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Research Papers

J. Vib. Acoust. 2012;134(4):041001-041001-8. doi:10.1115/1.4005032.

To investigate the effect of oil film force on a geared rotor system, a short journal bearing model was applied to represent nonlinear oil film force. A dynamic model of the geared rotor oil journal bearing system was presented. The nonlinear gear mesh force and nonlinear oil film force were considered in the model. The nonlinear dynamic responses of the system were investigated by numerical integration method. This article shows that when the rotational speed is relatively low, the vibration of the system is mainly affected by nonlinear mesh force. With the increase of rotational speed, the influence of nonlinear oil film force also increases gradually, and the subsynchronous forward precession phenomena appear. When the speed increases to a certain value, the amplitude of the subsynchronous forward precession exceeds the amplitude of the rotational frequency, and the nonlinear mesh force is greatly affected by the nonlinear oil film force. However, the linear oil film force does not affect the nonlinear mesh force. The subsynchronous forward precession is difficult to be predicted by linear oil film force which was previously applied. This experiment is performed to validate the correctness of the dynamic model presented, and the numerical integration results of low speeds are validated by the experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041002-041002-9. doi:10.1115/1.4005828.

This work examines the dynamic behavior of a system consisting of a mass-block on the rough surface of a simply supported plate, harmonically excited in the tangential direction. The vertical excitation emerges from roughness, tracked by the mass-block. Low-frequency sliding results in high-frequency vertical excitation up to the ultrasonic range. The conditions of the elastic contact between the two bodies are modeled in the form of vertical contact stiffness. A specific friction law with a behavior similar to an elastically coupled coulomb damper represents the tangential direction. The model allows for the study of the interaction between the tangential friction behavior and the vertical roughness-induced vibrations. Parameters of interest are friction velocity, mass-block weight, surface roughness, and contact material. Because of nonlinearities, the theoretical model must be solved within the time domain. The theoretical results are verified through experimental results of a corresponding setup. The subject combines material science, contact mechanics, and structural dynamics.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041003-041003-9. doi:10.1115/1.4005652.

The paper addresses the power flow suppression in an elastic beam of the tubular cross section (a pipe) at relatively low excitation frequencies by deploying a small number of equally spaced inertial attachments. The methodology of boundary integral equations is used to obtain an exact solution of the problem in vibrations of this structure. The power flow analysis in a pipe with and without equally spaced eccentric inertial attachments is performed and the effect of suppression of the energy transmission is demonstrated theoretically. These results are put in the context of predictions from the classical Floquet theory for an infinitely long periodic structure. Parametric studies are performed to explore sensitivities of this effect to variations in the number of attachments. The theoretically predicted eigenfrequencies and insertion loss are compared with the dedicated experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041004-041004-12. doi:10.1115/1.4005833.

Dynamic behavior of cylindrical shell structures is an important research topic since they have been extensively used in practical engineering applications. However, the dynamic analysis of circular cylindrical shells with general boundary conditions is rarely studied in the literature probably because of a lack of viable analytical or numerical techniques. In addition, the use of existing solution procedures, which are often only customized for a specific set of different boundary conditions, can easily be inundated by the variety of possible boundary conditions encountered in practice. For instance, even only considering the classical (homogeneous) boundary conditions, one will have a total of 136 different combinations. In this investigation, the flexural and in-plane displacements are generally sought, regardless of boundary conditions, as a simple Fourier series supplemented by several closed-form functions. As a result, a unified analytical method is generally developed for the vibration analysis of circular cylindrical shells with arbitrary boundary conditions including all the classical ones. The Rayleigh-Ritz method is employed to find the displacement solutions. Several examples are given to demonstrate the accuracy and convergence of the current solutions. The modal characteristics and vibration responses of elastically supported shells are discussed for various restraining stiffnesses and configurations. Although the stiffness distributions are here considered to be uniform along the circumferences, the current method can be readily extended to cylindrical shells with nonuniform elastic restraints.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041005-041005-16. doi:10.1115/1.4005847.

