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Research Papers

J. Vib. Acoust. 2017;140(3):031001-031001-12. doi:10.1115/1.4037955.

Grinding is a vital method in machining techniques and an effective way to process materials such as hardened steels and silicon wafers. However, as the running time increases, the unbalance of grinding wheels produce a severe vibration and noise of grinding machines because of the uneven shedding of abrasive particles and the uneven adsorption of coolant, which has a severe and direct impact on the accuracy and quality of parts. Online balancing is an important and necessary technique to reduce the unbalance causing by these factors and adjust the time-varying balance condition of the grinding wheel. A new active online balancing method using liquid injection and free dripping is proposed in this paper. The proposed online balancing method possesses a continuous balancing ability and the problem of losing balancing ability for the active online balancing method using liquid injection is solved effectively because some chambers are full of liquid. The residual liquid contained in the balancing chambers is utilized as a compensation mass for reducing rotor unbalance, where the rotor phase is proposed herein as a target for determining the machine unbalance. A new balancing device with a controllable injection and free dripping structure is successfully designed. The relationship between the mass of liquid in the balancing chamber and the centrifugal force produced by liquid is identified. The performance of the proposed method is verified by the balancing experiments and the results of these experiments show that the vibration of unbalance response is reduced by 87.3% at 2700 r/min.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(3):031002-031002-9. doi:10.1115/1.4038437.

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(3):031003-031003-11. doi:10.1115/1.4038578.

While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031004-031004-10. doi:10.1115/1.4038807.

This paper examines the nonlinear vibration of a single conductor with Stockbridge dampers. The conductor is modeled as a simply supported beam and the Stockbridge damper is reduced to a mass–spring–damper–mass system. The nonlinearity of the system stems from the midplane stretching of the conductor and the cubic equivalent stiffness of the Stockbridge damper. The derived nonlinear equations of motion are solved by the method of multiple scales. Explicit expressions are presented for the nonlinear frequency, solvability conditions, and detuning parameter. The present results are validated via comparisons with those in the literature. Parametric studies are conducted to investigate the effect of variable control parameters on the nonlinear frequency and the frequency response curves. The findings are promising and open a horizon for future opportunities to optimize the design of nonlinear absorbers.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031005-031005-8. doi:10.1115/1.4038865.

Running-in wear experiments were conducted on a spherical-on-disk tester. The vibration signals collected in the experiments were detected by a combination of harmonic wavelet packet transform (HWPT) and cross-correlation analysis (CCA) methods. Experimental results show that the friction vibration signals detected in tangential and normal directions have the characteristics of no time delay and strong correlation. Their root-mean-square (RMS) values gradually reduce and enter a steady-state of fluctuation with the experiments time, which are consistent with the variation of friction coefficient and reflect the change of wear states from the running-in wear to the stable wear. Therefore, the detection of friction vibration can be realized by a combination of HWPT and CCA methods.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031006-031006-10. doi:10.1115/1.4038906.

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031007-031007-13. doi:10.1115/1.4038733.

This paper proposes an isolation transmissibility for the bending vibration of elastic beams. At both ends, the elastic beam is considered with vertical spring support and free to rotate. The geometric nonlinearity is considered. In order to implement the Galerkin method, the natural modes and frequencies of the bending vibration of the beam are analyzed. In addition, for the first time, the elastic continuum supported by boundary springs is solved by direct numerical method, such as the finite difference method (FDM). Moreover, the detailed procedure of FDM processing boundary conditions and initial conditions is presented. Two numerical approaches are compared to illustrate the correctness of the results. By demonstrating the significant impact, the necessity of elastic support at the boundaries to the vibration isolation of elastic continua is explained. Compared with the vibration transmission with one-term Galerkin truncation, it is proved that it is necessary to consider the high-order bending vibration modes when studying the force transmission of the elastic continua. Furthermore, the numerical examples illustrate that the influences of the system parameters on the bending vibration isolation. This study opens up the research on the vibration isolation of elastic continua, which is of profound significance to the analysis and design of vibration isolation for a wide range of practical engineering applications.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031008-031008-7. doi:10.1115/1.4038681.

Presented is a test methodology for characterizing the vibration sensitivity of miniature microphones. An ordinary vibration sensitivity experiment becomes difficult because vibrating surfaces are also sources of sound. This sound is picked up by the microphone being tested, changing the result. The sound pressure will be correlated with the vibration signal such that averaging will not serve to increase the accuracy of that result.The previously described techniques reduce the correlated pressure using custom experimental equipment and have geometric limitations. In the improved technique, the microphone is treated like a linear two-input-one-output system. The two input signals (vibration and acoustic pressure) are measured, and the vibration sensitivity is determined using two different spectral analysis techniques. These techniques have good agreement between one another, and the measured values fit well into a simple acoustic model of the microphone. A technique for estimating the major source of measurement error indicates that this error is small enough for a reasonable estimate of vibration sensitivity to be made.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031009-031009-11. doi:10.1115/1.4038940.

