Modal Damping Values Research Articles

Dominant damping effects in friction brake noise, vibration and harshness: the relevance of joints

The experimental analysis of a single component of a brake system and an assembly consisting of three components is used to clarify the relevance of joints in terms of damping and non-linearity in state-of-the-art brake systems. For this purpose a series of experimental modal analyses are conducted. A comparison of the results obtained from the single component and from the assembly strongly indicate that the joints which necessarily exist in an assembled structure have a strong impact on the dynamic behaviour of the structure. The modal damping values of the jointed structure are a factor of up to 60 higher than those of the single-component values. Also, a significant amplitude dependence of the frequency response functions results. The observations demonstrate that joints are a major source of energy dissipation in friction brake systems and, in addition, that they introduce non-linear behaviour to the system which has the potential to limit squeal amplitudes. Therefore, mechanical joints in brake systems should be considered as decisive design elements for noise, vibration and harshness issues in brakes.

Reliability of Using Curvature TechniquesinStructural Damage Detection

A damage in a structure alters its dynamic characteristics; namely, natural frequencies, modal damping values, and mode shapes. Changes also occur in some of the structural parameters such as:the mass, dampingand stiffness matrices of the structure. Among different algorithms developed for structural damage identification, changes in eithermode shape curvature oruniform load surface (ULS) curvature, derived from measured modal properties,have shown promise for locating structural damage. However, to date there is not a study reported in the technical literature that directly compares these two promising methods. The numerical results in this paper attempt to fill this void in the study of damage detection methods. In this paper, a numerical study is investigated to compare the robustness of these two methodsin damage detection using the frequencies and mode shapes of the first few modes. Also, the application of a damage localization algorithm to these two methods in detecting and locating damage is demonstrated. The numerical results show that both of the two methods can accurately locate single damage with different damage characteristics (location and severity).However, thetwo methods have shownless sensitivity to specific types of damage when applied to multiple damage locations. Also, the results of the ULS curvature method contain less noise than that of the results of the mode shape curvature method.Finally, the mode shape curvature can pinpoint damage locations even with one of the lower mode shapes of the structure and it does not require the mode frequency.

Synergy of fiber length and content on free vibration and damping behavior of natural fiber reinforced polyester composite beams

This work addresses the results of experimental investigation carried out on free vibration characteristics of short sisal fiber (SFPC) and short banana fiber (BFPC) polyester composites. Influence of fiber length and weight percentage on mechanical properties and free vibration characteristics are analyzed. Composite beam specimen is fabricated with random fiber orientations at17MPa compression using compression molding machine. Natural frequencies and associated modal damping values of the composite laminates were obtained by carrying out the experimental modal analysis. It is found that an increase in fiber content increases the mechanical and damping properties. For SFPC, 3mm fiber length and 50wt% fiber content yielded better properties, whereas for BFPC, 4mm fiber length and 50wt% fiber content was the best combination. Scanning electron microscopy was performed to study the interfacial mechanism.

Estimation of elastic and modal parameters in composites using vibration analysis

This study presents the application of vibration analysis in the determination of elastic constants (i.e. Young’s modulus in fiber direction, transverse Young’s modulus, and shear modulus) and modal damping ratios of a unidirectional composite beam. The frequency domain approach is used for the estimation of material constants, whereas modal damping ratios are predicted by the use of short-time Fourier transform (STFT). An analytical expression of the STFT for the free vibration response of a viscously damped system has been derived using the Hanning window. Analysis of a simulated vibration for a three-degree-of-freedom system has revealed that the STFT is capable of predicting the modal damping ratios accurately even when they are considerably large. For the experimental assessment of modal damping values of a composite beam, longitudinal, flexural, and torsional vibration responses are analyzed by both the STFT and well-known Q-factor approximation, and the obtained results show very good agreement.

