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### Research Papers

J. Vib. Acoust. 2017;140(1):011001-011001-9. doi:10.1115/1.4037214.

This paper presents an experimental study to find out an effective parameter which is useful to enhance the progression rate of drifting vibro-impact systems excited by a harmonic force. It is assumed that the system performance would be better if the excitation force stays in a harmonious relationship with the natural motion of the impact mass. This hypothesis has been numerically analyzed and then experimentally verified. The phase lag between the excitation force and the motion of the impact mass is used to identify the best situation, where the system progression rate is maximal. It has been found that the highest progression rate of the system can be obtained when the phase lag is around one-eighth of the excitation period.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011002-011002-18. doi:10.1115/1.4037176.

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011003-011003-8. doi:10.1115/1.4037142.

This paper examines an approach for determining the entropy of coupled oscillators that does not rely on the assumption of weak coupling. The results of this approach are compared to the results for a weakly coupled system. It is shown that the results from each methodology agree in the case of weak coupling, and that a correction term is required for moderate to strong coupling. The correction term is shown to be related to the mixed energy term from the coupling spring as well as the geometry and stiffness of the system. Numerical simulations are performed for a symmetric system of identical coupled oscillators and an asymmetric system of nonidentical oscillators to demonstrate these findings.

Topics: Entropy
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011004-011004-9. doi:10.1115/1.4037300.

This research presents a study of the free vibration of thin, shallow elliptical shells. The equations of motion for the elliptical shell, which are developed from Love's equations, are coupled and nonlinear. In this research, a new approach is introduced to uncouple the transverse motion of the shallow elliptical shell from the surface coordinates. Through the substitution of the strain-compatibility equation into the differential equations of motion in terms of strain, an explicit relationship between the curvilinear surface strains and transverse strain is determined. This latter relationship is then utilized to uncouple the spatial differential equation for transverse motion from that of the surface coordinates. The approach introduced provides a more explicit relationship between the surface and transverse coordinates than could be obtained through use of the Airy stress function. Angular and radial Mathieu equations are used to obtain solutions to the spatial differential equation of motion. Since the recursive relationships that are derived from the Mathieu equations lead to an infinite number of roots, not all of which are physically meaningful, the solution to the eigenvalue problem is used to determine the mode shapes and eigenfrequencies of the shallow elliptical shell. The results of examples demonstrate that the eigenfrequencies of the thin shallow elliptical shell are directly proportional to the curvature of the shell and inversely proportional to the shell's eccentricity.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011005-011005-11. doi:10.1115/1.4037469.

Structural characteristic deflection shapes (CDSs) such as mode shapes which contain spatial knowledge of structures are highly sensitive for damage detection and localization. Nevertheless, CDSs are vulnerable to measurement noise, which degrades the accuracy of damage identification. In order to enhance CDS-based damage identification, contributions are made in three aspects. First, a robust CDS estimation approach is proposed based on common principal component analysis, which estimates the CDSs as the common diagonalizer of a set of covariance matrices by joint approximation diagonalization (JAD). Second, an adaptive gapped smoothing method (GSM) is proposed and validated to be more accurate than the traditional GSM. Third, a new damage identification index capable of localizing damage and indicating relative damage severity is defined without requiring information of healthy structures. Finally, numerical and experimental examples of beams and a frame with cracks are studied to demonstrate the advantages of the proposed damage identification method in terms of noise robustness and accuracy.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011006-011006-13. doi:10.1115/1.4037468.