This paper presents the analytical solutions for bilaterally infinite strings and infinite beams on which a point force is initially applied, which then moves on the structure at a constant velocity. The solutions are sought by first applying the Fourier transform to the spatial coordinate dependence, and then the Laplace transform to the time variable of dependence, of the governing equations of motion. For the strings, it is necessary to distinguish between the case of a sonic load (a force moving at the phase velocity of transverse waves) and the cases of subsonic and supersonic loads. This is achieved by a suitable expansion in polynomial ratios of the Laplace transform, before going back to the original Fourier transform, whose inverse is obtained by exact calculations of the integrals over the complex infinite domain. For the Euler-Bernoulli beam, the same process leads to the closed-form (exact) formula for the displacement, from which the stress can be deduced. The displacement consists of the sum of two integrals: one representing the transient part, and the other, the stationary part of the solution. The stationary part is observed in the vicinity of the force for a very long travel time. The transient part is observed at a finite position coordinate, in relative proximity to the starting point of the moving force. For the Timoshenko beam, the final step in the calculation of the displacement and rotation, which requires a numerical evaluation of the integrals, leads to Fourier cosine and sine transforms. The response of the beam depends on the load velocity, relative to the two characteristic velocities: those of shear waves and longitudinal waves. This demonstrates that the transient parts of the solutions, in the Euler-Bernoulli beam or in the Timoshenko beam, are quasi identical. However, classical theory fails to forecast high frequency responses, occurring with velocities of the load exceeding twenty per cent of the bar velocity. For a velocity greater than the velocity of the shear waves, classical theory wrongly forecasts the response. In addition, according to the Euler-Bernoulli beam theory, the flexural waves are able to exceed the bar velocity, which is not realistic. If the load moves for a long period, the solution in the vicinity of the load tends towards a stationary solution. It is important to note that the solution to the stationary problem must be completed by the solution to the associated homogeneous system to represent the physical stationary solution.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041006-041006-8. doi:10.1115/1.4005846.

The recurrence analysis method is used in the mechanical diagnosis of a gear transmission system using time domain data. The recurrence is a natural behavior of a periodic motion system, which tells the state of the system, after running some time, and will approach a certain past state. In this paper, some statistical parameters of recurrence qualification analysis are extensively evaluated for the use of mechanical diagnosis, based on fairly short acceleration time series; recurrence results are compared with those obtained from Fourier analysis, and the identification procedures for the failure gear transmission by recurrences is also presented. It is found that, using only fairly short time series, some statistical parameters in quantification recurrence analysis can give clear-cut distinction between a healthy and damaged state.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041007-041007-10. doi:10.1115/1.4005845.

The Bouc-Wen class models are widely used to portray different types of hysteretic behavior. This paper presents an effective genetic algorithms-based method for fitting a generalized Bouc-Wen model, proposed by Song and Der Kiureghian [2006, “Generalized Bouc-Wen Model for Highly Asymmetric Hysteresis,” ASCE J. Eng. Mech., 132 (6), p. 610618], to highly asymmetric experimental hysteretic loops. The performance function is based on integral relationships derived from the generalized Bouc-Wen differential equation for each of the six different phases of asymmetric hysteretic loops. The conditions, which must be satisfied by the model parameters to obtain closed and smooth hysteretic loops, are specified. The method is applied to fit the generalized Bouc-Wen model to hysteretic loops, which are obtained in laboratory experiments for a new type of mounts used for base isolation of forging hammers. By using a single degree of freedom (SDOF) system with the predicted hysteretic characteristics, a remarkably close agreement between the measured and simulated vibrations of hammer was obtained.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041008-041008-8. doi:10.1115/1.4006414.

