N.S. Ferguson

Variations in steepness of the probability density function of beam random vibration

Abstract Dynamic behaviour of a beam, subjected to stationary random excitation, has been investigated for the situation in which the response is different from the model of a Gaussian random process. The study was restricted to the case of symmetric non-Gaussian probability density functions of beam vibrations. There are two possible causes of deviations of the system response from the Gaussian model: the first, nonlinear behaviour, concerns the system itself and the second is external when the excitation is not Gaussian. Both cases have been considered in the paper. To clarity the conclusions for each case and to avoid interference of these different types of system behaviour, two beam structures, clamped-clamped and cantilevered, have been studied. A numerical procedure for prediction of the nonlinear random response of a clamped-clamped beam under the Gaussian excitations was based on a linear modal expansion. Monte Carlo simulation was undertaken using Runge–Kutta integration of the generalised coordinate equations. Probability density functions of the beam response were analysed and approximated making use of different theoretical models. An experimental study has been carried out for a linear system of a cantilevered beam with a point mass at the free end. A pseudo-random driving signal was generated digitally in the form of a Fourier expansion and fed to a shaker input. To generate a non-Gaussian excitation a special procedure of harmonic phase adjustment was implemented instead of the random choice. In so doing, the non-Gaussian kurtosis parameter of the beam response was controlled.

An adaptive anechoic termination for active vibration control

The active broadband control of the flexural vibration of a slender structure, in particular a beam, is obtained by the use of an adaptive anechoic termination. The anechoic termination, which absorbs any energy incident upon it, is implemented by applying a force close to one end of the structure. The force is determined by a feed-forward adaptive control that uses estimates of the incident and reflected waves as reference and error signals. Digital filters are implemented to estimate, in real-time, the amplitudes of these waves by filtering the outputs of an array of sensors. The reflected wave is used as the cost function in a filtered-X LMS adaptive control. The use of the propagating waves as reference and error signals also allows the method to be effective for resonant structures, a situation in which conventional approaches fail to be reliable. In order to compare the method with a conventional approach an anechoic termination that uses the primary excitation as reference is also considered. Numerical and experimental results demonstrate the method applied to semi-infinite and finite resonant structures. A broadband reduction of up to 20 dB in the ratio of the reflected and incident powers is demonstrated both numerically and experimentally. The use of the adaptive anechoic termination to reduce the vibration levels in structures is shown to be more effective than other typical feed-forward active control systems. Furthermore, it can be applied to cases where no reference signal, such as the primary excitation, is directly available.

Joint uncertainty propagation in linear structural dynamics using stochastic reduced basis methods

Uncertainties in the properties of joints produce uncertainties in the dynamic response of built-up structures. Line joints, such as glued or continuously welded joints, have spatially distributed uncertainty and can be modeled by a discretized random field. Techniques such as Monte Carlo simulation can be applied to estimate the output statistics, but computational cost can be prohibitive. This paper addresses how uncertainties in joints might be included straightforwardly in a finite element model, with particular reference to approaches based on fixed-interface (Craig– Bampton) component mode synthesis and a stochastic reduced basis method with two variants. These methods are used to determine the output statistics of a structure. Unlike perturbation-based methods, good accuracy can be achieved even when the coefficients of variation of the input random variables are not small. Undamped as well as proportionally damped components are considered. Efficient implementations are proposed based on an exact matrix identity that leads to a significantly lower computational cost if the number of joint degrees of freedom is sufficiently small compared with the structure’s overall number of degrees of freedom. A numerical example is presented. The proposed formulation is an efficient and effective implementation of a stochastic reduced basis projection scheme. It is seen that the method can be up to orders of magnitude faster than direct Monte Carlo simulation, while providing results of comparable accuracy. Furthermore, the proposed implementation is more efficient when fewer joints are affected by uncertainty.

Acoustic–structural interaction analysis using the component mode synthesis method

Abstract The main objective is to analyse the effects of the imposition of common velocity on the acoustic–structural interface via the Component Mode Synthesis Method (CMS). The original contribution of this analytical study is to show the importance of including kinematic compatibility on the structural-acoustic problem. Some background information about the method is provided as a basis for assisting the understanding of the process. Following this, the formulation of the structural-acoustic problem in terms of ‘components’ is described. The results obtained using CMS are compared to those obtained using both a one dimensional wave approach and standard modal analysis. Finally, conclusions are drawn based on the analysis of the results and the extension to three-dimensional acoustic systems discussed.

The effect of embedded optical fibres on the fatigue behaviour of composite plates

Finite element (FE) techniques are used to simulate the strain and stress concentrations in and around an optical fibre (OF) embedded in XAS/914 carbon fibre reinforced laminates. Analytical results produced show the location of high stresses and therefore the position of possible damage when specimens are subjected to tension and flexure. Also mechanical fatigue tests are carried out on specimens with optical fibres embedded within different orientation plies, in order to see the effect of the fibres on the fatigue behaviour of the specimens. Results are then compared with those found for a specimen without embedded optical fibre.