In this paper, a flexible pin-on-disk system is used to simulate how squeal noise can be generated in frictional contact. As the research object, the modeling process and transient simulation method of the flexible pin-on-disk system are introduced. By means of numerical simulation, the time-varying frictional squeal reappears by introducing periodic frictional coefficient generated from rotation. Afterward, the features of time-varying squeal are studied including time-domain features, frequency-domain features, transient deformation features of the disk and the pin on the occurrence of squeal, as well as energy features. Finally, the conception and mathematical expressions of modal contribution factor are defined, and the transient modal contribution factor features of every mode are studied to make clear the function of every mode. The relationship between mode contribution factors and the vibration is revealed. It reveals that modal contribution factors between squeal and not are quite different from each other. On no occurrence of squeal, the modal contribution factors of sine and cosine modes of the disk fluctuate in the way similar to harmonic wave, and the phase difference between the contribution factors of sine and cosine mode with the same nodal circle and the same nodal diameter is 90 deg. During squeal, the coupling mode may play the most important role but not all the time. At any time, the low-frequency modes play the leading role.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011007-011007-8. doi:10.1115/1.4037470.

In this paper, identification of energy dissipation in the joints of a lab-scale structure is accomplished. The identification is carried out by means of an energy flow analysis and experimental data. The devised procedure enables to formulate an energy balance in the vicinity of the joints to obtain local energy dissipation. In this paper, a damping matrix based on the locally identified damping coefficients is formulated. The formulated damping matrix is later used in a five-degrees-of-freedom (5DOF) system for validation. The results obtained with the proposed method are in good agreement with the experimental data, especially in the low frequency range.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011008-011008-10. doi:10.1115/1.4037471.

Inverse patch transfer functions (iPTF) method has been developed to reconstruct the sound field of irregularly shaped sources in a noisy environment. The iPTF method, which uses classic regularization methods to solve the ill-posed problems generally, would incur some sidelobes ghosting in the process of identifying sparse sources. In view of the fact that the algorithm in wideband holography (WBH) can promote sparsity of results, a technique combining iPTF method with WBH algorithm is proposed to identify sparsely distributed sources in the present work. In the proposed technique, double layer pressure measurements are used to replace the measurements of the pressure and normal velocity which uses costly p-u probes. A gradient descent algorithm and a filtering process are applied to solve the minimization problem of identifying the normal velocities of target sources, which can suppress ghosting sources rapidly by an iterative process. In simulations, the field reconstruction results of two antiphase square piston sources show good sparsity and accuracy by employing the technique, nearly without ghosting sources. At different distances and frequencies of the two sources, the technique still performs well. Experimental validations at 200 Hz and 400 Hz are carried out in the end. The results of experiments are also coinciding with those of simulations.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011009-011009-6. doi:10.1115/1.4037511.

An analysis is presented of the motion of a thin fiber, supported on each end, due to a sound wave that propagates in the direction perpendicular to its long axis. Predicted and measured results indicate that when fibers or hairs having a diameter measurably less than 1 μm are subjected to air-borne acoustic excitation, their motion can be a very reasonable approximation to that of the acoustic particle motion at frequencies spanning the audible range. For much of the audible range of frequencies resonant behavior due to reflections from the supports tends to be heavily damped so that the details of the boundary conditions do not play a significant role in determining the overall system response. Thin fibers are thus constrained to simply move with the surrounding medium. These results suggest that if the diameter or radius is chosen to be sufficiently small, incorporating a suitable transduction scheme to convert its mechanical motion into an electronic signal could lead to a sound sensor that very closely depicts the acoustic particle motion over a wide range of frequencies.

Topics: Fibers , Fluids , Acoustics
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011010-011010-14. doi:10.1115/1.4037521.

Due to its long-span structure and large flexibility, an electrified railway catenary is very sensitive to environmental wind load, especially the time-varying stochastic wind, which may lead to a strong forced vibration of contact line and deteriorate the current collection quality of the pantograph–catenary system. In this paper, in order to study the wind-induced vibration behavior of railway catenary, a nonlinear finite element procedure is implemented to construct the model of catenary, which can properly describe the large nonlinear deformation and the nonsmooth nonlinearity of dropper. The spatial stochastic wind field is developed considering the fluctuating winds in along-wind, vertical-wind, and cross-wind directions. Using the empirical spectra suggested by Kaimal, Panofsky, and Tieleman, the fluctuating wind velocities in three directions are generated considering the temporal and spatial correlations. Based on fluid-induced vibration theory, the model of fluctuating forces acting on catenary are developed considering the spatial characteristics of catenary. The time- and frequency-domain analyses are conducted to study the wind-induced vibration behavior with different angles of wind deflection, different angles of attack, as well as different geometries of catenary. The effect of spatial wind load on contact force of pantograph–catenary system is also investigated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011011-011011-8. doi:10.1115/1.4037514.

