Vibration of a rectangular plate with a central power-law profiled groove by the Rayleigh-Ritz method

The prediction of natural frequencies of rectangular plates where a profiled indentation is present is made using a Rayleigh-Ritz variational energy method. Panels with holes are often found for access cables and access gaps, and it is shown that the application of damping to the profile leads to a more efficient method of reducing vibration than covering a whole rectangular plate, which is advantageous where weight saving is necessary

Automotive tyre cavity noise modelling and reduction

Noise and vibration in automotive vehicles relates to a feeling of luxury. Noise, Vibration and Harshness engineers spend significant time tuning designs to achieve this. Low noise must be achieved against a requirement to reduce weight, installation time, manufacturing complexity, achieve a carbon reduction and an increase in fuel economy. One particularly annoying noise originates in the pressurised air cavity bounded by the metal wheel and tyre rubber surfaces and is referred to as “tyre cavity noise”. It is a particularly problematic resonance due to the low frequency (approximately 200 - 250Hz) and the low loss factor of air, causing high amplitude sound. Traditionally, this is addressed through the careful choice of suspension natural frequencies to avoid coupling resonances and addition of mass damping layers to the cabin and transmission paths. In this paper, a numerical model of the tyre cavity is shown with passive resonators to reduce the noise. Complications that arise due to wheel loading, speed, temperature changes and manufacturing durability are discussed, with an optimisation routine used to obtain tuned Helmholtz resonators for inclusion in wheel spokes. A stationary experimental rig is introduced as a validation tool, with an array of microphones used to find the actual sound pressures

Damping of flexural vibrations in circular plates with tapered central holes

The paper develops a numerical approach to the calculation of mobilities for a circular plate with a tapered central hole of power-law profile. The exact solution of the corresponding flexural wave equation that exists for m = 2 has been used in the process of the numerical solution of the corresponding boundary problem. Note that this value of 171 belongs to the power-law range m >= 2 associated with zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation. Two cases of added damping in the central hole area have been considered: a thin absorbing layer and a constrained layer. Cross and point mobilities have been calculated for both these cases. The obtained results for point and cross mobilities show a substantial suppression of resonant peaks (up to 17 dB), in comparison with the cases of a plate with an uncovered hole of the same power-law profile and of a reference circular plate of constant thickness covered or uncovered by a thin absorbing layer. Further theoretical and experimental research is needed to examine applications of the obtained numerical results to more practical situations, e.g. to rectangular plates or other structures with arbitrary locations of tapered holes. (C) 2010 Elsevier Ltd. All rights reserved

Enhancement of the mode purity of shear horizontal mode of a thickness-shear transducer through design changes

In ultrasonic guided waves, arrays of thickness-shear piezoelectric transducers are often used to generate Lamb and shear-horizontal waves in plates and longitudinal/torsional waves in pipes. The shear-horizontal modes (torsional modes in pipes) are particularly useful for guided wave testing. Although the ultrasonic output of such transducers are well known both numerically and experimentally, few results are available in the literature regarding the influence of geometry, electrode layout and materials on the ultrasonic output of the transducer: in particular, the influence of those parameters on the mode purity of the generated shear horizontal mode in plates requires further investigation. Numerical simulations with finite element modelling (Comsol Multiphysics) have been conducted on a thickness-shear transducer on a plate to understand the influence of these parameters. The study has been conducted both in frequency domain and time domain: the former was used to calculate the frequency response function of the transducer-waveguide system while the latter was used to verify the proportionality between different modes. Different configurations of the transducers have been designed and tested numerically, and the in- and out-of-plane displacements generated are compared for all the three configurations. The effect of geometry and electrode layout are at first assessed in terms of purity of the shear horizontal mode; the most performing configuration is then further modified to enhance the amplitude and the signal to noise ratio of the generated mode. Design changes can then be predicted and suggested

Damping of flexural vibrations in rectangular plates using the acoustic black hole effect

The reduction of flexural vibration in plate structures has been investigated using the recently reported acoustic black hole effect for flexural wave reflection in plates with the local thickness varying according to h(x) = epsilon x(m) and m >= 2. Since sharp edges of such plates (wedges) are always truncated before x=0, the real reflection coefficients are relatively high, therefore the application of a small amount of damping is required to achieve large reductions in vibration amplitude. This paper presents a numerical model of a plate incorporating an acoustic black hole wedge, with predictions for vibration amplitudes. These are compared to equivalent experimental measurements for a range of applied damping layers. It is concluded that the above-mentioned power-law wedges can be used as effective vibration dampers in plate structures over a wide frequency range of interest. (C) 2010 Elsevier Ltd. All rights reserved