Field Testing of Old Narrow-Gauge Railway Steel Truss Bridge

Investigation results of a historic narrow-gage railway steel truss bridge built in 1936, still in use, is presented. During the World War II the bridge was exploded and has been restored later after the war (1946). The original design documentation was lost. The aim of this study is to investigate the structural condition and the behaviour of the riveted steel truss bridge with the aid of full-scale static and dynamic testing. The field load tests have been conducted to develop an analytical model, to be used for assessment of bridge capacity. Static and dynamic tests of the bridge using two original locomotives were performed. Supplementary dynamic tests using impulse excitation were also carried out. The responses (stresses, static and dynamic displacements, accelerations, mode shapes, corresponding resonant frequencies and modal damping values) of bridge superstructure were determined. Research has shown that the bridge exhibit sufficient reserve of capacity for safe operation.

Estimation of Modal Dampings for Unmeasured Modes

ABSTRACTDamping effects are of great interest for structural analysis and evaluations. Structuralmodal damping characteristics can be obtained from experiments. This paper introducesnew possibilities for the modelling of the damping of a dynamic system with classical normalmodes and provides an overview of the known methods for formulating a damping matrixbase with experimental modal damping values. The proposed method offers an opportunityto extrapolate modal damping values for unmeasured modes by a regression method basedon the measured modal properties. The points of view on the choice of an analytical formfor damping regression functions are examined. An analytical form of regression functionscan be chosen as the modal decay rate versus the square of the frequency or the modaldamping ratio versus the frequency. Damping regressions can be performed based ona group of typical vibration modes, such as bending, torsion and lateral, symmetrical oranti-symmetrical modes. The regression data obtained for the damping constants can thenbe applied in a finite element model for further structural analysis.

동특성 변화를 이용한 감쇠 구조물의 손상예측

A damage in structure alters its dynamic characteristics. The change is characterized by changes in the modal parameter, i.e., modal frequencies, modal damping value and mode shape associated with each modal frequency. Changes also occur in some of the structural parameters; namely, the mass, damping, stiffness matrices of the structure. In this paper, evaluation of changes in stiffness matrix of a structure is presented as a method not only for identifying the presence of the damage but also locating the damage. It is shown that changed stiffness matrix can be accurately estimated a sensitivity coefficient matrix derived from modifying mode shapes, First, with 4 story shear structure models, the effect of presence of damage in a structure on its stiffness matrix is studied. By using these analytical model, the effectiveness of using change of stiffness matrix in detecting and locating damages is demonstrated. To validate the predicted changing stiffness and its location, the obtained results are compared to the reanalysis result which shows good agreement.

Sensitivity Study on Damage Indexes of Cable-Stayed Bridges

Damages in a structure alter its static and dynamic characteristics. These changes occur in some structural parameters such as the mass, the stiffness, the flexibility and the damping matrices of the structure and can be characterized by changes in the modal parameters, i.e., modal frequencies, modal damping values and mode shapes, and their derivatives, such as the modal curvature and modal stress energy. According to the properties of cable-stayed bridges, various damage indexes of static and dynamic are constructed to indicate damage of cable, tower and girder respectively. A comprehensive index accounting for their interaction and the whole bridge damage is presented which is robust to measurement noises and uncertainties in ambient conditions. The sensitivities of these damage indexes are illustrated by numerical studies. The effectiveness of the proposed damage detection method of cable-stayed bridges is demonstrated through an engineering project.

Real-time performance monitoring of tuned mass damper system for a 183 m reinforced concrete chimney

A 183 m reinforced concrete chimney for a coal-fired power station was instrumented in the latter part of its life during the construction of a replacement chimney. Because of concerns about large-amplitude response induced by interference effects from the new chimney in the prevailing upwind direction, a response monitoring system was installed, quickly followed by a tuned mass damper (TMD) system. As well as providing live display of the chimney response, the monitoring system was also used to check the functioning of the TMD. The monitoring system featured a direct implementation of the stochastic subspace identification procedure in the ‘virtual instrument’ controlling the system, so that modal damping values for the system were displayed automatically, in real-time. The system thus provided an immediate visual indication of increased damping levels during strong winds, showing the correct functioning of the TMD. The paper describes the chimney, the monitoring system and its installation, the data processing and system identification procedure, together with performance data before, during and after installation of the TMD.