Inspired by fractal photonic/phononic crystals, the self-similar fractal technique is applied to design acoustic metamaterial. By replacing the straight channel of coiling up space with a smaller coiling up space, a class of topological architectures with fractal coiling up space is developed. The significant effect of the fractal-inspired hierarchy on the band structure with fractal coiling up space is systematically investigated. Furthermore, sound wave propagation in the acoustic metamaterial with the fractal coiling up space is comprehensively highlighted. Our results show that the acoustic metamaterial with higher-order fractal coiling up space exhibits deep subwavelength bandgaps, in which the sound propagation will be well blocked. Thus, this work provides insights into the role of the fractal hierarchy in regulating the dynamic behavior of the acoustic metamaterial and provides opportunities for the design of a robust filtering device in a subwavelength scale.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011012-011012-13. doi:10.1115/1.4037513.

An accurate and robust geometrically exact beam formulation (GEBF) is developed to simulate the dynamics of a beam with large deformations and large rotations. The undeformed configuration of the centroid line of the beam can be either straight or curved, and cross sections of the beam can be either uniform or nonuniform with arbitrary shapes. The beam is described by the position of the centroid line and a local frame of a cross section, and a rotation vector is used to characterize the rotation of the cross section. The elastic potential energy of the beam is derived using continuum mechanics with the small-strain assumption and linear constitutive relation, and a factor naturally arises in the elastic potential energy, which can resolve a drawback of the traditional GEBF. Shape functions of the position vector and rotation vector are carefully chosen, and numerical incompatibility due to independent discretization of the position vector and rotation vector is resolved, which can avoid the shear locking problem. Numerical singularity of the rotation vector with its norm equal to zero is eliminated by Taylor polynomials. A rescaling strategy is adopted to resolve the singularity problem with its norm equal to $2mπ$, where m is a nonzero integer. The current formulation can be used to handle linear and nonlinear dynamics of beams under arbitrary concentrated and distributed loads. Several benchmark problems are simulated using the current formulation to validate its accuracy, adaptiveness, and robustness.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011013-011013-10. doi:10.1115/1.4037700.

The inside-out ceramic turbine (ICT) is a promising concept to increase turbine inlet temperatures in microturbines by integrating individual monolithic ceramic. This architecture uses a carbon–polymer composite rim to support the blades mainly in compression. High tangential velocities lead to elevated radial displacement of the rim, and therefore, the rotor hub needs to have sufficient compliance to follow this radial displacement. However, the rotordynamics of a flexible hub is not widely understood. This paper presents the rotordynamic analysis of a highly flexible hub for an ICT architecture. Finite element modeling (FEM) is used to design a simplified turbine prototype that maximizes the hub flexibility to explore the limits of the concept. The rotordynamics behavior of the highly flexible hub is measured by spinning a 171-mm diameter prototype up to 49 krpm. This paper highlights three principal challenges of this particular rotordynamics. First, critical speeds mode shape becomes highly coupled with bearings displacement, shaft bending, and hub deformation. At high-speed, the hub deforms out of phase with the shaft, which can cause high stresses in the hub. Second, the angular position between unbalance masses of the flexible hub and the composite rim changes the unbalance response significantly. Finally, vibration causes high stresses in the hub, due to the relative displacement between the composite rim and the shaft, which could lead to failure of the hub. Nevertheless, the rotordynamics of an ICT configuration is manageable as long as the vibration-induced stress in the hub is kept under its limit.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011014-011014-9. doi:10.1115/1.4037508.