A new formulation for the NDIF method (the nondimensional dynamic influence function method) is introduced to efficiently extract eigenvalues and mode shapes of arbitrarily shaped, homogeneous membranes with the fixed boundary. The NDIF method, which was developed by the authors for the accurate free vibration analysis of arbitrarily shaped membranes and plates including acoustic cavities, has the feature that it yields highly accurate solutions compared with other analytical methods or numerical methods (the finite element method and the boundary element method). However, the NDIF method has the weak point that the system matrix of the method is not independent of the frequency parameter and as a result the method needs the inefficient procedure of searching eigenvalues by plotting the values of the determinant of the system matrix in the frequency parameter range of interest. An improved formulation presented in the paper does not require the above-mentioned inefficient procedure because a newly developed system matrix is independent of the frequency parameter. Finally, the validity of the proposed method is shown in several case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to those calculated by exact, analytica, or numerical methods.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041009-041009-7. doi:10.1115/1.4005840.

Firstly, a calculation for percentiles of von Mises stress in linear structures subjected to Gaussian random loads is extended to the case of Gaussian random loads having nonzero mean values, i.e.,the inclusion of static loads. The development is restricted to the case of plane stress. The method includes calculation of a given percentile of von Mises stress to any desired accuracy, a rapid estimate of the percentile, and upper and lower bounds on the von Mises stress. The calculation expands the cumulative distribution function of the von Mises stress as a series of noncentral chi-square distributions. Summation of a sufficient number of terms of the series calculates the percentile to the desired accuracy. The rapid estimate of the percentile interpolates the distribution of the von Mises stress in a small number of inverse noncentral chi-square2 distribution functions. The upper and lower bounds on the percentiles take advantage of the noncentral chi-square distribution of summations of normally distributed stress components. Second and third calculation methods arise from approximations of the distribution of quadratic forms of noncentral normal variables, or equivalently, linear combinations of noncentral chi-square variables. These methods provide rapid estimates of percentiles of von Mises stress in linear structures under random loads having nonzero mean values. The accuracy and computational efficiency of the methods are reviewed and compared. The methods are expected to have wide application in design of and prognostics for components subjected to constant structural loads coupled with random loading arising from vibrations caused by wind, waves, seismic events, engines, turbulence, acoustic noise, etc.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041010-041010-6. doi:10.1115/1.4005837.

Vibration-based energy harvesters are usually designed to exhibit natural frequencies that match those of the excitation for maximum power output. This has spurred interest into the design of devices that respond to variable frequency sources. In this work, an electromagnetic energy harvester in the form of a base excited trapezoidal plate is proposed. The plate geometry is designed to achieve two closely spaced vibration modes in order to harvest energy across a broader bandwidth. The ensuing bending and twisting vibrations are utilized in this capacity by placing a magnet on the plate tip that moves past a stationary coil. A dynamic model is presented to predict the system performance and is verified experimentally.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041011-041011-11. doi:10.1115/1.4005836.

The parametric instability of planetary gears having elastic continuum ring gears is analytically investigated based on a hybrid continuous-discrete model. Mesh stiffness variations of the sun-planet and ring-planet meshes caused by the changing number of teeth in contact are the source of parametric instability. The natural frequencies of the time invariant system are either distinct or degenerate with multiplicity two, which indicates three types of combination instabilities: distinct-distinct, distinct-degenerate, and degenerate-degenerate instabilities. By using the structured modal properties of planetary gears and the method of multiple scales, the instability boundaries are obtained as simple expressions in terms of mesh parameters. Instability existence rules for in-phase and sequentially phased planet meshes are also discovered. For in-phase planet meshes, instability existence depends only on the type of gear mesh deformation. For sequentially phased planet meshes, the number of teeth on the sun (or the ring) and the type of gear mesh deformation govern the instability existence. The instability boundaries are validated numerically.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041012-041012-4. doi:10.1115/1.4005835.