The Experimental Performance of a Nonlinear Dynamic Vibration Absorber

This paper investigates the physical behaviour and effectiveness of a nonlinear dynamic vibration absorber (NDVA). The nonlinear absorber considered involves a nonlinear hardening spring which was designed and attached to a cantilever beam excited by a shaker. The cantilever beam can be considered at low frequencies as a linear single degree-of-freedom system. The nonlinear attachment is designed to behave as a hardening Duffing oscillator. The nonlinearity of the attachment is due to the particular geometrical configuration undergoing a large amplitude response. The experiment investigated the potential for vibration reduction of the system Analytical and numerical results are presented and compared. From the measured results it was observed that the NDVA had a much wider effective bandwidth compared to a linear absorber. The frequency response curve of the NDVA has the effect of moving the second resonant peak to a higher frequency away from the tuned frequency so that the device is robust to mistuning.

The development of a Component Mode Synthesis (CMS) model for three-dimensional fluid–structure interaction

Our main aim in this paper is to develop analytically the three-dimensional Component Mode Synthesis method and to use it on fluid–structure interaction problems, such as sound transmission between coupled volumes. This will be shown for simple volume geometries, but, in principle, the same procedure can be applied when the component modes are obtained from numerical techniques, such as the Finite Element Model (FEM) or Boundary Element Method (BEM). The modal behavior of acoustic volumes and a partition is implemented in two steps. The first extension here is based on a one-dimensional model where the transverse acoustic modes of the volumes are incorporated into the formulation. The second extension, which is more general, considers not only the transverse acoustic modes of the volumes, but also structural modes of the partition. A comparison is made with predictions based on a modal model using the normal modes of rigid walled enclosures separated by a simply supported partition. For the latter modal m...

On the optimization of a hybrid tuned mass damper for impulse loading

The present paper deals with the optimization of a hybrid tuned mass damper (TMD) in reducing the transient structural response due to impulse loading. In particular, a unit impulse excitation has been assumed, acting as base displacement, which is a situation that may occur in different real applications. The proposed hybrid TMD is composed of a previously optimized passive TMD and an added optimized active controller. Such configuration has been conceived in view of reducing both the global and the peak response. Especially on the latter task, the introduction of the active controller brings in a significant contribution. Prior, a bounded-input-bounded-output stability analysis on the control gains is developed. Different control laws have been investigated, assuming as primary structures, first a single-degree-of-freedom benchmark system and then a multi-degree-of-freedom building, in order to point out the most appropriate control law for the given structural context. In particular, a new control law, based on a linear combination of acceleration and velocity, allowed for remarkable peak response reduction. The achieved dynamic response exhibits a time settling weakly oscillating response, an indication of a stable behavior, and therefore represents a suitable option for the active controller, in view of various engineering applications.

Dynamic behaviour of a rotating cracked beam

This paper presents a new approach to investigate and analyse the vibrational behaviour of cracked rotating cantilever beams, which can for example represent helicopter or wind turbine blades. The analytical Hamiltonian method is used in modelling the rotating beam and two numerical methods, the Rayleigh-Ritz and FEM, are used to study the natural frequencies and the mode shapes of the intact rotating beams. Subsequently, a crack is introduced into the FE model and simulations are performed to identify the modal characteristics for an open cracked rotating beam. The effect of various parameters such as non-dimensional rotating speed, hub ratio and slenderness ratio are investigated for both the intact and the cracked rotating beam, and in both directions of chordwise and apwise motion. The veering phenomena in the natural frequencies as a function of the rotational speed and the buckling speed are considered with respect to the slenderness ratio. In addition, the mode shapes obtained for the apwise vibration are compared using the modal assurance criterion (MAC). Finally, a new three dimensional design chart is produced, showing the effect of crack location and depth on the natural frequencies of the rotating beam. This chart will be subsequently important in identifying crack defects in rotating blades.

Variability of automotive interior noise from engine sources

A statistical analysis of a series of interior vehicle noise measurements on a set of 1106 automotive vehicles, both petrol and diesel versions, from one manufacturer is presented: a small hatchback model and a mid-sized family 5-door car. The engines were run at 50 rpm intervals over therange from 1000 rpm up to 4000 and 5950 rpm for the diesel and petrol variants respectively, with full load in econd gear whilst the vehicle was on a dynamometer roller test rig, comprising a smooth rolling surface.The measured interior noise at four positions corresponding to passenger ear locations were subsequently analysed in third octave bands as well as the overall levels, with statistical tests being performed on the linear rms pressures. The normalised standard deviation of the linear data decreases with increasing frequency. It is typically less than 0.1 over the whole audio frequency range irrespective of vehicle type or engine. A lognormal distribution provides the best fit to the majority of the engine noise results and the overall engine noise could be described by a lognormal or gamma distribution. A lognormal distribution fit implies that the values in dB are normally distributed.