The uncertainty present in many vibrating systems has been modeled in the past using several approaches such as probabilistic, fuzzy, interval, evidence, and grey system-based approaches depending on the nature of uncertainty present in the system. In most practical vibration problems, the parameters of the system such as stiffness, damping and mass, initial conditions, and/or external forces acting on the system are specified or known in the form of intervals or ranges. For such cases, the use of interval analysis appears to be most appropriate for predicting the ranges of the response quantities such as natural frequencies, free vibration response, and forced vibration response under specified external forces. However, the accuracy of the results given by the interval analysis suffers from the so-called dependency problem, which causes an undesirable expansion of the intervals of the computed results, which in some case, can make the results unacceptable for practical implementation. Unfortunately, there has not been a simple approach that can improve the accuracy of the basic interval analysis. This work considers the solution of vibration problems using universal grey system (or number) theory for the analysis of vibrating systems whose parameters are described in terms of intervals or ranges. The computational feasibility and improved accuracy of the methodology, compared to interval analysis, are demonstrated by considering one and two degrees-of-freedom (2DOF) systems. The proposed technique can be extended for the uncertainty analysis of any multi-degrees-of-freedom system without much difficulty.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031010-031010-13. doi:10.1115/1.4038946.

A crucial problem of turbomachinery is the oil film instability on increasing the angular speed, which is correlated with the asymmetry of the bearing stiffness matrix and resembles the hysteretic instability somehow. As a beneficial effect is exerted on the latter by the anisotropy of the support stiffness, some favorable effects have been recently found by the author also for the former, whence a systematic analysis has been undertaken. The instability thresholds may be detected by the usual conventional methods, but a detailed analysis may be carried out by closed-form procedures in the hypothesis of symmetry of the rotor-shaft-support system, which condition approaches the real working of turbomachines quite often. Altogether, the results point out an improvement of the rotor stability for low Sommerfeld numbers by softening and locking the support stiffness in the vertical and horizontal directions, respectively. Nonetheless, the partial support release on one plane implies lower instability thresholds for large Sommerfeld numbers, but this drawback may be obviated by a sort of “two-mode” stiffness management, with some vertical flexibility for heavy loads and full blocking for light loads. Otherwise, it is possible to combine the anisotropic supports with journal bearing types that offer favorable stability behavior in the range of large Sommerfeld numbers. Basing on approximate but realistic models, the present analysis elucidates the changes of the rotor-shaft unstable trend on varying the external stiffness of the supports and gives tools for a rapid calculation of the expected instability thresholds.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031011-031011-12. doi:10.1115/1.4038945.

Squeak is an unwanted, annoying noise generated by self-excited, friction-induced vibration. A unique squeak test apparatus that can generate squeak noises consistently was developed by modifying and employing a sprag-slip mechanism. Such an apparatus enables building database that accurately ranks squeak propensity of material pairs and will be highly useful for noise, vibration, and harshness (NVH) engineers and vehicle interior designers. An analytical model of the apparatus was developed to identify instability conditions that induce unstable, large-amplitude vibration, therefore squeak noises. A finite element model was established and studied in this work to refine the design of the apparatus and better understand underlying phenomena of the squeak generation. Complex eigenvalue analysis (CEA) was used to study the instability of the system and results show that the instability occurs by the coalescence of two modes, which makes the effective damping of one of the coalesced modes negative. The instability condition from the CEA shows good agreement with the results obtained from the analytical model. Furthermore, dynamic transient analysis (DTA) was performed to investigate the stability of the system and confirm the instability conditions identified from the CEA. The effects of main design parameters on the stability were investigated by DTA. The results obtained from the actual tests show that the test apparatus consistently generates unstable vibration of a very large amplitude, indicating generation of squeak noises.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031012-031012-11. doi:10.1115/1.4038950.

For practical applications of the elastic metamaterials, dynamic behavior of finite structures made of elastic metamaterials with frequency dependent properties are analyzed theoretically and numerically. First, based on a frequency-dependent mass density and Young's modulus of the effective continuum, the global dynamic response of a finite rod made of elastic metamaterials is studied. It is found that due to the variation of the effective density and Young's modulus, the natural frequency distribution of the finite structure is altered. Furthermore, based on the spectral approach, the general wave amplitude transfer function is derived before the final transmitted wave amplitude for the finite-layered metamaterial structure with decreasing density is obtained using the mathematical induction method. The analytical analysis and finite element solutions indicate that the increased transmission wave displacement amplitude and reduced stress amplitude can be controlled by the impedance mismatch of the adjacent layers of the layered structure.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031013-031013-11. doi:10.1115/1.4038948.

