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IN THIS ISSUE

### Research Papers

J. Vib. Acoust. 2017;139(3):031001-031001-16. doi:10.1115/1.4035482.

A semi-analytic method is presented to analyze free and forced vibrations of combined conical–cylindrical–spherical shells with ring stiffeners and bulkheads. First, according to locations of discontinuity, the combined shell is divided into one opened spherical shell and a number of conical segments, cylindrical segments, stiffeners, and bulkheads. Meanwhile, a semi-analytic approach is proposed to analyze the opened spherical shell. The opened spherical shell is divided into narrow strips, which are approximately treated as conical shells. Then, Flügge theory is adopted to describe motions of conical and cylindrical segments, and stiffeners with rectangular cross section are modeled as annular plates. Displacement functions of conical segments, cylindrical segments, and annular plates are expanded as power series, wave functions, and Bessel functions, respectively. To analyze arbitrary boundary conditions, artificial springs are employed to restrain displacements at boundaries. Last, continuity and boundary conditions are synthesized to the final governing equation. In vibration characteristics analysis, high accuracy of the present method is first demonstrated by comparing results of the present method with ones in literature and calculated by ansys. Further, axial displacement of boundaries and open angle of spherical shell have significant influence on the first two modes, and forced vibrations are easily affected by bulkheads and external force.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031002-031002-7. doi:10.1115/1.4035485.

This paper presents an efficient impedance eduction method for grazing flow incidence tube by using a surrogating model along with the Wiener–Hopf method, which enables rapid acoustic predictions and effective impedance eductions over a range of parametric values and working conditions. The proposed method is demonstrated by comparing to the theoretical results, numerical predictions, and experimental measurements, respectively. All the demonstrations clearly suggest the capability and the potential of the proposed solver for parametric studies and optimizations of the lining methods.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031003-031003-18. doi:10.1115/1.4035480.

The vibration signal decomposition is a critical step in the assessment of machine health condition. Though ensemble empirical mode decomposition (EEMD) method outperforms fast Fourier transform (FFT), wavelet transform, and empirical mode decomposition (EMD) on nonstationary signal decomposition, there exists a mode mixing problem if the two critical parameters (i.e., the amplitude of added white noise and the number of ensemble trials) are not selected appropriately. A novel EEMD method with optimized two parameters is proposed to solve the mode mixing problem in vibration signal decomposition in this paper. In the proposed optimal EEMD, the initial values of the two critical parameters are selected based on an adaptive algorithm. Then, a multimode search algorithm is explored to optimize the critical two parameters by its good performance in global and local search. The performances of the proposed method are demonstrated by means of a simulated signal, two bearing vibration signals, and a vibration signal in a milling process. The results show that compared with the traditional EEMD method and other improved EEMD method, the proposed optimal EEMD method automatically obtains the appropriate parameters of EEMD and achieves higher decomposition accuracy and faster computational efficiency.

Topics: Bearings , Vibration , Signals
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031004-031004-8. doi:10.1115/1.4035378.

The coupling matrix in structural-acoustic systems carries the entire information about the coupled resonances. We have found an elegant way of presenting this matrix and computing its determinant analytically (in a closed-form) for light fluid loading cases. The determinant gets factorized into a product. This form can be used to gain an insight into the new order of the coupled resonances. The specific example of a rectangular panel backed by a cavity is taken to demonstrate the method. This being the primary objective of the work, secondarily, the form of the matrix so derived is used to compute the new coupled resonances using a simple iterative scheme requiring a starting guess. Numerical values are compared with those given in the literature and also using the commercial package virtual lab.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031005-031005-15. doi:10.1115/1.4035382.