Inspired by the phenomenon of localized response intensification in wideband random vibration, a novel procedure is proposed to determine the optimal locations of piezoelectric patch attaching on wideband random point-driven beam for vibration energy harvesting application. The optimization objective is to maximize the mean output voltage, and the optimal locations lie on the vicinities of the excited point and its symmetric point. The optimal locations keep invariable regardless of typical symmetric boundary conditions (such as the clamped, simply supported, free, and torsional spring supports), the lower and upper cutoff frequencies of the band-limited white noise, and the external damping provided that the excited point is not too close to boundaries and the bandwidth of excitation covers enough modes of primary structure. The robustness of optimal locations is illustrated from an electromechanical coupling model and is qualitatively verified through experimental testing on a random-excited aluminum beam with piezoelectric patches attached on its surface.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011015-011015-13. doi:10.1115/1.4037510.

This paper describes a computationally efficient method to determine optimal locations of sensor/actuator (s/a) pairs for active vibration reduction of a flexible structure. Previous studies have tackled this problem using heuristic optimization techniques achieved with numerous combinations of s/a locations and converging on a suboptimal or optimal solution after multithousands of generations. This is computationally expensive and directly proportional to the number of sensors, actuators, possible locations on structures, and the number of modes required to be suppressed (control variables). The current work takes a simplified approach of modeling a structure with sensors at all locations, subjecting it to external excitation force or structure base excitation in various modes of interest and noting the locations of n sensors giving the largest average percentage sensor effectiveness. The percentage sensor effectiveness is measured by dividing all sensor output voltage over the maximum for each mode using time and frequency domain analysis. The methodology was implemented for dynamically symmetric and asymmetric structures under external force and structure base excitations to find the optimal distribution based on time and frequency responses analysis. It was found that the optimized sensor locations agreed well with the published results for a cantilever plate, while with very much reduced computational effort and higher effectiveness. Furthermore, it was found that collocated s/a pairs placed in these locations offered very effective active vibration reduction for the structure considered.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011016-011016-13. doi:10.1115/1.4037520.

Various vibration problems occur in rotating machinery. Specifically, the large amplitude vibration may occur in the vertical pump using a journal bearing. In an actual vertical pump, the stator's structure supporting the pump shaft may be relatively flexible. In such a case, rotor's motion such as amplitude of the self-excited vibration is not able to be predicted accurately without considering the nonlinear fluid film force reacting in the relative motion between the shaft and the flexibly supported bearing stator. However, the vibration characteristics in such situations have not been explained theoretically so far. In this paper, the vibration characteristics of a vertical rotating shaft with journal bearing are investigated. The nonlinear steady-state vibration analysis of the self-excited vibration is demonstrated, and the influences of the parameters, such as fluid viscosity, radial clearance, and stiffness and damping coefficients of the flexible support of bearing stator, on the vibration characteristics of the system are explained. Moreover, these theoretical results of the self-excited vibration in the vertical rotating shaft with journal bearing are verified both numerically and experimentally.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011017-011017-10. doi:10.1115/1.4037512.

Adding damping devices to the rotor supports is a frequently used technological solution for reducing vibrations of rotating machines. To achieve their optimum performance, their damping effect must be adaptable to the current operating speed. This is offered by magnetorheological squeeze film dampers. The magnetorheological oils are liquids sensitive to magnetic induction and belong to the class of fluids with a yielding shear stress. Their response to the change of a magnetic field is not instantaneous, but it is a process called the delayed yielding. The developed mathematical model of the magnetorheological squeeze film damper is based on the assumptions of the classical theory of lubrication. The lubricant is represented by a bilinear material, the yielding shear stress of which depends on magnetic induction. The delayed yielding process is described by a convolution integral with an exponential kernel. The developed mathematical model of the damper was implemented in the computational procedures for transient analysis of rotors working at variable operating speed. The carried-out simulations showed that the delayed yielding effect could have a significant influence on performance of magnetorheological damping devices. The development of a novel mathematical model of a magnetorheological squeeze film damper, the representation of the magnetorheological oil by bilinear material, taking the delayed yielding phenomenon into consideration, increased numerical stability of the computational procedures for transient analysis of flexible rotors, and extension of knowledge on behavior of rotor systems damped by magnetorheological squeeze film dampers are the principal contributions of this paper.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011018-011018-7. doi:10.1115/1.4037701.

