesaadi and Nicholas E. Wierschem
J. Vib. Acoust   doi: 10.1115/1.4040045
In this study, a novel passive vibration control device, the three-element vibration absorber-inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned mass-damper-inerter (TMDI), which is an inerter-base tuned mass damper, and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional tuned mass damper (TMD), TEVA, and the TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and RMS response of the underlying structure in comparison to the TMD, TEVA, and TMDI.
TOPICS: Vibration, Passive control, Dampers, Vibration absorbers, Excitation, Optimization, Mass (Physics), Rotation, Vibration control equipment
Carole Mei
J. Vib. Acoust   doi: 10.1115/1.4039961
In this paper, natural frequencies and mode shapes of a transversely vibrating Euler-Bernoulli beam carrying a discrete two degrees-of-freedom spring-mass system are obtained from a wave vibration point of view in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external forces applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam and two degrees-of-freedom spring-mass system, the vibrating discrete spring-mass system injects waves into the distributed beam through the spring forces at the two spring attached points. Assembling these wave relations in the beam provides an analytical solution to vibrations of the combined system. Accuracy of the proposed wave analysis approach is validated through comparisons to available results. This wave based approach is further extended to analyze vibrations in a planar portal frame that carries a discrete two degree-of-freedom spring-mass system, where in addition to the transverse motion, the axial motion must be included due to the coupling effect at the angled joint of the frame. The wave vibration approach is seen to provide a systematic and concise technique for solving vibration problems in combine distributed and discrete systems.
TOPICS: Waves, Degrees of freedom, Free vibrations, Springs, Vibration, Discrete systems, Mode shapes, Structural elements (Construction), Gates (Closures)
Emmanuel Gourdon, Alireza Ture Savadkoohi and Valentin Alamo Vargas
J. Vib. Acoust   doi: 10.1115/1.4039960
Targeted energy transfer from one acoustical mode to an Helmholtz resonator with nonlinear behavior is studied. For the Helmholtz resonator, nonlinear restoring forces and nonlinear damping are taken into account. A time multiple scale method around a 1:1 resonance is used to detect slow invariant manifold of the system, its equilibrium and singular points. Analytical predictions are compared with those which are obtained by direct numerical integration of system equations. Experimental verifications are performed and presented for free and forced vibrating system.
TOPICS: Energy transformation, Acoustics, Equilibrium (Physics), Damping, Manifolds, Resonance
David H Diamond and P.S. Heyns
J. Vib. Acoust   doi: 10.1115/1.4039931
Blade Tip Timing is a non-contact method for measuring turbomachinery blade vibration. Proximity sensors are mounted circumferentially around the turbomachine casing and used to measure the tip displacements of blades during operation. Tip deflection data processing is non-trivial due to complications such as aliasing and high levels of noise. Specialized BTT algorithms have been developed to extract the utmost amount of information from the signals. The effectiveness of these algorithms is, however, influenced by the circumferential spacing between the proximity sensors. If the spacing is sub-optimal, an algorithm can fail to measure dangerous blade vibration. This article presents a novel optimization approach that determines the optimal spacing between proximity sensors.
TOPICS: Sensors, Design, Rotors, Blades, Algorithms, Turbomachinery, Vibration, Deflection, Signals, Optimization, Noise (Sound)
Hamed Salmani and G.H Rahimi
J. Vib. Acoust   doi: 10.1115/1.4039932
It has been shown that exponentially tapering the width of a vibration based piezoelectric energy harvester will result in increasing electric power per mass in a specified frequency. In this paper a nonlinear solution of an exponentially decreasing width piezoelectric energy harvester is presented. Piezoelectric, inertial, and geometric nonlinearities are included in the presented model, while the exponentially tapered piezoelectric beam's mass normalized mode shapes are utilized in Galerkin discretization. The developed nonlinear coupled Equations of Motion (EoM) are solved using Method of Multiple Scales (MMS), and the steady states results are verified by experiment in high amplitude excitation. Finally, the exponentially tapering parameter effect is studied, and it is concluded that the voltage per mass of the energy harvester is improved by tapering at high exciting acceleration amplitudes.
