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Research Papers

J. Vib. Acoust. 2019;141(5):051001-051001-9. doi:10.1115/1.4043353.

Nonlinear energy interaction is a fascinating feature of nonlinear oscillators and has been drawing the attention of researchers since the last few decades. Omnipresent friction in mechanical systems can play a crucial role in modifying these interactions. Using post-buckled flexible inverted pendulum as a candidate system we characterize here, theoretically and experimentally, significant changes in the nonlinear energy transfer in the presence of friction at the input side. Particularly, even with relatively low friction, the energy gets transferred in the higher harmonics of excitation close to a resonant mode as against the transfer to higher modes reported previously. We term this new phenomenon as “excitation harmonic resonance locking.” Theoretical modeling and simulations, considering large deformations, based on assumed modes method, and using a simple friction model reasonably capture the experimental observation. In summary, the paper explicates the role of friction in shifting energy transfer frequencies and can be useful in understanding and designing of oscillators and nonlinear vibrating systems.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051002-051002-13. doi:10.1115/1.4043411.

The authors present an improved formulation for the axisymmetric solid harmonic finite element (FE) modeling of a flexible, spinning rotor. A thorough comparison of beam-type FE and axisymmetric solid FE rotor models is presented, indicating the errors that result from beam FE usage for various nondimensional rotor topologies. The axisymmetric rotor is meshed in only two dimensions: axial and radial, with both displacement fields being represented with Fourier series expansions. Centrifugal stress-stiffening and spin-softening effects are included in all elements and most importantly in modeling flexible disks. Beam FE and axisymmetric FE natural frequencies, mode shapes, and critical speeds are compared to identify shaft geometries where the beam model yields a significant error. Finally, limitations of beam FE models and guidance for utilizing axisymmetric solid FE models in rotor dynamic simulations are provided.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051003-051003-11. doi:10.1115/1.4042932.

A simple passive technique of vibration isolation for flexible structures by nonlinear boundaries is investigated, which to our best knowledge is the first study of its kind reported in the literature. The equations of the structure are derived with Hamilton’s principle. An iterative analytic method is investigated to improve the accuracy of the response prediction. The effect of nonlinear boundaries of the structure is studied compared with the linear structure. It is found that stronger nonlinearities in the boundary make the system more stable. Analytical and simulation results show that nonlinear boundaries can significantly reduce the vibration and stress of flexible structures. It is important to point out that with the help of nonlinear boundaries, structural vibration and stress control can be achieved without altering the original structure.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051004-051004-12. doi:10.1115/1.4043508.

Wayside acoustic defective bearing detector (ADBD) system is a potential technique in ensuring the safety of traveling vehicles. However, Doppler distortion and multiple moving sources aliasing in the acquired acoustic signals decrease the accuracy of defective bearing fault diagnosis. Currently, the method of constructing time-frequency (TF) masks for source separation was limited by an empirical threshold setting. To overcome this limitation, this study proposed a dynamic Doppler multisource separation model and constructed a time domain-separating matrix (TDSM) to realize multiple moving sources separation in the time domain. The TDSM was designed with two steps of (1) constructing separating curves and time domain remapping matrix (TDRM) and (2) remapping each element of separating curves to its corresponding time according to the TDRM. Both TDSM and TDRM were driven by geometrical and motion parameters, which would be estimated by Doppler feature matching pursuit (DFMP) algorithm. After gaining the source components from the observed signals, correlation operation was carried out to estimate source signals. Moreover, fault diagnosis could be carried out by envelope spectrum analysis. Compared with the method of constructing TF masks, the proposed strategy could avoid setting thresholds empirically. Finally, the effectiveness of the proposed technique was validated by simulation and experimental cases. Results indicated the potential of this method for improving the performance of the ADBD system.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051005-051005-6. doi:10.1115/1.4043509.

The Lamb wave propagation through a thin plate with periodic spatiotemporal variation of material property was investigated through numerical simulations. It was found that regular oscillations of Young's modulus in both space and time can lead to the creation of distinct band gaps for different modes of Lamb wave. Moreover, the dispersion relation for each mode was dependent on the direction of wave propagation (i.e., nonreciprocal). These results allow the Lamb wave modes to be reduced to a single mode traveling in a single direction for specific frequencies. This frequency range was observed to widen with an increasing modulation amplitude of Young's modulus but was not significantly altered by the modulation frequency. The insights derived from this study indicate that spatiotemporal control of material property can be used to effectively isolate Lamb wave modes and reduce reflections, leading to an improvement in the accuracy of the structural health monitoring of materials.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2019;141(5):051006-051006-11. doi:10.1115/1.4043510.

This paper considers the problem of controlling the vibration of a lightweight thin-walled rotor with a distributed actuation magnetic bearing (DAMB). A theoretical flexible rotor model is developed that shows how multiharmonic vibration arises due to small noncircularity of the rotor cross section. This model predicts a series of resonance conditions that occur when the rotational frequency matches a subharmonic of a system natural frequency. Rotor noncircularity can be measured offline, and the measurement data used to cancel its effect on the position sensor signals used for feedback control. A drawback of this approach is that noncircularity is difficult to measure exactly and may vary over time due to changing thermal or elastic state of the rotor. Moreover, any additional multiharmonic excitation effects will not be compensated. To overcome these issues, a harmonic vibration control algorithm is applied that adaptively modifies the harmonic components of the actuator control currents to match a target vibration control performance, but without affecting the stabilizing feedback control loops. Experimental results for a short thin-walled rotor with a single DAMB are presented, which show the effectiveness of the techniques in preventing resonance during operation. By combining sensor-based noncircularity compensation with harmonic vibration control, a reduction in vibration levels can be achieved without precise knowledge of the rotor shape and with minimal bearing forces.

Commentary by Dr. Valentin Fuster

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