Identification of damping in a bridge using a moving instrumented vehicle

In recent years, there has been a significant increase in the number of bridges which are being instrumented and monitored on an ongoing basis. This is in part due to the introduction of bridge management systems designed to provide a high level of protection to the public and early warning if the bridge becomes unsafe. This paper investigates a novel alternative; a low-cost method consisting of the use of a vehicle fitted with accelerometers on its axles to monitor the dynamic behaviour of bridges. A simplified half-car vehicle-bridge interaction model is used in theoretical simulations to test the effectiveness of the approach in identifying the damping ratio of the bridge. The method is tested for a range of bridge spans and vehicle velocities using theoretical simulations and the influences of road roughness, initial vibratory condition of the vehicle, signal noise, modelling errors and frequency matching on the accuracy of the results are investigated.     

Disk model for wheels moving over highway bridges with rough surfaces

In most previous analyses of vehicle-bridge interaction (VBI) problems in highways involving surface roughness, the wheels of vehicles have been treated as points, referred to as the point model, and the tracks as a series of hills and valleys. The point model is unrealistic for wheels, as they are of finite size and cannot touch the bottom of valleys. In this study, each wheel will be modeled instead as a rigid disk of finite size, referred to as the disk model, neglecting the tire deformations. The VBI element will be modified accordingly for computing the vehicle and bridge responses. Numerical examples are prepared to illustrate the effect of wheel size on the dynamic responses of the bridge and passing vehicles. It is concluded that the point model tends to introduce some unrealistic high-frequency vibrations on the system responses, while underestimating the amplitude of vehicle frequency in the vehicle response. The disk model should be adopted, if the velocity and acceleration responses of the bridge and the dynamic responses of the moving vehicle are of major concern.     

A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source

The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behaviour due to occurrence of damage, are determined using a time-domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.     

Critical speed for the dynamics of truck events on bridges with a smooth road surface

Simple numerical models of point loads are used to represent single and multiple vehicle events on two-lane bridges with a good road profile. While such models are insufficiently complex to calculate dynamic amplification accurately, they are presented here to provide an understanding of the influence of speed and distance between vehicles on the bridge dynamic response. Critical combinations of speed as a function of main bridge natural frequency and meeting point of two vehicles travelling in opposite directions are identified. It is proposed that such simple models can be used to estimate the pattern of critical speeds versus dynamic amplification of the bridge response for trucks on a relatively smooth surface. The crossing of a three-dimensional spring-dashpot truck is simulated over a bridge plate model to test this hypothesis for a range of road roughness. Further validation is carried out using the site-specific mean pattern associated to field measurements of bridge strains when traversed by a truck population. The latter is found to be closely resembled by the theoretical pattern derived from simple point load models.     

Equivalent linear stochastic seismic response of isolated bridges

Stochastic response of bridges seismically isolated by lead-rubber bearings (LRB) is investigated. The earthquake excitation is modeled as a non-stationary random process (i.e. uniformly modulated broad-band excitation). The stochastic response of isolated bridge is obtained using the time-dependent equivalent linearization technique as the force-deformation behavior of the LRB is highly nonlinear. The non-stationary response of isolated bridge is compared with the corresponding stationary response in order to study the effects of non-stationary characteristics of the earthquake input motion. For a given isolated bridge system and excitation, it was observed that there exists an optimum value of the yield strength of LRB for which the root mean square (rms) absolute acceleration of bridge deck attains the minimum value. The optimum yield strength of LRB is investigated under important parametric variations such as isolation period and damping ratio of the LRB and the frequency content and intensity of earthquake excitation. It is shown that the above parameters have significant effects on the optimum yield strength of LRB. Finally, closed-form expressions for the optimum yield strength of LRB and corresponding response of the isolated bridge system are proposed. These expressions were derived based on the model of bridge with rigid deck and pier condition subjected to stationary white-noise excitation. It was observed that there is a very good comparison between the proposed closed-form expressions and actual optimum parameters and response of the isolated bridge system. These expressions can be used for initial optimal design of seismic isolation system for the bridges.     

Characterisation of pavement profile heights using accelerometer readings and a combinatorial optimisation technique

Pavement surface profiles induce dynamic ride responses in vehicles which can potentially be used to classify road surface roughness. A novel method is proposed for the characterisation of pavement roughness through an analysis of vehicle accelerations. A combinatorial optimisation technique is applied to the determination of pavement profile heights based on measured accelerations at and above the vehicle axle. Such an approach, using low-cost inertial sensors, would provide an inexpensive alternative to the costly laser-based profile measurement vehicles. The concept is numerically validated using a half-car roll dynamic model to infer measurements of road profiles in both the left and right wheel paths.     