Combined systems consisting of linear structures carrying lumped attachments have received considerable attention over the years. In this paper, the assumed modes method is first used to formulate the governing equations of the combined system, and the corresponding generalized eigenvalue problem is then manipulated into a frequency equation. As the number of modes used in the assumed modes method increases, the approximate eigenvalues converge to the exact solutions. Interestingly, under certain conditions, as the number of component modes goes to infinity, the infinite sum term in the frequency equation can be reduced to a finite sum using digamma function. The conditions that must be met in order to reduce an infinite sum to a finite sum are specified, and the closed-form expressions for the infinite sum are derived for certain linear structures. Knowing these expressions allows one to easily formulate the exact frequency equations of various combined systems, including a uniform fixed–fixed or fixed-free rod carrying lumped translational elements, a simply supported beam carrying any combination of lumped translational and torsional attachments, or a cantilever beam carrying lumped translational and/or torsional elements at the beam's tip. The scheme developed in this paper is easy to implement and simple to code. More importantly, numerical experiments show that the eigenvalues obtained using the proposed method match those found by solving a boundary value problem.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031006-031006-12. doi:10.1115/1.4035700.

This paper presents a comprehensive comparison and analysis for the effect of time delay on the five most representative semi-active suspension control strategies, and refers to four unsolved problems related to semi-active suspension performance and delay mechanism that existed. Dynamic characteristics of a commercially available continuous damping control (CDC) damper were first studied, and a material test system (MTS) load frame was used to depict the velocity-force map for a CDC damper. Both inverse and boundary models were developed to determine dynamic characteristics of the damper. In addition, in order for an improper damper delay of the form $t+τ$ to be corrected, a delay mechanism of controllable damper was discussed in detail. Numerical simulation for five control strategies, i.e., modified skyhook control SC, hybrid control (HC), COC, model reference sliding mode control (MRSMC), and integrated error neuro control (IENC), with three different time delays: 5 ms, 10 ms, and 15 ms was performed. Simulation results displayed that by changing control weights/variables, performance of all five control strategies varied from being ride comfort oriented to being road handling oriented. Furthermore, increase in delay time resulted in deterioration of both ride comfort and road handling. Specifically, ride comfort was affected more than road handling. The answers to all four questions were finally provided according to simulation results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031007-031007-14. doi:10.1115/1.4035701.

Unsteady separated flow from deployed weapons bay doors can interact with the highly unsteady flow in the open bay cavity, which is known to exhibit strong acoustic content and could lead to fluid-resonance and high-intensity acoustic noise. The culmination of these unique flow physics can potentially excite structural modes of the doors, aircraft surfaces, or externally carried munitions and fuel tanks and can ultimately lead to aeroelastic instabilities, such as buffet, flutter, limit-cycle oscillations, or fatigue-induced failures. A hybrid Reynolds-averaged Navier–Stokes large eddy simulation (RANS/LES) method with low-dissipation schemes is developed to improve flow and acoustics predictive capabilities for supersonic weapons bays. Computational simulations are conducted for a weapons cavity with different deployed bay doors configurations, including the effect of dynamically moving doors, to assess the tonal content and unsteady aerodynamic loads on the doors. Wind tunnel testing is also carried out to provide unsteady experimental data for use in validating the high-fidelity simulation capability. The simulation results in terms of unsteady pressure, velocity fluctuations, and pressure resonant frequencies are computed and presented. The results suggest that the deployed doors energize the shear layer and cause it to go deeper into the cavity and produce higher unsteady fluctuations on the weapons cavity floor and aft wall. The deployed doors also cause a shift in the dominant resonant modes.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031008-031008-10. doi:10.1115/1.4035717.

We propose two methods to broaden the operation bandwidth of a nonlinear pinned–pinned piezoelectric bimorph power harvester. The energy-scavenging structure consists of a properly poled and electroded flexible bimorph with a metallic layer in the middle, and is subjected to flexural vibration. Nonlinear effects at large deformations near resonance are considered by taking the in-plane extension of the bimorph into account. The resulting output powers are multivalued and exhibit jump phenomena. Two methods to broaden the operation bandwidth are proposed: The first method is to extend the operation frequency to the left single-valued region through optimal design. The second method is to excite optimal initial conditions with a voltage source. Larger output powers in the multivalued region of the nonlinear harvester are obtained. Hence, the operation bandwidth is broadened from the left single-valued region to the whole multivalued region.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031009-031009-14. doi:10.1115/1.4035702.

A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031010-031010-24. doi:10.1115/1.4035814.