TOPICS: Energy harvesting, Steady state, Mode shapes, Excitation, Electricity (Physics), Equations of motion, Vibration
Tudor Sireteanu, Ovidiu Solomon, Ana-Maria Mitu and Marius Giuclea
J. Vib. Acoust   doi: 10.1115/1.4039933
In this paper, is presented a new approach for linearization of piecewise linear systems with variable dry friction, proportional with absolute value of relative displacement. The transmissibility factors of considered systems, defined in terms of r.m.s. values, are obtained by numerical time integration of motion equations for a set of harmonic inputs with constant amplitude and different frequencies. A first order linear differential system is attached to the considered piecewise linear system such as the first component of solution vector of attached system to have the same transmissibility factor as the chosen output of nonlinear system. This method is applied for the semi-active control of vibration with balance logic strategy. Applications to base isolation of rotating machines and vehicle suspensions illustrate the effectiveness of the proposed linearization method.
TOPICS: Vibration, Linear systems, Dry friction, Displacement, Machinery, Suspension systems, Equations of motion, Nonlinear systems
Yuanchang Chen, Dagny Joffre and Peter Avitabile
J. Vib. Acoust   doi: 10.1115/1.4039800
Expansion of real-time operating data from limited measurements to obtain full field displacement data has been performed for structures in air. This approach has shown great success and its main advantage is that the applied forces do not need to be identified. However, there are applications where structures may be immersed in water and the full field real time response may be needed for design and structural health assessments. This paper presents the results of a structure submersed in water to identify full field response using only a handful of measured data. The same approach is used to extract the full field displacements and the results are compared to the actual full field measured response. The advantage of this approach is that the force does not need to be identified and, most importantly, the damping and fluid structure interaction does not need to be identified in order to perform the expansion. The results show excellent agreement with the measured data.
TOPICS: Damping, Design, Displacement, Dynamic response, Water, Fluid structure interaction
Vinícius Nunes Carvalho, Bruno Resende Ferreira Rende, Arinan Dourado Guerra Silva, Aldemir Ap. Cavalini Jr. and Valder Steffen Jr.
J. Vib. Acoust   doi: 10.1115/1.4039801
Unbalance is one of the most common malfunctions found in rotating machines generating high vibration amplitudes that can lead to fatigue and wear of rotor elements. There are several well-known balancing techniques wherein one of the most widespread approaches is the so-called influence coefficients method (IC method). Aiming to increase the robustness of the standard IC method, in this paper a revised IC balancing methodology for rotating machines is proposed. In this sense, a preprocessing stage is applied to access the uncertainties affecting the rotating machine. In this sense, measurement data sets evaluated under the fuzzy logic approach are used. Thus, the rotor vibration responses measured over a long period are considered by means of a fuzzy transformation (defining unbalance fuzzy sets). The unbalance condition of the rotating machine is determined through a defuzzification process. This unbalance condition is then introduced in the IC method algorithm aiming at obtaining correction weights and associated angular positions that increase the balancing robustness as compared with the classical approach. Numerical and experimental studies are used to evaluate the effectiveness of the proposed methodology. The obtained results illustrate the capacity to increase the balancing overall robustness.
TOPICS: Machinery, Fuzzy logic, Robustness, Uncertainty, Fatigue, Wear, Algorithms, Rotor vibration, Rotors, Vibration
Jing Yang, Huajiang Ouyang, Dan Stancioiu, Shancheng Cao and Xuhui He
J. Vib. Acoust   doi: 10.1115/1.4039799
This paper presents an experimental and theoretical study of vibration of a four-span continuous plate with two rails on top and four extra supports excited by one or two moving model cars, which is meant to represent vehicle-track-bridge dynamic interaction. Measured natural frequencies of the plate structure are used to update the Finite Element (FE) model of the structure. Four laser displacement transducers are placed on the ground to measure the displacements of the plate. A Laser-Doppler Vibrometer is used to measure the real-time speed of the moving cars which reveals that the speeds decrease with time at a small and almost constant deceleration which can affect the structural dynamic response. A fascinating experiment is the use of two cars connected in series, which is very rare and has never been done on a multi-span structure. Vibration of the plate structure excited by two moving cars separated at a distance is also measured and exhibits interesting dynamic behaviour too. A theoretical model of the whole structure is constructed and an iterative method is developed to determine the dynamic response. The numerical and the experimental results are found to agree very well, in particular when deceleration is considered in the theoretical model.
