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IN THIS ISSUE

### TECHNICAL PAPERS

J. Vib. Acoust. 2006;129(4):397-405. doi:10.1115/1.2424968.

In this paper, a method for designing and fabricating broadband vibration absorbers (BBVAs) for structural noise control is described. The BBVA’s consist of a series of cantilevered masses, closely spaced in frequency and sharing a common hub that attaches to the host structure. To accommodate applications involving shell structures, both translational and rotational degrees of freedom are considered in the analysis. The BBVA is modeled with a simple, three-by-three impedance matrix to facilitate its subsequent incorporation into a larger structural optimization study. In order to validate this modeling method, an experimental impedance identification method was developed. This method was applied to a physical BBVA consisting of 12, cantilevered masses emanating from a common hub and attached to a solid base plate that simulates the degrees of freedom of a shell structure. Analytical and experimental results are in excellent agreement, demonstrating the efficacy of the approach. The proposed modeling and fabrication method provides a simple and straightforward way to incorporate BBVAs in optimization studies applied to the design of quiet structures.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):406-416. doi:10.1115/1.2748457.

This paper investigates the pressure pulsations caused by each mass flow rate through the suction valves and ports of a multicylinder compressor in order to attribute high-pressure pulsation responses to certain valves. By staggering the valve configurations appropriately, it is shown that the level of gas pulsations in the suction manifold of a multicylinder automotive compressor can be reduced. First, the equation for a compression cycle, a Bernoulli-Euler linear differential beam equation for the suction valves, and the piston kinematics are considered in order to calculate the mass flow rates through the compressor suction valves. The pressure pulsations in the suction manifold are then predicted based on the characteristic cylinder method using the calculated mass flow rates. In order to investigate the effects of each mass flow rate, the characteristics and phases of the mass flow rates through the suction valves are changed by modifying the clearance volume.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):417-424. doi:10.1115/1.2748459.

In this paper, vibration behavior of engine on the nonlinear hydraulic engine mount, including inertia track and decoupler, is studied. In this regard, after introducing the nonlinear factors of this mount (i.e., inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between the rubber and the hydraulic engine mounts, a six-degree-of-freedom four-cylinder V-shaped engine under shaking and balancing mass forces and torques is considered. By solving the time domain nonlinear equations of motion of the engine on three inclined mounts, translational and rotational motions of an engine body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of a hydraulic one in the low-frequency region.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):425-433. doi:10.1115/1.2748463.

A mechanical model describing finite motions of nonshallow cables around the initial catenary configurations is proposed. An exact kinematic formulation accounting for finite displacements is adopted, whereas the material is assumed to be linearly elastic. The nondimensional mechanical parameters governing the motions of nonshallow cables are obtained via a suitable nondimensionalization, and the regions of their physically plausible values are portrayed. The spectral properties of linear unforced undamped vibrations around the initial static configurations are investigated via a Galerkin-Ritz discretization. A classification of the modes is obtained on the basis of their associated energy content, leading to geometric modes, elastostatic modes (with prevalent transverse motions and appreciable stretching), and elastodynamic modes (with prevalent longitudinal motion). Moreover, an extension of Irvine’s model to moderately nonshallow cables is proposed to determine the frequencies and mode shapes in closed form.

Topics: Cables
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):434-440. doi:10.1115/1.2748464.

In this paper, a method for identifying the damping coefficients of a directional well sucker-rod pumping system is put forward by means of the chain code method of pattern recognition. The 24-directional chain code is provided to encode the dynamometer card curve. The parametric equation of the dynamometer card curve is transformed into Fourier series whose coefficients can be computed according to the curve’s chain codes. By means of these coefficients, shape characteristics of the curve are extracted. The Euclidean distance is introduced as the measurement of similar degree between the shape characteristics of measured dynamometer card and that of simulated dynamometer card. Changing the value of viscous damping coefficient and Coulomb friction coefficient in the simulation program, different simulated dynamometer cards are obtained. Substituting their shape characteristics to the Euclidean distance, respectively, a series of distances are acquired. When the distance is less than the given error, the corresponding values of the damping coefficients in the simulation program are regarded as real damping coefficients of the sucker-rod pumping system of directional well. In the end, an example is provided to show the correctness and effectiveness of the presented method.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):441-447. doi:10.1115/1.2748466.

A novel signal analysis technique capable of detecting periodic bursts of exponentially decaying oscillation from noisy discrete-time observations is presented. The time-frequency distribution of the signal is viewed as a series of time signals corresponding to different frequency variables, and each time signal is processed with the technique of synchronous average scanning over a frequency region of interest. The energies of the outputs corresponding to different frequency bands and different average reference frequencies are recorded in a 2D array and depicted as a gray level image. Detection of the signal of interest leads itself to the identification of the spot in the image. The period of the impulse train and the frequency of the oscillation can be further estimated from the location of the spot. Examples that diagnose machine faults under complicated conditions are given to confirm the validity of the approach.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):448-457. doi:10.1115/1.2731407.

