Authors' reply

Thank you for the complementary comments on the experimental work reported in reference [1]. As you note, when considering the vibration of curved beams, it is important to acknowledge the work of L. S. D. Morley in the early 1960s. In reference [2], Morley developed a unified theory for the vibration of curved rods where the neutral axis forms a curve of constant radius of curvature. Morley's theory included the effects of rotary inertia and radial shear in a manner analogous to that of Timoshenko's theory for straight rods. Morley's theory also included the effect of extension of the neutral axis. It was shown in reference [2] that when the curvature is slight, the equations can be simplified and a Timoshenko-type equation can be obtained for the flexural motion. For this case, it was shown that the extension of the neutral axis has no effect upon the flexural motion. When the rod has pronounced curvature these simplifications are no longer valid and the more general equations must be considered

Measurement of vibrational energy flow in a plate with high energy flow boundary crossing using electronic speckle pattern interferometry

The measurement of vibrational energy flow is an important tool in understanding the vibrational behaviour of structures. In the past, because of transducer constraints, the measurement of vibrational energy flow was mostly restricted to single point measurements. However, recent developments in advanced laser measurement techniques, such as electronic speckle pattern interferometry (ESPI), have gained interest in applying two-dimensional, multi-point measurement techniques to the estimation of vibrational energy flow. This paper addresses the measurement of vibrational energy flow in a plate by using an ESPI based vibrational energy flow measurement technique. A radially symmetric bending wave plate vibration model is introduced and theoretical expressions for energy-based quantities are derived. To assess the accuracy of the measurement method, these theoretical quantities are compared to synthetic results derived from the ESPI energyflowmeasurement technique. The ESPI measurement technique is also applied to an experimental ‘infinite’ plate. Thus, a specially designed experimental apparatus was constructed so as to minimise undesired wave reflections in the plate and, thus, achieve a high energy flow boundary crossing at the edges of the plate. To reduce the effect of optical noise contamination on the ESPI measured out-of-plane plate displacement data, optimal filters were applied prior to the vibrational energy flow computation. To appraise the accuracy of the experimental method, measured vibrational power on the plate is compared with measured vibrational input power. A difference of less than 1 dB between both quantities indicates that vibrational energy flow within a rectangular plate that contains radially symmetric wave propagation can be measured to a good degree of accuracy if appropriate filtering is applied

Transfer function phase of a diffuse vibrational field

Transfer function phase of a diffuse vibrational fiel

Reduction of vehicle power assisted steering noise

Introduction: To achieve low levels of noise and vibration in the interior of a vehicle, the noise levels from major sources such as the engine and transmission have been greatly reduced in recent years. Unfortunately, this has meant that the noise from ancillary components has become relatively more prominent. One such component is the power assisted steering (PAS) system, the noise from which is a problem on nearly all vehicles. This paper reports an investigation into the moaning noise produced when the steering wheel is turned at idle, commonly known as PAS moan. The major factors involved in PAS moan are: the transmission of structure-borne and air-borne noise through the vehicle; the transmission of pressure ripples in the hydraulic circuit of the PAS system; and the generation of flow ripples at the PAS pump. In section 3 the results of a study into the reduction of PAS moan is reported. Section 3.1 outlines the experimental set-up and measurement technique. Section 3.2 reports on the effect on vehicle interior noise of the installation of the of the PAS system. Section 3.3 reports on the influence of tuning hoses in the PAS hydraulic circuit and section 3.4 gives an assessment of the reduction in interior noise due to a modification of the power steering pump. The findings outlined in this paper are part of more detailed study into power steering noise reported in reference [1]

Investigation into the phase characteristics of wave fields

The aim of the work reported in this paper is to establish a method of determining the diffusivity of an SEA subsystem using the phase of transfer functions. Specifically, this paper reports an investigation into the phase characteristics of transfer functions obtained using two flat plate structures. In the first experiment the phase characteristics of bending waves in a directional field are obtained using a perspex plate with additive damping. In the second experiment the phase characteristics of bending waves in a diffuse field are obtained from a freely suspended steel plate. The experimental data are normalised and compared to theoretical formula and limits for the diffuse field and direct field proposed