TOPICS: Plates (structures), Automobiles, Dynamic response, Vibration, Iterative methods, Rails, Laser Doppler vibrometers, Displacement, Transducers, Vehicles, Lasers, Bridges (Structures), Structural dynamics, Finite element analysis
Farzam Mortazavi and Alan Palazzolo
J. Vib. Acoust   doi: 10.1115/1.4039725
The American Petroleum Institute (API) level II vibration stability analysis for impellers requires higher fidelity models to predict the dynamic forces of the whirling impeller. These forces are in turn required to predict the vibration stability, critical speeds and steady state vibration response of the shaft-bearing-seal-impeller system. A transient CFD-based approach is proposed which is applicable to non-axisymmetric turbomachinery components such as the volute and/or diffuser vanes, unlike its predecessor models like the Bulk-flow or the quasi-steady model. The key element of this approach is the recent advancements in mesh deformation techniques which permit less restrictive motion boundary conditions to be imposed on the whirling impeller. The results quantify the contributions of the volute and/or the diffuser to the total forces which guides the analyst on whether to include these components in the model. The numerical results obtained by this approach are shown to agree well with experimental measurements, and to be superior to the earlier quasi-steady alternative in terms of accuracy. Furthermore, several volute shapes were designed and analyzed for the sensitivity of the solution to the geometrical properties of the volute. The design flow rotordynamic forces show a significant dependence on the presence of the volutes in the model, with the specific shape of the volute having a lesser influence. The dimensionless forces are shown to be almost independent of the spin speed.
TOPICS: Diffusers, Vibration, Turbomachinery, Impellers, Stability, Flow (Dynamics), Whirls, American Petroleum Institute, Shapes, Steady state, Boundary-value problems, Rotation, Deformation, Spin (Aerodynamics), Transients (Dynamics), Particle spin, Bearings, Computational fluid dynamics, Design
Zuguang Ying, Y.Q. Ni and Ronghua Huan
J. Vib. Acoust   doi: 10.1115/1.4039726
The vibration control of a sandwich beam with supported mass subjected to random support motion excitations can be performed using magneto-rheological visco-elastomer core with adjustable dynamic properties. The period distributions of geometrical and physical parameters of the sandwich beam can improve its vibration response characteristics. To further improve characteristics or reduce responses, the quasi-periodic sandwich beam with supported mass under random excitations is studied. The facial layer thickness and core layer modulus of the sandwich beam are considered as quasi-period distributions. The partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived, and converted into ordinary differential equations for multi-degrees-of-freedom vibration. The expressions of frequency response and response spectral densities of the sandwich beam are obtained. Numerical results are given to illustrate the greatly improvable vibration response characteristics of the sandwich beam and the outstanding relative reduction localization of anti-resonant responses. The proposed active quasi-period distribution and analysis method can be used for the vibration control design of sandwich beams subjected to random excitations.
TOPICS: Elastomers, Rheology, Vibration, Excitation, Random excitation, Vibration control, Design, Differential equations, Resonance, Frequency response, Partial differential equations
Technical Brief  
Zhiguang Song, Tian-Zhi Yang, Feng-Ming Li, Erasmo Carrera and Peter Hagedorn
J. Vib. Acoust   doi: 10.1115/1.4039724
In traditional active flutter control, piezoelectric materials are used to increase the stiffness of the aeroelastic structure by providing an active stiffness, and usually the active stiffness matrix is symmetric. That is to say that the active stiffness not only cannot offset the influence of the aerodynamic stiffness which is an asymmetric matrix, but also will affect the natural frequency of the structural system. In other words, by traditional active flutter control method, the flutter bound can just be moved backward but cannot be eliminated. In this investigation, a new active flutter control method which can suppress the flutter effectively and without affecting the natural frequency of the structural system is proposed by exerting active control forces on some discrete points of the structure. In the structural modeling, the Kirchhoff plate theory and supersonic piston theory are applied. From the numerical results, it can be noted that the present control method is effective on the flutter suppression, and the control effects will be better if more active control forces are exerted. After being controlled by the present control method, the natural frequency of the structure remains unchanged.