Considering both nonlinear oil film force and unsymmetrical stiffness, this paper presents a mechanical model of a generator-bearing system. The complex mode synthesis method is used to reduce the linear degrees of freedom of the high order model in the rotating coordinates, and one-order modal differential equations are obtained which may not be solved directly by Newmark-$β$ method. To solve this problem, a modified Newmark-$β$ method is presented to investigate dynamic effects of the asymmetry of rotor stiffness, the viscosity of oil, the rotor unbalance and the ratio of length to diameter of bearings. Three-dimension diagrams and unfiltered vibration curves are used as tools to examine the dynamic behavior of the system, and some insights into the dynamic behavior are given. Numerical results show that instability of the system may be improved by modifying these parameters.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):458-470. doi:10.1115/1.2748467.

This paper presents a kurtosis-based hybrid thresholding method, K-hybrid, for denoising mechanical fault signals. The threshold used in the hybrid thresholding method is determined based on kurtosis, which is an important indicator of the signal-to-noise ratio (SNR) of a signal. This together with its sensitivity to outliers and data-driven nature makes a kurtosis-based threshold particularly suitable for on-line detection of mechanical faults featuring impulsive signals. To better reflect the signal composition, the proposed hybrid thresholding rule divides the wavelet transformed input signals into four zones associated with different denoising actions. This alleviates the difficulties present in the simple keep-or-remove and shrink-or-remove approaches adopted by the hard- and soft-thresholding rules. The boundaries of the four zones are on-line adjusted in response to the kurtosis change of the signal. Our simulation results suggest that the mean squared error (MSE) is unable to distinguish the results in terms of the amount of falsely identified impulses. It is therefore inappropriate to use MSE alone for evaluating the denoising results of mechanical signals. As such, a combined criterion incorporating both MSE and false identification power $Pfalse$ is proposed. Our analysis has shown that the proposed K-hybrid approach outperforms the soft, hard, and BayesShrink thresholding methods in terms of the combined criterion. It also compares favorably to the MAP thresholding method for signals with low kurtosis or low SNR. The proposed approach has been successfully applied to noise reduction and fault feature extraction of bearing signals.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):471-477. doi:10.1115/1.2748471.

An elevator rope for a high-rise building is forcibly excited by the displacement of the building caused by wind forces. Regarding the rope, there are two boundary conditions. In the first case, one end moves with time and the other end is fixed, while in the second case, both ends move with time. A theoretical solution to the forced vibration of a rope where one end is moving has been already obtained. In this paper, a theoretical solution to the forced vibration of a rope where both ends are moving is presented, based on the assumption that rope tension and movement velocity are constant, and that the damping coefficient of the rope is zero or small. The virtual sources of waves, which can be assigned to reflecting waves, are used to obtain the theoretical solution. Finite difference analyses of rope vibration are also performed to verify the validity of the theoretical solution. The calculated results of the finite difference analyses are in fairly good agreement with that of the theoretical solution. The effects of the changing rate of rope length and the damping factor on the maximum rope displacement are quantitatively clarified.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):478-483. doi:10.1115/1.2748472.

A finite element formulation is developed for solving the problem related to thermoelastic damping in beam resonator systems. The perturbation analysis on the governing equations of heat conduction, thermoleasticity, and dynamic motion leads to a linear eigenvalue equation for the exponential growth rate of temperature, displacement, and velocity. The numerical solutions for a simply supported beam have been obtained and shown in agreement with the analytical solutions found in the literature. Parametric studies on a variety of geometrical and material properties demonstrate their effects on the frequency and the quality factor of resonance. The finite element formulation presented in this work has advantages over the existing analytical approaches in that the method can be easily extended to general geometries without extensive computations associated with the numerical iterations and the analytical expressions of the solution under various boundary conditions.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):484-494. doi:10.1115/1.2748473.

This study provides a theoretical and experimental investigation of the effect of the thread and bearing friction coefficients on the self-loosening of threaded fasteners that are subjected to cyclic transverse loads. The friction coefficients are varied by using different types of coating and lubrication. A phosphate and oil coating and an olefin and molydisulfide solid film lubricant are used on the bolts tested. A mathematical model is developed to evaluate the self-loosening behavior in threaded fasteners when subjected to cyclic transverse loads. An experimental procedure and test setup are proposed in order to collect real-time data on the loosening rate (rate of clamp load loss per cycle) as well as the rotational angle of the bolt head during its gradual loosening. The experimental values of the friction coefficients are used in the mathematical model to monitor their effect on the theoretical results for the loosening rate. Experimentally, the friction coefficients are modified by changing the coating or the lubrication applied to the fasteners. The theoretical and experimental results are presented and discussed.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):495-506. doi:10.1115/1.2748475.