The incoherent transport of ultrasound waves in water-saturated sintered glass bead packings is experimentally investigated. The spectral energy density of scattered high-frequency waves is explained by a diffusion wave equation. Immersion broadband transducers with central frequencies of 1 MHz are positioned at a distance of 73 mm to the porous sample. The diffusion coefficient and quality factor are predicted from a diffusion approximation of the time-dependent intensity curve to the ensemble-averaged measurement data. From the diffusion coefficient, we deduce a mean-free path for scattering events at $l*=0.87±0.03$ mm close to the range of particle diameters of the samples ($1.0 mm). Results are in good agreement with observations from Jia (2004, “Codalike Multiple Scattering of Elastic Waves in Dense Granular Media,” Phys. Rev. Lett., 93(15), p. 154303) observed for nonsintered and consolidated bead packings ($0.6 mm). The low-quality factor $Q=190±10$ indicates a high amount of intrinsic damping of the scattered waves although water was used as saturating and coupling fluid.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011019-011019-7. doi:10.1115/1.4037852.

The Ormia ochracea, a species of parasitic fly, has a remarkable localization ability despite the tiny interaural distance compared with the incoming wavelength. The mechanical coupling between its ears enhances the differences of the two received signals, the main cues to locate the source. Inspired by the coupling mechanism, we present a miniature coupled two-microphone array for estimating sound source horizontal bearing. The coupled array consists of a standard two-microphone array and a two-input, two-output filter which implements the coupling. The relationship between filter parameters and time delay magnification is investigated to provide theoretical support for array design. With appropriate parameters, the time delay of received signals can be linearly magnified. Based on the linear magnification, we present a method for estimating source direction using the coupled array. The influence of time delay magnification on time delay estimation accuracy is explored through the general cross-correlation (GCC) method. Experiments are conducted to verify the coupled array and demonstrate its advantages on improving the resolution of estimation of time delay and accuracy of bearing estimation compared with the standard array with the same element spacing.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Vib. Acoust. 2017;140(1):014501-014501-7. doi:10.1115/1.4037509.

Fast time-varying (FTV) phenomena, such as significant speed changes, FTV stiffness, and vibration signals with fast-oscillated instantaneous frequency (IF), carry critical fault information of high-speed rotating machines. However, the mechanism of FTV phenomenon remains unclear, and conventional methods cannot characterize the FTV features. In this study, the FTV vibration mechanism for rotor–stator contact systems is first revealed, and then, a novel fast-modulation-based rub-impact detection method (FRiDM) is significantly developed to extract the FTV features and thus promote the effectiveness of rub-impact diagnosis. The FTV vibration mechanism indicates that the fast-oscillated modulation of the vibration signal is the physical property, and the fast oscillation of IF is the mathematical nature. By theoretical and experimental study, it is demonstrated that the FTV features of the rotor–stator contact system are periodic for the periodic motion but aperiodic for the quasi-periodic and chaotic motions. Finally, the validity of the proposed FTV vibration mechanism and FRiDM is verified by the application to the rub-impact diagnosis of a bearing life testing rig and a dual-rotor turbine engine. The study results provide a potential way to nonlinear behavior identification and fault localization of sophisticated rotor systems.

Commentary by Dr. Valentin Fuster