Due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, nonsynchronous limit-cycle vibration exists. In such undesirable situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. However, a comprehensive study into this nonlinear behavior of an imbalanced planar-rigid rotor/autobalancing device (ABD) system mounted on a general bearing holding asymmetric damping and stiffness forces including nonconservative effects cross-coupling ones has not been fully conducted. Therefore, this research primarily focuses on the unstable nonsynchronous limit-cycle behavior and the synchronous balancing condition of system under the influence of the general bearing support. Here, solutions for rotor limit-cycle amplitudes and the corresponding whirl speeds are obtained via a harmonic balance approach. Furthermore, the limit-cycle stability is assessed via perturbation and Floquet analysis, and all the possible responses including undesirable coexistence for the bearing parameters and operating speeds have been thoroughly studied. It is found that, due to asymmetric behavior of bearing support, the multiple limit cycles are encountered in the range of supercritical speeds and more complicate coexistences are invited into the ABD–rotor system compared to the case with idealized symmetric bearing supports. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems mounted on a asymmetric general bearing support.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031011-031011-7. doi:10.1115/1.4035781.

The inevitable manufacturing errors of rotational machineries cause vibration of multifrequency. This paper presents a multidynamic vibration absorber (MDVA) to suppress the vibration of multifrequency. The MDVA consists of two parts, and each part includes three dynamic vibration absorbers (DVAs) with equal mass but different stiffness values. In order to improve the robustness of the system, an optimization method to obtain the optimal damping values of each DVA is proposed based on dynamic response. The objective function of optimization aims to flatten the frequency response of the primary system with the changeable excitation and reduce the vibration level in a limited frequency bandwidth. The multifrequency vibration suppression is experimentally verified. To achieve the optimal damping values, the magnetic dampers are applied in the tests. The experimental results indicate that the sensitivity of the system is reduced and the robustness of the system is enhanced, which are coincident with the simulations.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031012-031012-12. doi:10.1115/1.4036098.

This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the stability limit (bifurcation point). A third-order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced-order model, with modes concerning the bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031013-031013-10. doi:10.1115/1.4035959.

A dynamic model is developed for small-scale robots with multiple high-frequency actuated compliant elastic legs and a rigid body. The motion of the small-scale robots results from dual-direction motion of piezoelectric actuators attached to the legs, with impact dynamics increasing robot locomotion complexity. A dynamic model is developed to describe the small-scale robot motion in the presence of variable properties of the underlying terrain. The dynamic model is derived from beam theory with appropriate boundary and loading conditions and considers each robot leg as a continuous structure moving in two directions. Robot body motion is modeled in up to five degrees-of-freedom (DOF) using a rigid body approximation for the central robot chassis. Individual modes of the resulting multimode robot are treated as second-order linear systems. The dynamic model is tested with two different centimeter-scale robot prototypes having an analogous actuation scheme to millimeter-scale microrobots. In accounting for the interaction between the robot and ground, a dynamic model using the first two modes of each leg shows good agreement with experimental results for the centimeter-scale prototypes, in terms of both magnitude and the trends in robot locomotion with respect to actuation conditions.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031014-031014-7. doi:10.1115/1.4036097.

The converse flexoelectric effect, i.e., the polarization (or electric field) gradient-induced internal stress (or strain), can be utilized to actuate and control flexible structures. This study focuses on the microscopic actuation behavior and effectiveness of a flexoelectric actuator patch laminated on an elastic ring shell. An atomic force microscope (AFM) probe is placed on the upper surface of the flexoelectric patch to induce an inhomogeneous electric field resulting in internal stresses of the actuator patch. The flexoelectric stress-induced membrane control force and bending control moment regulate the ring vibration and their actuation mechanics, i.e., transverse and circumferential control actions, are, respectively, studied. For the transverse direction, the electric field gradient quickly decays along the ring thickness, resulting in a nonuniform transverse distribution of the induced stress, and this distribution profile is not influenced by the actuator thickness. The flexoelectric-induced circumferential membrane control force and bending control moment resemble the Dirac delta functions at the AFM contact point. The flexoelectric actuation can be regarded as a localized drastic bending to the ring. To evaluate the actuation effect, dynamic responses and controllable displacements of the elastic ring with flexoelectric actuations are analyzed with respect to design parameters, such as the flexoelectric patch thickness, AFM probe radius, ring thickness, and ring radius.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031015-031015-8. doi:10.1115/1.4036096.

