A New Approach for Computing the Normal Forms of High Dimensional Nonlinear Systems

Normal form theory is very useful for direct bifurcation and stability analysis of nonlinear differential equations modeled in real life. This paper develops a new computation method for obtaining a significant refinement of the normal forms for high dimensional nonlinear systems. The method developed here uses the lower order nonlinear terms in the normal form for the simplifications of higher order terms. In the theoretical model for the nonplanar nonlinear oscillation of a cantilever beam, the computation method is applied to compute the coefficients of the normal forms for the case of two non-semisimple double zero eigenvalues. The normal forms of the averaged equations and their coefficients for non-planar non-linear oscillations of the cantilever beam under combined parametric and forcing excitations are calculated.

Quantify Resonance Inspection With Finite-Element-Based Modal Analyses

Resonance inspection uses the natural acoustic resonances of a part to identify anomalous parts. Modern instrumentation can measure the many resonant frequencies rapidly and accurately. Sophisticated sorting algorithms trained on sets of good and anomalous parts can rapidly and reliably inspect and sort parts. This paper aims at using finite-element-based modal analysis to put resonance inspection on a more quantitative basis. A production-level automotive steering knuckle is used as the example part for our study. First, the resonance frequency spectra for the knuckle are measured with two different experimental techniques. Next, scanning laser vibrometry is used to determine the mode shape corresponding to each resonance. The material properties including anisotropy are next measured to high accuracy using resonance spectroscopy on cuboids cut from the part. Then, finite element model (FEM) of the knuckle is generated by meshing the actual part geometry obtained with computed tomography (CT). The resonance frequencies and mode shapes are next predicted with a natural frequency extraction analysis after extensive mesh size sensitivity study. The good comparison between the predicted and the experimentally measured resonance spectra indicate that finite-element-based modal analyses have the potential to be a powerful tool in shortening the training process and improving the accuracy of the resonance inspection process for a complex, production level part. The finite element based analysis can also provide a means to computationally test the sensitivity of the frequencies to various possible defects such as porosity or oxide inclusions especially in the high stress regions that the part will experience in service.

Simultaneous Monitoring of Rolling-Element and Journal Bearings Using Analysis of Structure-Born Ultrasound Acoustic Emissions

The application of Acoustic Emission technology for monitoring rolling element or hydrodynamic plain bearings has been addressed by several authors in former times. Most of these investigations took place under idealized conditions, to allow the concentration on one single source of emission, typically recorded by means of a piezoelectric sensor. This can be achieved by either eliminating other sources in advance or taking measures to shield them out (e. g. by placing the acoustic emission sensor very close to the source of interest), so that in consequence only one source of structure-born sound is present in the signal. With a practical orientation this is often not possible. In point of fact, a multitude of potential sources of emission can be worth considering, unfortunately superimposing one another. The investigations reported in this paper are therefore focused on the simultaneous monitoring of both bearing types mentioned above. Only one piezoelectric acoustic emission sensor is utilized, which is placed rather far away from the monitored bearings. By derivation of characteristic values from the sensor signal, different simulated defects can be detected reliably: seeded defects in the inner and outer race of rolling element bearings as well as the occurrence of mixed friction in the sliding surface bearing due to interrupted lubricant inflow.

A Moving Zonal Method in the Time-Domain Simulation for Acoustic Propagation

Conventional time-domain schemes have limited capability in modeling long-range acoustic propagation because of the vast computer resources needed to cover the entire region of interest with a computational domain. Many of the long-range acoustic propagation problems need to consider propagation distances of hundreds or thousands of meters. It is thus very difficult to maintain adequate grid resolution for such a large computational domain, even with the state-of-the-art capacity in computer memory and computing speed. In order to overcome this barrier, a moving zonal-domain approach is developed. This concept uses a moving computational domain that follows an acoustic wave. The size and interval of motion of the domain are problem dependent. In this paper, an Euler-type moving domain in a stationary coordinate frame is first tested. Size effects and boundary conditions for the moving domain are considered. The results are compared and verified with both analytical solutions and results from the non-zonal domain. Issues of using the moving zonal-domain with perfectly-matched layers for the free-space boundary are also discussed.

Fluctuating Shear Stress Calibration Method Using a Channel Flow

Fluctuating wall shear stress causes vibration and radiated noise from a structure. In the past wall shear stress has been measured indirectly using hot wires and hot films. Recently direct shear sensors have been developed. In this paper a calibration device consisting of a 305 mm × 60 mm × 5 mm channel filled with glycerin is used to calibrate a direct shear stress sensor with amplitudes up to 10 Pa of shear stress over a frequency range from 10 Hz to 1 kHz. The analytically known flow field caused by an oscillating plate 5 mm from the sensor is verified using laser Doppler velocimetry (LDV). The flow field is derived using a frequency-wavenumber approach thereby allowing for a known spatial and temporal field to be generated by specifying a derived plate vibration.