PRACTICAL ASPECTS IN MOVING LOAD IDENTIFICATION

Several methods have been developed in recent years to identify moving loads on top of a continuous beam using measured vibration responses. The methods can identify the forces with some accuracy, but they have not been tested under field measurement conditions with a bridge-vehicle system. This paper discusses the weaknesses and merits of two methods when applied to a single-span bridge deck. The influence, on the moving load identification, of practical aspects such as measurement noise, sampling frequency, a small number of measured response modes, a small number of measuring points, road surface roughness and non-uniform velocity or braking of vehicle is studied in simulations and experiment. Results show that finite element approach with orthogonal function approximation of the responses give more accurate results, in general, than the exact solution approach for all the studies presented in this paper. The road surface roughness and a large variation in the speed are identified as the two main obstacles leading to erroneous results.     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.     

Optimization of a quarter-car suspension model coupled with the driver biomechanical effects

In this paper a Human-Vehicle-Road (HVR) model, comprising a quarter-car and a biomechanical representation of the driver, is employed for the analysis. Differential equations are provided to describe the motions of various masses under the influence of a harmonic road excitation. These equations are, subsequently, solved to obtain a closed form mathematical expression for the steady-state vertical acceleration measurable at the vehicle-human interface. The solution makes it possible to find optimal parameters for the vehicle suspension system with respect to a specified ride comfort level. The quantitative definition given in the ISO 2631 standard for the ride comfort level is adopted in this paper for the optimization procedure. Numerical examples, based on actually measured road profiles, are presented to prove the validity of the proposed approach and its suitability for the problem at hand.     

放大系统在惠斯通电桥灵敏度研究中的应用

基于惠斯通电桥原理,在电位比较的基础上,加入了放大系统,通过调节放大系统的电阻,得出了在该模型下且在一定范围内,惠斯通电桥灵敏度具有一定的可调性,并发现在该模型下与待测电阻同路的电阻阻值与待测电阻阻值越接近越能获得高灵敏度,同时给出了此模型最佳适用条件。     

Studies of the performance of particle dampers under dynamic loads

This paper presents a systematic investigation of the performance of particle dampers (vertical and horizontal) attached to a primary system (single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF)) under different dynamic loads (free vibration, stationary random excitation as well as nonstationary random excitation, with single component or multi-component), and the optimum operating regions are all determined. The amount of dissipated energy due to impact and friction, and the concept of “Effective Momentum Exchange” are shown to be suitable “global” measures to interpret the physics involved in the behavior of particle dampers. Using the well-established discrete element method, the motion of vertical particle dampers can be analyzed and classified into three different regions, and the associated damping characteristics can be interpreted. The first mode of a MDOF primary system can be effectively controlled by a properly designed particle damper; however, the higher modes are more affected by other parameters. Consequently, extensive parametric studies are presented to evaluate the effects of various system parameters, such as: mass ratio, primary system damping, coefficient of restitution, container dimensions, excitation amplitude and components, input locations and damper locations.     

Torsional friction damper optimization

A new approach for the analysis of friction dampers is presented in this work. The exact form of the steady-state solution for a friction damper implemented on a primary system is developed and numerical solutions are used to determine the optimum friction in a friction damper applied to a specific primary system. When compared to classical results presented by earlier authors, the new approach provides a more optimal solution. In addition, viscous damping in the primary system may be included with the new analysis approach. The ability to optimize a friction damper when viscous damping is included in the primary system is a significant improvement over earlier methods and shows potential for serving as a guide to realizing a more accurate estimate of the optimal damping for friction dampers.     

Laser hyperacoustic spectroscopy of single crystal germanium

Using a photothermal laser deflection technique the profiles of laser-induced hyperacoustic pulses in single crystal germanium were studied at a subnanosecond time resolution. It is shown that the hyperacoustic pulses are excited due to an electron-deformation interaction of photogenerated carriers with the crystal lattice, which is much more effective than the thermoelastic mechanism of the acoustic wave generation. Evolution of the hyperacoustic pulse profiles related to the diffraction and acoustic absorption effects was studied. An analysis of the hyperacoustic signal profiles allowed us to estimate the coefficient of ambipolar diffusion of the photogenerated charge carriers and the coefficient of hyperacoustic wave damping. It is established that the front of the electron-hole plasma laser-excited in germanium at room temperature propagates at a supersonic velocity.     

