A.N. Thite

The Quantification of Structure-Borne Transmission Paths by Inverse Methods - Part 1: Improved Singular Value Rejection Methods

Structure-borne sound from installed machinery is often transmitted into a receiver structure via many connection points and several co-ordinate directions at each of them. In order to quantify the contributions from the various connection points, the operational forces at the interfaces, or an equivalent set of forces at some other locations, should be determined. These forces may be combined with measured transfer functions to determine their contributions to the sound at the receiver locations. Inverse methods are becoming widely used, in which a matrix of measured accelerances is inverted at each frequency and used with operational acceleration data to find the forces. Due to poor conditioning of this matrix, however, the results can often be unreliable. In this paper, using both simulations and measurements, an assessment is made of the success and failure of various strategies for dealing with the problems of ill conditioning, in particular over-determination and singular value rejection. In each case the test structure is a rectangular plate, and a wide frequency range is covered to include regions of both low and high modal overlap. Critical for the rejection of singular values is a suitable threshold. It is established that previously used thresholds, based on estimates of error in either accelerances or operational responses, cannot be used universally. An alternative approach is developed in which the accelerance matrix is perturbed by a different amount for each sample of the operational responses. Based on this approach a more robust strategy is proposed which takes account simultaneously of the effect of errors in both the accelerances and operational responses.

The quantification of structure-borne transmission paths by inverse methods. Part 2: Use of regularization techniques

The inversion of an ill-conditioned matrix of measured data lies at the heart of procedures for the quantification of structure-borne sources and transmission paths. In an earlier paper the use of over-determination, singular value decomposition and the rejection of small singular values was discussed. In the present paper alternative techniques for regularizing the matrix inversion are considered. Such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography. The application to structure-borne sound transmission involves matrices, which vary much more with frequency and from one element to another. In this study Tikhonov regularization is used with the ordinary cross-validation method for selecting the regularization parameter. An iterative inversion technique is also studied. Here a form of cross-validation is developed allowing an optimum value of the iteration parameter to be selected. Simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques. Experiments are also performed to validate the results. Both techniques are found to give considerably improved results compared to singular value rejection.

Suspension parameter estimation in the frequency domain using a matrix inversion approach

The dynamic lumped parameter models used to optimise the ride and handling of a vehicle require base values of the suspension parameters. These parameters are generally experimentally identified. The accuracy of identified parameters can depend on the measurement noise and the validity of the model used. The existing publications on suspension parameter identification are generally based on the time domain and use a limited degree of freedom. Further, the data used are either from a simulated ‘experiment’ or from a laboratory test on an idealised quarter or a half-car model. In this paper, a method is developed in the frequency domain which effectively accounts for the measurement noise. Additional dynamic constraining equations are incorporated and the proposed formulation results in a matrix inversion approach. The nonlinearities in damping are estimated, however, using a time-domain approach. Full-scale 4-post rig test data of a vehicle are used. The variations in the results are discussed using the modal resonant behaviour. Further, a method is implemented to show how the results can be improved when the matrix inverted is ill-conditioned. The case study shows a good agreement between the estimates based on the proposed frequency-domain approach and measurable physical parameters.

Development of a Refined Quarter Car Model for the Analysis of Discomfort due to Vibration

In the automotive industry, numerous expensive and time-consuming trials are used to “optimize” the ride and handling performance. Ideally, a reliable virtual prototype is a solution. The practical usage of a model is linked and restricted by the model complexity and reliability. The object of this study is development and analysis of a refined quarter car suspension model, which includes the effect of series stiffness, to estimate the response at higher frequencies; resulting Maxwells model representation does not allow straightforward calculation of performance parameters. Governing equations of motion are manipulated to calculate the effective stiffness and damping values. State space model is arranged in a novel form to find eigenvalues, which is a unique contribution. Analysis shows the influence of suspension damping and series stiffness on natural frequencies and regions of reduced vibration response. Increase in the suspension damping coefficient beyond optimum values was found to reduce the modal damping and increase the natural frequencies. Instead of carrying out trial simulations during performance optimization for human comfort, an expression is developed for corresponding suspension damping coefficient. The analysis clearly shows the influence of the series stiffness on suspension dynamics and necessity to incorporate the model in performance predictions.

Development of an experimental methodology to evaluate the influence of a bamboo frame on the bicycle ride comfort

In the current environment of increased emphasis on sustainable transport, there is manifold increase in the use of bicycles for urban transport. One concern which might restrict the use is the ride comfort and fatigue. There has been limited research in addressing the difficulty in bicycle ride comfort quantification. The current study aims to develop a methodology to quantify bicycle discomfort so that performance of bicycles constructed from bamboo and aluminium alloy can be compared. Experimentally obtained frequency response functions are used to establish a relation between the road input and the seat and rider response. A bicycle track input profile based on standard road profiles is created so as to estimate the acceleration responses. The whole-body-vibration frequency weighting is applied to quantify the perception of vibration intensity so that eventual discomfort ranking can be obtained. The measured frequency response functions provide an insight into the effect of frame dynamics on the overall resonant behaviour of the bicycles. The beneficial effect of frame compliance and damping on lower modes of vibration is very clear in the case of bamboo frame, in turn affecting seat and rider response. In the bamboo frame, because of multiple resonances, the frequency response of the handlebar is smaller at higher frequencies suggesting effective isolation. Further improvements may have come from the joints made from natural composites. Overall, based on the comparative analysis and the methodology developed, bamboo frame shows significant improvement in ride comfort performance compared with the aluminium frame.