Damping of flexural vibrations in plates containing ensembles of tapered indentations of power-law profile

In this work, we report experimental results on damping flexural vibrations in rectangular plates containing tapered indentations (pits) of power-law profile, the centres of which are covered by a small amount of absorbing material. In the case of quadratic or higher-order profiles, such indentations materialise two-dimensional acoustic 'black holes' for flexural waves. Initially, the effects of single pits have been investigated. It has been found that, in order to increase the damping efficiency of power-law profiled indentations, their absorption crossections should be enlarged by drilling a central hole of sufficiently large size (14 mm), while keeping the edges sharp. Such pits, being in fact curved power-law wedges, result in substantially increased damping. The next and the major part of this investigation involved using multiple indentations in the same rectangular plates to increase damping. Plates with combinations from two to six equal indentations have been investigated. The results show that, when multiple indentations are used, the associated damping increases substantially with the increase of a number of indentations. For the plate with 6 indentations, the resulting damping becomes comparable if not greater than that achieved by a wedge of power-law profile

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor. (c) 2011 Acoustical Society of America. [DOI: 10.1121/1.3585844

Development of accurate pneumatic tyre finite element models based on an optimization procedure

A novel method for extracting the geometric and constitutive material properties of pneumatic tyres from available numerical or experimental data for the development of realistic and reliable tyre numerical models is proposed. This method involves an optimization procedure, which incorporates a finite element model as a solver (ABAQUS) properly coupled with an optimiser function (MATLAB). Following that, an initial tyre model (P235/75R17) is developed, and then its properties are suitably adjusted via the optimization process, in order for the former to best fit a target model available in the literature, with respect to eigenfre-quency analysis results. After the termination of the algorithm, the “optimum” tyre model (i.e. the model which best conforms to the target model) is obtained, the response of which is further investigated to ensure its realistic behaviour, which warrants its use for various numerical simulations. The results of this study show clearly the efficiency of the optimization procedure proposed, as well as the realistic response of the tyre model developed

Dynamic response of rigid wheels on deformable terrains

Off-road vehicle performance, such as vehicle mobility, maneuverability, and traction performance is generally affected by the pneumatic tyre-off-road terrain interaction. Modelling of such cases is usually based on empirical and semi-empirical solutions, which have limited applicability in real situations due to their inherent weaknesses. In this study, numerical simulation of the dynamic mobility of a rigid wheel on a deformable terrain is performed through a series of transient nonlinear dynamic finite element analyses with the use of the finite element code ABAQUS (v. 6.13). The dynamic interaction of a rigid wheel with the underlying soil during off-road vehicle travel is simulated. The effects of the vertical load carried by the wheel, the tread pattern, the longitudinal and lateral tread parameters, and the slip ratio of the wheel on the wheel performance are investigated and useful results are extracted. The numerical results reveal that the effects of the tread pattern, particularly tread depth and the terrain constitutive properties, such as soil cohesion can be of high importance for the general wheel response

Damping of flexural vibrations in thin plates using one and two dimensional acoustic black hole effect

The reduction of flexural vibration in thin plates is examined using the acoustic black hole effect associated with nearly zero reflection of quasi-plane waves from a lightly damped wedge or tapered hole where the profile varies according to a power-law. The flexural wave propagation can be determined through the application of geometrical acoustics approximation or exact analytical solutions. For a plate of thickness of power-law profile, the wave slows down and grows in amplitude. In the ideal case of no truncation of the quadratic (or higher) profile, the phase speed asymptotically decreases to zero and the wave never reaches the end. Manufactured plates always have a truncation, leading to relatively high reflection coefficients, however, the application of small damping layers leads to substantial decreases in the reflection coefficients and thus large reductions in mobility amplitudes. This paper contains the results of numerical models and experimental measurements of point mobility for structural plates incorporating tapered holes for validation. A rectangular plate with a 1D wedge on one end is examined, in addition to a circular plate with a quadratic profile in the centre. In both cases, the measurements show significant reductions in resonant peaks of mobility, in good agreement to numerical predictions