Note on the Stability of a Slowly Rotating Timoshenko Beam with Damping

This paper continues the senior author's previous investigation of the slowly rotating Timoshenko beam in a horizontal plane whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. It was shown before that this system preserves the total energy. We consider the problem of stability of the system after introducing a particular type of damping. We show that the energy of only part of the system vanishes. We illustrate obtained solution with the critical case of the infinite value of the damping coefficient.     

Experimental and computational investigation of coupled resonator–cavity systems

Launch vehicle noise is broadband in nature and the noise transmitted into the payload fairing is reduced by treating its interior with an acoustic absorption layer. The latest generation payload fairings are made from composite material which offer poor noise attenuation at low frequencies. One possible solution for reducing the low frequency noise is to use Helmholtz resonators tuned to a few of the dominant low frequency components, such as shell ring frequency or the first few cavity modes of the fairing. The paper presents a simplified modelling approach for numerical simulation of a coupled cavity–resonator system which is validated by experiments. The influence of damping and resonator volume fraction on the coupled system performance, to suppress the first axial mode in a cylindrical cavity, is shown and the resonator volume fraction required for significantly (more than 5 dB) suppressing the cavity axial mode is established.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper

This paper presents a consistent and concise analysis of the free and forced vibration of a mass supported by a parallel combination of a spring and an elastically supported damper (a Zener model). The results are presented in a compact form and the physical behaviour of the system is emphasised. This system is very similar to the conventional single-degree-of freedom system (sdof)—(Voigt model), but the dynamics can be quite different depending on the system parameters. The usefulness of the additional spring in series with the damper is investigated, and optimum damping values for the system subject to different types of excitation are determined and compared.There are three roots to the characteristic equation for the Zener model; two are complex conjugates and the third is purely real. It is shown that it is not possible to achieve critical damping of the complex roots unless the additional stiffness is at least eight times that of the main spring. For a harmonically excited system, there are some possible advantages in using the additional spring when the transmitted force to the base is of interest, but when the displacement response of the system is of interest then the benefits are marginal. It is shown that the additional spring affords no advantages when the system is excited by white noise.     

Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles

An investigation into the dynamics of vehicle-occupant-structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of the dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span, while the maximum bending moment occurs at ±20% of the mid-span point. It is shown that one can find a critical speed at which the maximum values of the bridge dynamic deflection and the bending moment attain their global maxima.     

Damping characteristics of elastic-viscoelastic composite curved bars and helical springs

The paper deals with the analysts of damping characteristics of a curved composite shaft. The composite shaft consists of an outer elastic curved tube with a similarly curved rod placed inside. The annular space between the tube and the rod is filled with viscoelastic material. The composite shaft is clamped at one end and a concentrated load (varying harmonically) acts on a radial arm fixed to the outer shell at the free end. It is shown that optimum design values exist for maximizing the total damping capacity of the system. It also is indicated that direct use of this method for increasing the damping capacity is not effective, as the damping factor reduces sharply after reaching a maximum value. It is shown how this difficulty can be overcome and how helical springs, possessing considerable damping capacity, can be designed. Sometimes this may help in simplifying the design of vibration isolators which will take the shape of a simple spring only.     

Index for vehicle acoustical comfort inside a passenger car

Sound quality is among the main factors that influence customers’ preference for choosing good automobile products. It all started more than 10 years ago and grows up so fast due to high competition in the automotive industries. A-weighted noise levels and sound power are usually utilised to measure the noise but they are not adequate to characterise the impact sound inside a car. The most popular approach to determine sound quality of a product is to define an annoyance or specific index, which involves both subjective and objective evaluations. Subjective and objective tests should be studied concurrently in order to determine the sound quality inside a passenger car. This approach is used in this paper to evaluate vehicle comfort index according to most frequently used sound quality metrics, namely; Zwicker loudness, sharpness, roughness and fluctuation strength. As a result researchers of different fields of automotive acoustics investigations can use this index according to the type of road (international road roughness) without any need to perform time-consuming jury tests. The metrics are correlated with jury test results that show which of them and how much has affected the acoustical comfort of the vehicle. The relation between road roughness and vehicle acoustical comfort index is another point of interest in this research.