TOPICS: Air flow, Flutter (Aerodynamics), Stiffness, Plate theory, Modeling, Pistons, Piezoelectric materials
Mahmoud Alfouneh and Liyong Tong
J. Vib. Acoust   doi: 10.1115/1.4039571
This article presents a novel moving iso-surface threshold (MIST) method for designing flexible structures using graded materials with multi-volume fractions and constraints and viscous or hysteretic damping under harmonic loadings. By employing a unit dynamic load with the same frequency of an applied load, the displacement amplitude at chosen degrees of freedom (DOFs) can be expressed in an integral form in terms of mutual modal strain and kinetic energy densities over the entire design domain. Such integrals enable the introduction of novel physical response functions for solving a range of topology optimization problems, including single and multiple objectives with single and multiple volume fractions and/or constraints, e. g. SISO and MIMO. Numerical examples are presented to validate the efficiency and capability of the present extended MIST method. Experiments are also conducted on rectangular plates with and without damping layer, fully and optimally covered, to demonstrate the benefits of the optimal damping layer design.
TOPICS: Damping, Design, Flexible structures, Stress, Degrees of freedom, Topology, Optimization, Plates (structures), Displacement, Kinetic energy
Mao Liu and Weidong Zhu
J. Vib. Acoust   doi: 10.1115/1.4039570
Different from elastic waves in linear periodic structures, those in phononic crystals with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot predict band-gap variations due to intensity of wave motion; creating nonlinear phononic crystals remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler-Bernoulli beam using their exact Green-Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear phononic crystals.
TOPICS: Modeling, Nonlinear waves, Energy gap, Phononic crystals, Wave propagation, Elastic waves, Finite element methods, Vibration control, Dispersion relations, Chain, Engineering systems and industry applications, Waves, Nonlinear systems, Discrete systems, Wavelets, Periodic structures, B-splines, Wave motion
Jin Zhu, Wei Zhang and Mengxue Wu
J. Vib. Acoust   doi: 10.1115/1.4039569
Evaluating the driving safety of moving vehicles on slender coastal bridges as well as the bridge safety are important to provide supporting data to make decisions on continuing or closing the operations of bridges under extreme weather conditions. However, such evaluations could be complicated due to the complex dynamic interactions of vehicle-bridge-wind-wave system. The present study proposes a comprehensive evaluation methodology on vehicle ride comfort and the driving safety on the slender coastal bridges subject to vehicle, wind, and wave loads. After a brief introduction of the vehicle-bridge-wind-wave coupling dynamic system and obtaining the dynamic responses of the vehicles, the vehicle ride comfort is evaluated using the advanced procedures as recommended in the ISO 2631-1 standard based on the overall vibration total value (OVTV). The vehicle driving safety is analyzed based on two evaluation criteria, i.e., the roll safety criteria (RSC) and the sideslip safety criteria (SSC), through the vehicle contact force responses at the wheels. Finally, the proposed methodology is applied to a long-span cable-stayed bridge for vehicle ride comfort and driving safety evaluation.
TOPICS: Bridges (Structures), Safety, Vehicles, Shorelines, Wind, Waves, Cable-stayed bridges, Dynamic systems, Stress, Vibration, Dynamic response, Wheels
Nir Dick, Scott Grutzik, Christopher Wallin, B. Robert Ilic, Slava Krylov and Alan Zehnder
J. Vib. Acoust   doi: 10.1115/1.4039568
A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.
TOPICS: Resonance, Separation (Technology), Cantilevers, Vacuum, Finite element analysis, Dynamic response, Piezoelectric actuators, Microcantilevers, Modal analysis, Excitation, Lasers, Interferometry

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