Effect of Release Holes on Micro-Scale Solid-Solid Phononic Crystals

Solid-solid phononic crystals (solid inclusions in a solid matrix) exhibit wider bandgaps than those observed with air-solid phononic crystals (air inclusions in a solid matrix). In a solid-solid phononic crystal operating in the low MHz range, it is essential to place release holes in the center of the inclusions to release devices from the substrate. It is necessary to release, and therefore suspend the phononic crystal to avoid propagation losses through the substrate. In this report we investigate the effect of release holes on phononic bandgaps and highlight the need for careful design to avoid compromising the phononic bandgap. Studying release issues for solid-solid phononic crystals is essential for the successful fabrication of such devices.

Prediction of Changes in System Vibration Response Using Empirical Sensitivity Functions

To improve noise, vibration, and harshness (NVH) performance in a mechanical system, engineers make changes in the mass, damping, or stiffness properties of components in the system. A system response prediction method using a sensitivity function is suggested to reduce the cost in the design modification process. Embedded sensitivity functions derived solely from empirical data have been applied to identify optimal design modifications for reducing vibration resonance problems. In this paper, those sensitivity functions are used to predict the changes in vibration behavior of a system with respect to the design parameter modification. The cost and time for building many prototypes and testing actual parts can be reduced by identifying the best parameters to be changed and determining the amount of modification in those design variables through the prediction of the system response before actual components are built. The method is applied to a single degree of freedom analytical model to study the accuracy of the predictions. Finite element analyses are then conducted on a three-story structure with modifications to the stiffness and mass distributions to demonstrate the feasibility of these predictions in applications to more complicated structural systems.

Resonance Avoidance of Offshore Wind Turbines

Coincidence of structural resonances with wind turbine dynamic forces can lead to large amplitude stresses and subsequent accelerated fatigue. For this reason, the wind turbine system is designed to avoid resonance coincidence. In particular, the current practice is to design the wind turbine support structure such that its fundamental resonance does not coincide with the fundamental rotational and blade passing frequencies of the rotor. For offshore wind turbines, resonance avoidance is achieved by ensuring that the support structure fundamental resonant frequency lies in the frequency band between the rotor and blade passing frequencies over the operating range of the turbine. This strategy is referred to as “soft-stiff” and has major implications for the structural design of the wind turbine. This paper details the technical basis for the “soft-stiff” resonance avoidance design methodology, investigates potential vulnerabilities in this approach, and explores the sensitivity of the wind turbine structural response to different aspects of the system’s design. The assessment addresses the wind turbine forcing functions, the coupled dynamic responses and resonance characteristics of the wind turbine’s structural components, and the system’s susceptibility to fatigue failure. It is demonstrated that the design practices for offshore wind turbines should reflect the importance of aerodynamic damping for the suppression of deleterious vibrations, consider the possibility of foundation degradation and its influence on the support structure’s fatigue life, and include proper treatment of important ambient sources such as wave and gust loading. These insights inform potential vibration mitigation and resonance avoidance strategies, which are briefly discussed.

Vibration Energy Harvesting of a Hydraulic Engine Mount Using a Turbine

The hydraulic engine mount (HEM) has been designed to provide a vibration isolation characteristic to control road and engine induced vibrations in vehicles by using two fluid passages known as decoupler and inertia track. These types of engine mounts are known for their best noise, vibration, and harshness (NVH) suppression performance among other different types of engine mounts. However, a low cost technique to recycle the dissipated energy of the system in the process of vibration suppression is significantly advantageous. A novel design structure in which the decoupler is replaced with a water turbine to capture and restore the vibration energy of the system is presented in this paper. The turbine design and selection has been done based on the upper and lower chamber pressures and the fluid flow rates in the system’s resonant frequency. The mount vibration isolation and energy generation performance is studied in both frequency and time domains. The simulation results demonstrate that a considerable amount of energy can be harvested from the engine vibration sources. This recent study demonstrates a novel energy harvesting technique in vehicles that require minimum design modifications of conventional hydraulic mounts.

Estimating the Performance of Sound Restoration Hearing Protectors by Using the Speech Intelligibility Index

Despite advances in engineering noise controls and the use of administrative controls, miners are still dependent on hearing protection devices for prevention of noise-induced hearing loss. However, miners often raise concerns about the audibility of spoken communication when wearing conventional hearing protectors. Electronic technologies that selectively process and restore sounds from outside of hearing protectors have been suggested as a partial remedy to the audibility problem. To assess the potential benefits of this technology for miners, NIOSH tested the impact of nine electronic sound restoration hearing protectors on speech intelligibility in selected mining background noises. Because of the number of devices and potential settings of those devices, it was necessary to narrow the choices before conducting human subject testing. This was done by testing the nine devices on an acoustic test fixture (ATF) to acquire one-third-octave-band data, and then calculating the speech intelligibility index (SII) to determine estimates of performance across device, noise and setting. The estimates of speech intelligibility obtained with the SII are highly correlated with the intelligibility of speech under adverse listening conditions such as noise, reverberation, and filtering. The results of fixture based testing indicate that performance varies little between most devices, with few showing exceptionally good or poor estimated speech intelligibility. The most significant differences in estimated performance using the devices were between the different noise sources used, regardless of device or setting. The findings of this research were used to select the devices and settings for subsequent human subject based speech intelligibility testing. The human subject testing results largely concurred with the findings from the acoustic test fixture testing and calculation of speech intelligibility index. Specifically, variations in background noise led to the greatest differences in speech intelligibility.