A new light-activated shape memory polymer (LaSMP) smart material exhibits shape memory behaviors and stiffness variation via ultraviolet (UV) light exposures. This dynamic stiffness provides a new noncontact actuation mechanism for engineering structures. Isogeometric analysis (IGA) utilizes high order and high continuity nonuniform rational B-spline (NURBS) as basis functions which naturally fulfills C1-continuity requirement of Euler–Bernoulli beam and Kirchhoff plate theories. Compared with the traditional finite elements of beams and plates, IGA does not need extra rotational degrees-of-freedom while providing accurate results. The UV light-activated frequency control of LaSMP fully and partially laminated beam and plate structures based on the IGA is presented in this study. For the analysis of LaSMP partially laminated plates, the finite cell approach in the framework of IGA is proposed to handle NURBS geometries containing trimming features. The accuracy and efficiency of the proposed isogeometric approach are demonstrated via several numerical examples in frequency control. The results show that, with LaSMPs, broadband frequency control of beam and plate structures can be realized. Furthermore, changing LaSMP patch sizes on beams and plates further broadens its frequency control ranges. Studies suggest that: (1) the newly developed IGA combining finite cell approach is an effective numerical tool and (2) the maximum frequency manipulation ratios of beam and plate structures, respectively, reach 24.30% and 16.75%, which demonstrates the feasibility of LaSMPs-induced vibration control of structures.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031014-031014-6. doi:10.1115/1.4038942.

In order to broaden the sound absorption bandwidth of a perforated panel in the low frequency range, a lightweight membrane-type resonator is installed in the back cavity of the perforated panel to combine into a compound sound absorber (CSA). Because of the great flexibility, the membrane-type resonator can be vibrated easily by the incident sound waves passing through the holes of the perforated panel. In the low frequency range, the membrane-type resonator and the perforated panel constitute a two degrees-of-freedom (DOF)-resonant type sound absorption system, which generates two sound absorption peaks. By tuning the parameters of the membrane type resonator, a wide frequency band having a large sound absorption coefficient can be obtained. In this paper, the sound absorption coefficient of CSA is derived analytically by combining the vibration equation of the membrane-type resonator with the acoustic impedance equation of the perforated panel. The influences of the parameters of the membrane-type resonator on the sound absorption performance of the CSA are numerically analyzed. Finally, the wide band sound absorption capacity of the CSA is validated by the experimental test.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031015-031015-15. doi:10.1115/1.4038949.

This paper presents a novel formulation and exact solution of the frequency response function (FRF) of vibration energy harvesting beam systems by the distributed transfer function method (TFM). The method is applicable for coupled electromechanical systems with nonproportional damping, intermediate constraints, and nonclassical boundary conditions, for which the system transfer functions are either very difficult or cumbersome to obtain using available methods. Such systems may offer new opportunities for optimized designs of energy harvesters via parameter tuning. The proposed formulation is also systematic and amenable to algorithmic numerical coding, allowing the system response and its derivatives to be computed by only simple modifications of the parameters in the system operators for different boundary conditions and the incorporation of feedback control principles. Examples of piezoelectric energy harvesters with nonclassical boundary conditions and intermediate constraints are presented to demonstrate the efficacy of the proposed method and its use as a design tool for vibration energy harvesters via tuning of system parameters. The results can also be used to provide benchmarks for assessing the accuracies of approximate techniques.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031016-031016-9. doi:10.1115/1.4038951.

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031017-031017-8. doi:10.1115/1.4038947.

Machining process dynamics can be described by state-space delayed differential equations (DDEs). To numerically predict the process stability, diverse piecewise polynomial interpolation is often utilized to discretize the continuous DDEs into a set of linear discrete equations. The accuracy of discrete approximation of the DDEs generally depends on how to deal with the piecewise polynomials. However, the improvement of the stability prediction accuracy cannot be always guaranteed by higher-order polynomials due to the Runge phenomenon. In this study, the piecewise polynomials with derivative-continuous at joint nodes are taken into consideration. We develop a recursive estimation of derived nodes for interpolation approximation of the state variables, so as to improve the discretization accuracy of the DDEs. Two different temporal discretization methods, i.e., second-order full-discretization and state-space temporal finite methods, are taken as demonstrations to illustrate the effectiveness of applying the proposed approach for accuracy improvement. Numerical simulations prove that the proposed approach brings a great improvement on the accuracy of the stability lobes, as well as the rate of convergence, compared to the previous recorded ones with the same order of interpolation polynomials.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):031018-031018-7. doi:10.1115/1.4038944.