Among the advanced techniques of the predictive maintenance, the vibratory analysis proves to be very effective, in particular, for monitoring rotating components such as the bearings. Their damage creates cyclic efforts which are at the origin of the processing of vibratory measurements. This processing can be made by temporal methods, frequential methods, or by time-scale methods using the wavelets for 2 decades. The wavelet transform is a very effective processing, however, the difficulties of application and interpretation of the results slow down their employment. The determination of the parameters of the wavelets makes its use all the more difficult. Moreover, the use of these time-scale methods is very expensive in time computation. This paper proposes a wavelet adapted to the mechanical shock response of a structure with $n$ degrees of freedom. In addition, we developed a procedure for analysis of signals by this wavelet which makes it possible to accelerate the process and to improve detection in the case of disturbed signals. This methodology is compared with the traditional time-scale methods and is implemented to detect defects of different sizes on outer rings and inner rings of ball bearings.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(4):507-513. doi:10.1115/1.2731417.

It has been known that it is difficult to establish a fuzzy logic model with effective fuzzy rules and the associated membership functions. Neural network with its learning capability has been incorporated to make the fuzzy model more adaptive and effective. A self-organized neuro-fuzzy model by integrating the Mamdani fuzzy model and the backpropagation neural network is developed in this paper for system identification. The five-layer network adaptively adjusts the membership functions and dynamically optimizes the fuzzy rules. A benchmark test is applied to validate the model accuracy in nonlinear system identification. Experimental verifications on the dynamics of a composite smart structure and on an acoustics system also demonstrate that the neuro-fuzzy model is superior to the neural network and to an adaptive filter in system identification. The model can be established systematically and is shown to be effective in engineering applications.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):514-519. doi:10.1115/1.2748479.

In this paper we demonstrate both numerically and experimentally that it is possible to make a pinned-pinned shallow arch snap to and remain vibrating on the other side by harmonic excitation in the longitudinal direction at the end. One end of the arch is fixed in space, while the other end is attached to a mechanical shaker via a spring. The shaker-mount is first moved a small distance toward the arch to ensure that the arch assembly possesses two stable equilibrium positions, one on each side of the base line. The spring connecting the arch end and the mechanical shaker is carefully chosen such that a small shaker stroke can induce a large vibration amplitude in the arch. The natural frequencies of the two (initial and snapped, respectively) positions are measured first. By adjusting the excitation frequency of the mechanical shaker to the first natural frequency of either position of the arch, we demonstrate that the arch can be snapped to and remain vibrating on the other side when the magnitude of the electric current flowing through the shaker is properly chosen. The vibrant snapping action of the arch recorded in the experiment is confirmed by numerical simulation.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Vib. Acoust. 2007;129(4):520-524. doi:10.1115/1.2748462.

The traditional ball-type automatic balancer consisting of several balls moving on a circular orbit is widely used in the optical disk drive industry for vibration reduction. Under proper working conditions, the balls can counterbalance the imbalance of a disk by positioning to appropriate angles relative to the mass center of the disk. This particular equilibrium position is referred to as the perfect balancing position. The proper working conditions are closely related to the stability of the perfect balancing position, which, in turn, depends on the parameters of the system, such as rotational speed, imbalance ratio, and damping ratios. To achieve perfect balancing, the system parameters must lie in the stable region of the perfect balancing position in the parameter space. An automatic balancer with a wider stable region can tolerate a larger amount of variations in the system parameters and hence is more robust. In this study, we propose a modified ball-type balancer composed of several ball-rod-spring units. In each unit, the ball can slide along the rod while the rod rotates freely about the spindle. The ball’s displacement along the rod is restrained by a radial spring. The additional degree of freedom in the radial direction could broaden the stable region of the perfect balancing position. To understand the fundamental properties of the modified balancer, we studied the dynamic characteristics of a modified balancer with one ball-rod-spring unit. Specifically, we built a theoretical model for an optical disk drive packed with the modified balancer, and investigated how equilibrium positions and the associated stability are related to primary system parameters and the effects of the stiffness of the radial spring on the stable region of the perfect balancing position. Numerical results indicate that the ball-rod-spring balancer may possess a larger stable region of the perfect balancing position compared to the traditional fixed-orbit balancer.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2007;129(4):525-529. doi:10.1115/1.2748775.

Acoustic emission sensors were used to detect contact between a moving tape and the flange of a tape guide. The influence of tape drive operating conditions on the tape edge contact force was studied. A one-dimensional model was developed to predict the magnitude of tape/flange impact. The model fits the experimental data well.

Commentary by Dr. Valentin Fuster

### CLOSURE

J. Vib. Acoust. 2007;129(4):530. doi:10.1115/1.2750154.
FREE TO VIEW

The author has commented that magnetic fields add vectorially and thus the addition of a second magnet results in a magnetic field with exactly twice the radial component.  This is indeed true and is simply the result of the superposition of the two magnetic fields as was carried out and stated in the paper.  The effect of this superposition gives the appearance of a “compressed” magnetic field. The use of the word “compressed” was intended to be descriptive, not technical.

Commentary by Dr. Valentin Fuster