In this paper, a novel vibration isolator based on a foldable cylinder with a torsional buckling pattern, which is also called Kresling's pattern, is proposed, and the performance of the proposed isolator in terms of preventing structural vibration is numerically evaluated. It is known that foldable cylinders with a torsional buckling pattern provide bistable folding motions under specific conditions. For simplification, a foldable cylinder with a torsional buckling pattern is modeled using horizontal, longitudinal, and diagonal truss elements connected by rotational joints and enforced by rigid frames, which are also called Rahmen, while maintaining the bistability of the structure. Additional linear springs are incorporated into the structure in order to obtain a nonlinear spring with quasi-zero-stiffness characteristics. It is numerically established that: (i) the resonance of the combined structure is effectively suppressed and (ii) the structure decreases the vibration response even at high frequencies when it is used around the equilibrium position at which the spring stiffness is quasi-zero.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):031016-031016-13. doi:10.1115/1.4036110.

The work investigates the application of a novel frame model to reduce computational cost of the mistuning analysis of bladed disk systems. A full-scale finite element (FE) model of the bladed disk is considered as benchmark. The frame configuration for a single blade is identified through structural identification via an optimization process. The individual blades are then assembled by three-dimensional (3D) springs, whose parameters are determined by means of a calibration process. The dynamics of the novel beam frame assembly is also compared to those obtained from three state-of-the-art FE-based reduced order models (ROMs), namely: a lumped parameter approach, a Timoshenko beam assembly, and component mode synthesis (CMS)-based techniques with free and fixed interfaces. The development of these classical ROMs to represent the bladed disk is also addressed in detail. A methodology to perform the mistuning analysis is then proposed and implemented. A comparison of the modal properties and forced response dynamics between the aforementioned ROMs and the full-scale FE model is presented. The case study considered in this paper demonstrates that the beam frame assembly can predict the variations of the blade amplitude factors, and the results are in agreement with full-scale FE model. The CMS-based ROMs underestimate the maximum amplitude factor, while the results obtained from beam frame assembly are generally conservative. The beam frame assembly is four times more computationally efficient than the CMS fixed-interface approach. This study proves that the beam frame assembly can efficiently predict the mistuning behavior of bladed disks when low-order modes are of interest.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Vib. Acoust. 2017;139(3):034501-034501-4. doi:10.1115/1.4035813.

Obtaining head-related transfer functions (HRTFs) is a challenging task, in spite of its importance in localizing sound in a three-dimensional (3D) environment or improving the performance of hearing aids, among their various applications. In this paper, an optimized finite element method through adaptive dimension size based on wavelength (frequency) for acoustic scattering analyses using ansys is presented. Initial investigation of the validity of our method is conducted by simulating scattered sound field for a solid sphere exposed to a far-field plane sound wave at 100 (equally spaced in logarithmic scale) frequencies between 20 and 20 kHz. Comparison of the equivalent HRTF results between the two methods shows a maximum deviation of less than 0.6 dB between our method and the analytical solution depending on the angle of rotation of the sphere with respect to sound source.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;139(3):034502-034502-5. doi:10.1115/1.4035715.

A platform supported by a hexapod of quasi-zero-stiffness (QZS) struts is proposed to provide a solution for low-frequency vibration isolation in six degrees-of-freedom (6DOFs). The QZS strut is developed by combining a pair of mutually repelling permanent magnets in parallel connection with a coil spring. Dynamic analysis of the 6DOFs QZS platform is carried out to obtain dynamic responses by using the harmonic balance method, and the vibration isolation performance in each DOF is evaluated in terms of force/moment transmissibility, which indicates that the QZS platform perform a good function of low-frequency vibration isolation within broad bandwidth, and has notable advantages over its linear counterpart in all 6DOFs.

Commentary by Dr. Valentin Fuster