In this work, we investigate numerically the propagation of Lamb waves in a film bulk acoustic resonator (FBAR) structure formed by piezoelectric ZnO layer sandwiched between two Mo electrodes coupled with Bragg reflectors; the system is thus considered as a phononic-crystal (PnC) plate. The aim is to suppress the first-order symmetric Lamb wave mode considered as a spurious mode caused by the establishment of a lateral standing wave due to the reflection at the embedded lateral extremities of the structure; this spurious mode is superposing to the main longitudinal mode resonance of the FBAR. The finite element study, using harmonic and eigen-frequency analyses, is performed on the section of FBAR structure coupled with the PnC. In the presence of PnC, the simulation results show the evidence of a selective band gap where the parasitic mode is prohibited. The quality factor of the FBAR is enhanced by the introduction of the PnC. Indeed, the resonance and antiresonance frequencies passed from 1000 and 980 (without PnC) to 2350 and 1230 (with PnC), respectively. This is accompanied by a decrease in the electromechanical coupling coefficient from 10.60% to 6.61%.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Vib. Acoust. 2018;140(3):034501-034501-8. doi:10.1115/1.4038680.

Numerical optimizations are very useful in liner designs for low-noise aeroengines. Although modern computational tools are already very efficient for a single aeroengine noise propagation simulation run, the prohibitively high computational cost of a broadband liner optimization process which requires hundreds of thousands of runs renders these tools unsuitable for such task. To enable rapid optimization using a desktop computer, an efficient analytical solver based on the Wiener–Hopf method is proposed in the current study. Although a Wiener–Hopf-based solver can produce predictions very quickly (order of a second), it usually assumes an idealized straight duct configuration with a uniform background flow that makes it arguable for practical applications. In the current study, we employ the Wiener–Hopf method in our solver to produce an optimized liner design for a semi-infinite annular duct setup and compare its noise-reduction effect with an optimized liner designed by the direct application of a numerical finite element solver for a practical aeroengine intake configuration with an inhomogeneous background flow. The near-identical near- and far-field solutions by the Wiener–Hopf-based method and the finite element solvers clearly demonstrate the accuracy and high efficiency of the proposed optimization strategy. Therefore, the current Wiener–Hopf solver is highly effective for liner optimizations with practical setups and is very useful to the preliminary design process of low-noise aeroengines.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):034502-034502-6. doi:10.1115/1.4039030.

In this work, two model identification methods are used to estimate the nonlinear large deformation behavior of a nonlinear resonator in the time and frequency domains. A doubly clamped beam with a slender geometry carrying a central intraspan mass when subject to a transverse excitation is used as the highly nonlinear resonator. A nonlinear Duffing equation has been used to represent the system for which the main source of nonlinearity arises from large midplane stretching. The first model identification technique uses the free vibration of the system and the Hilbert transform (HT) to identify a nonlinear force–displacement relationship in the large deformation region. The second method uses the frequency response of the system at various base accelerations to relate the maximum resonance frequency to the nonlinear parameter arising from the centerline extensibility. Experiments were conducted using the doubly clamped slender beam and an electrodynamic shaker to identify the model parameters of the system using both of the identification techniques. It was found that both methods produced near identical model parameters; an excellent agreement between theory and experiments was obtained using either of the identification techniques. This follows that two different model identification techniques in the time and frequency domains can be employed to accurately predict the nonlinear response of a highly nonlinear resonator.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2018;140(3):034503-034503-4. doi:10.1115/1.4038956.

We revisit Mindlin's theory for flexural dynamics of plates using two correction factors, one for shear and one for rotary inertia. Mindlin himself derived and considered his equations with both correction factors, but never with the two simultaneously. Here, we derive optimal values of both factors by matching the Mindlin frequency–wavenumber branches with the exact Rayleigh–Lamb dispersion relations. The thickness shear resonance frequency is obtained if the factors are proportional but otherwise arbitrary. This degree-of-freedom allows matching of the main flexural mode dispersion with the exact Lamb wave at either low or high frequency by choosing the shear correction factor as a function of Poisson's ratio. At high frequency, the shear factor takes the value found by Mindlin, while at low frequency, it assumes a new explicit form, which is recommended for flexural wave modeling.

Commentary by Dr. Valentin Fuster

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