Quantification of Human Discomfort in a Vehicle Using a Four-Post Rig Excitation:

The ride comfort of a vehicle is a vital aspect determining competitiveness of vehicles. The comfort is intricately related to feelings of discomfort due to vibration. The discomfort depends on various dynamic aspects of the suspension-seat and surrounding system. In industry, the discomfort due to vibration is assessed by road testing on various surfaces; these road tests may not be accurately repeatable. Discomfort, in general, can be assessed by measurements based on a shaker table and seat combination. These results when used for “in vehicle situations” may not accurately indicate the level of human discomfort in a vehicle. In view of this, to quantify seated human discomfort in a vehicle, measurements were performed using a four-post rig simulator; the setup allows controlled in-situ experiments to be conducted. A group of six subjects were exposed to sinusoidal vibration at five magnitudes in the vertical direction for heave, roll and pitch motion. The objective is to develop a discomfort metric which could be used to compare vehicles. The preliminary results show varying significance of roll, pitch and heave motion. The results, however, confirm the nonlinear variation of perception as a function of the physical stimulus. The test setup can be used to study the effects of complex road inputs and eventually may contribute towards reduced reliance on road tests.

Experimentally validated dynamic results of a relaxation-type quarter car suspension with an adjustable damper

Models of varying degree of sophistication are used in vehicle dynamic studies. For ride comfort, Kelvin–Voigt arrangement is preferred and for impact harshness analysis, a relaxation-type suspension model, Zener or Maxwell type is used. The nonconsideration of relaxation-type models in ride comfort studies can result in significant errors for frequencies below ∼30 Hz. The object of the paper is to show the influence of the series stiffness on the effective suspension damping both experimentally and numerically. A frequency domain analysis of two-degree of freedom Zener quarter car model is performed to find the complex relation between effective damping coefficient and the limiting value of damping ratio for a given series stiffness. The nonlinear relation between shock absorber damping and the natural frequencies is clearly illustrated. A novel four-post rig set-up is used to validate the results by measuring transmissibilities, giving damping ratios for varying shock absorber settings. A closed form solution, based on a simplified partial model, of optimal damping coefficient, which is a nonlinear function of stiffnesses, shows good agreement with numerical simulations of the complete system. The nonlinearities in shock absorbers also influence the outcome. These findings can be a great value at early design stage.

Estimation of Sound Transmission through Extruded Panels Using a Coupled Waveguide Finite Element-Boundary Element Method

A coupled waveguide finite element and wavedomain boundary element method is presented. This numerical method is suitable for analysing systems with uniform properties along one direction, but with complex cross-sections. Subsequently the transmission loss through an extruded aluminium panel, of a type commonly used in railway carriages, is calculated and compared to measurements.

Experimental identification of shock absorber knocking noise using various input waveforms

Shock absorber transient noise, often referred as clonk or knock noise, has been a challenging vehicle noise and vibration concern. As the comfort standards have been rising and quieter power trains (quieter engines, hybrid power trains and electric drives) have been introduced, secondary noise sources could become a significant concern. This study investigates the shock absorber knocking noise on 11 fully adjustable, twin-tube gas-filled automotive shock absorbers, using industry standard damper dynamometer, and a new experimental setup involving the adaptation of one of the shakers of a four post rig to perform tests in isolation. Four of the shock absorbers were returned from the field for knocking noise. The noise was successfully reproduced using triangular and sinusoidal wave inputs with frequency of 10 to 20 Hz on the four post rig setup, while no noise was detected on the same shock absorbers with the damper dynamometer setup. Unlike previously published results, the �noisy� shock absorbers could be successfully identified with a high degree of certainty based exclusively on the performance curve that includes the effects of higher frequencies. The inter-cycle inconsistency in performance curve was the main differentiating aspect. The statistical measures proposed have robustly identified the �noisy� shock absorbers.

A sustainable approach of damping treatment for aluminium honeycomb sandwich structures

The damping plays a vital role in structural dynamic and acoustic performance of aluminium honeycomb sandwich structures. The viscoelastic damping treatment of skins is most common. An alternative, the use of sustainable cork inserts to improve the damping of cores and the whole assembly is investigated in this study. Structures with different filling degrees are analysed, as well as the optimum location for inserts is determined. The structural dynamic as well as the vibro-acoustic performance is estimated numerically. Average squared displacement amplitude reduction efficiency E d 2 ¯ ¯ is defined as the target parameter for structural dynamic performance, whereas average transmission loss effectiveness E TL ¯ is designed for vibro-acoustic performance. The structural dynamic models are validated by experimental vibration analysis, whereas the vibro-acoustic models are validated against published data. Different ways of bonding the inserts to the host structure are analysed in order to maximise damping. The highest improvement is obtained with a filling degree of 64% honeycomb voids and 9.76% increase in mass, for which an average squared displacement amplitude reduction of 35.25% and an average increase in transmission loss of 1.5 dB is achieved. The transmission loss increase in relation to the added mass is much higher than that achieved by doubling of mass in the mass law region. The introduction of cork inserts spreads the energy in local modes to a larger space, effectively decreasing the resonance amplitudes. Interestingly, damping does not increase with the number of inserts in a monotonic way and the improvement depends on the spatial distribution of inserts.