Investigation of analytical beam and annular plate models for automotive disc brake vibration

In this paper two analytical models of automotive disc brake vibration will be presented and compared to experimental measurements. The first model approximates the brake disc as a simple beam structure with cyclo-symmetric boundary conditions. Since the beam model is a one-dimensional approach and, therefore, the modelling of the inner boundary conditions of the brake disc is impossible, a second model based upon Kirchhoff’s plate theory is also presented. The mode shapes and natural frequencies of a static disc with different inner boundary conditions are calculated and compared to experimental vibration and sound pressure measurements of a brake disc made upon a static test rig. Additionally, a set of initial measurements made upon a spinning disc rig are also discussed

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

Measurement of phase accumulation in the transfer functions of beams and plates

Previous research into the phase of transfer functions from beam and plate-type structures has shown that the accumulated phase has different characteristics depending on whether the vibrational field is direct, diffuse, or between these two extremes. In this paper, these accumulated phase characteristics are numerically and experimentally investigated. Existing phase accumulation theories for direct and reverberant vibrational fields are presented. Predictions of the accumulated phase are then compared to measurements of the accumulated phase from the transfer mobilities of a number of beam and plate structures. It is shown that selection of the correct FFT frequency resolution in the experiment is vital in obtaining an accurate measurement of the phase of the transfer function. A criterion based upon the half-power bandwidth of the analysis frequency band is proposed as a basis to select the correct FFT frequency resolution. It is also shown that the location of the excitation may affect the measured value of the accumulated phase. Experimental results also show that the accumulated phase in a vibrational wave field between that of a direct field and a diffuse field is related to the source-receiver separation distance and to the damping in the structure. It is shown that the resulting accumulated phase curve lies between the direct field phase limit and the reverberant field phase limit

Prediction of the spatial characteristics of higher mode sound transmission through a periodic slit screen

Periodic slit screens are often installed in rectangular apertures either to mask the opening or to reduce transmitted noise. This investigation considers the higher-order scattered and transmitted sound from a point source through a periodic screen mounted in a rigid baffle. In particular, this paper considers the spatial characteristics, or directivity, of the scattered field for a particular higher order mode. Uncoupled higher-order mode analysis is used to estimate the scattered and transmitted sound fields for the selected mode of the aperture without the presence of the screen. Transmission coefficients for the screens are then calculated using the well established equivalent mass layer effect and applied to the calculated higher-order mode scattered and transmitted sound pressures. Using an anechoic chamber, measurements were made over a small arc of the scattered sound field through a range of screens of different aspect ratios but the same porosity. The screens consisted of equally spaced open slits and solid laths and the number of slits was reduced to change the aspect ratio. In each case the point source was positioned on the impinging side of the aperture so as to drive one particular scattered higher-order aperture mode at or near cut-on. Comparison of the measured and predicted sound pressures indicate that good estimates of the sound field can be obtained through the approach of applying simple corrections for the presence of the screens to the estimates for the open aperture established using uncoupled calculations for the higher-order modes. It is also shown that the results for a specific mode excited at one particular frequency are applicable at other excitation frequencies provided that the correct non-dimensionalisation is applied

Transfer function phase prediction for a flat plate

This paper reports an investigation into the phase accumulation characteristics in the transfer function of a flat plate for bending waves. The paper starts with an overview of previous research on the phase characteristics in an ideal vibrational wave field i.e. either a completely direct field or a completely diffuse field. This initial research is extended by considering the phase accumulation characteristics of a non-ideal vibrational wave field i.e. a wave field between a direct field and a diffuse field. Various factors likely to influence the phase accumulation are discussed. Based on these factors and a pole and zero model of the direct field phase and the diffuse field phase, two mathematical models are presented for predicting the transfer function phase of a flat plate supporting a non-ideal wave field. Computer simulation results are given which compare the characteristics of the different models