This technical note is concerned with the free vibration problem of a cantilever beam with constant thickness and exponentially decaying width. Existing analytical results for such a vibration beam problem are found to be incomplete because lower frequencies could not be obtained. Presented herein is the exact characteristic equation for generating the complete vibration frequencies for the considered vibrating beam problem. Also the note treated for the first time such a tapered cantilever beam with a tip mass. The exact solutions (frequencies and mode shapes) are important to engineers designing such tapered beams and the results serve as benchmarks for assessing the validity, convergence and accuracy of numerical methods and solutions.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041013-041013-8. doi:10.1115/1.4006409.

Maintenance personnel in the U.S. military are interested in developing methods of damage detection for composite materials that are field expedient and less dependent on the operator’s experience than the current methods. A vibration-based method was developed for detecting damage in composite materials based on a measurement of the nonlinear forced response that damaged materials are assumed to exhibit. A damage feature was extracted for a structural component by quantifying the degree to which the reciprocity between two input-output structural paths fail due to the nonlinearities associated with damage. A dynamic nonlinear theoretical model was used to develop a better understanding of why reciprocity fails for networks of nonlinear components. Experimental results were obtained from carbon fiber composite specimens subjected to various levels of damage. It was determined that reciprocity measurements were capable of identifying damage due to impact energies of 10.8 N·m; however, the method was not capable of discerning damage that was not directly beneath the sensor locations. The levels of damage that could be consistently detected using the new methodology could be discovered through a close visual inspection. In comparison to currently employed methods of damage detection, the proposed methodology is less subjective but also less sensitive to damage. More development work will be required to propose this technology as a replacement for current methods such as ultrasound and tap testing.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041014-041014-10. doi:10.1115/1.4006410.

In this paper, time domain data from piezoelectric active-sensing techniques is utilized for structural health monitoring (SHM) applications. Piezoelectric transducers have been increasingly used in SHM because of their proven advantages. Especially, their ability to provide known repeatable inputs for active-sensing approaches to SHM makes the development of SHM signal processing algorithms more efficient and less susceptible to operational and environmental variability. However, to date, most of these techniques have been based on frequency domain analysis, such as impedance-based or high-frequency response functions-based SHM techniques. Even with Lamb wave propagations, most researchers adopt frequency domain or other analysis for damage-sensitive feature extraction. Therefore, this study investigates the use of a time-series predictive model which utilizes the data obtained from piezoelectric active-sensors. In particular, time series autoregressive models with exogenous inputs are implemented in order to extract damage-sensitive features from the measurements made by piezoelectric active-sensors. The test structure considered in this study is a composite plate, where several damage conditions were artificially imposed. The performance of this approach is compared to that of analysis based on frequency response functions and its capability for SHM is demonstrated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):041015-041015-14. doi:10.1115/1.4006413.

The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Vib. Acoust. 2012;134(4):044501-044501-6. doi:10.1115/1.4005844.

We studied free surface oscillations of a fluid in a cylinder tank excited by an electric motor with limited power supply. We investigated the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Numerical experiments are carried out to present the existence of several types of regular and chaotic attractors. For the first time powers (power of the motor, power consumed by the damping force under fluid free surface oscillations, and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2012;134(4):044502-044502-6. doi:10.1115/1.4005839.

A weakly nonlinear vibration absorber is used to suppress the primary resonance vibrations of a single degree-of-freedom weakly nonlinear oscillator with periodic excitation, where the two linearized natural frequencies of the integrated system are not under any internal resonance conditions. The values of the absorber parameters are significantly lower than those of the forced nonlinear oscillator, as such the nonlinear absorber can be regarded as a perturbation to the nonlinear primary oscillator. The characteristics of the nonlinear primary oscillator change only slightly in terms of its new linearized natural frequency and the frequency interval of primary resonances after the nonlinear absorber is added. The method of multiple scales is employed to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions. Selection criteria are developed for the absorber linear stiffness (linearized natural frequency) and nonlinear stiffness in order to achieve better performance in vibration suppression. Illustrative examples are given to show the effectiveness of the nonlinear absorber in suppressing nonlinear vibrations of the forced oscillator under primary resonance conditions.

Commentary by Dr. Valentin Fuster

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