New Improved g Method for Flutter Solution

T HE field of aircraft engineering is entering an era of high technology. Over the past decade there has been a great deal of progress in almost all the subfields in aeronautics. However, in the aeroelastic field, despite the complexity of coupling three distinct engineering disciplines, aerodynamics, structures, and dynamics into a unified aeroelastic analysis capability, computational aeroelasticity has enjoyed a significant number of successes over its course of development. Today, every manned vehicle that flies through our atmosphere undergoes some level of aeroelastic analysis before flight. Also every major unmanned flight vehicle is similarly analyzed. Furthermore, flutter is a catastrophic aeroelastic phenomenon that must be avoided at all costs, and all flight vehicles must be clear of flutter and many other aeroelastic phenomena in their flight envelope. Flight and wind tunnel testing are two ways to clear a vehicle for flutter, but both are expensive and occur late in the design process. Therefore, engineers rely heavily on computational methods to assess the aeroelastic characteristics of flight vehicles. The successes of computational aeroelasticity are rooted in this aeroelastic characterization process. Traditionally flutter calculations in frequency domain are performed using either theKmethod or theP-Kmethod. TheKmethod is generally very fast and quite simple, but it has a downfall in that sometimes the frequency and damping values “loop” around themselves and yield multivalue frequency and damping as a function of velocity. TheKmethod solution is only valid when g 0 (g refers to damping) and the structural motion is neutrally stable and matches the aerodynamic motion which is also neutrally stable. The P-K method is acknowledged to provide more accurate modal damping values than the K method. Gradually, the P-K method has become the most widely used method in aeroelastic engineering. In recent years, a g method was proposed by P. C. Chen, who uses the analytic property of unsteady aerodynamics and a damping perturbation approach. Although these two methods of P-K method and g method are different in the equation form, they share the same stability criterion, i.e., eigenroot of aeroelastic equation is solved and a root with positive real part indicates flutter. In addition, the g method uses a reduced-frequency sweep technique to search for the roots of the flutter solution and a predictorcorrector scheme to ensure the robustness of the sweep technique. This g method includes a first-order damping term in the flutter equation that is rigorously derived from the Laplace-domain aerodynamics. In the paper, however, the improved g method increases a second-order damping term in the flutter equation. It is also valid in the entire reduced frequency domain and up to the second order of damping.

VIBRATION-BASED DAMAGE DETECTION IN A BEAM STRUCTURE WITH MULTIPLE DAMAGE LOCATIONS

During the last two decades structural damage identification using dynamic parameters of the structure has become an important research area for civil, mechanical, and aerospace engineering communities. The basic idea of the vibration‐based damage detection methods is that a damage as a combination of different failure modes in the form of loss of local stiffness in the structure alters its dynamic characteristics, i.e., the modal frequencies, mode shapes, and modal damping values. A great variety of methods have been proposed for damage detection by using dynamic structure parameters; however, most of them require modal data of the healthy state of structure as a reference. In this paper a vibration‐based damage detection method, which uses the mode shape information determined from only the damaged state of the structure is proposed. To establish the method, two aluminium beams containing different sizes of mill‐cut damage at a single location as well as two aluminium beams containing different sizes of mill‐cut damage at multiple locations are examined. The experimental modal frequencies and the corresponding mode shapes for the first 15 flexural modes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. In order to exclude the influence of measurement noise on the modal data and misleading damage indices, it is proposed to use the sum of mode shape curvature squares for each mode. With the example of the beams with free‐free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. The extent of mill‐cut damage is identified via the modal frequencies by using mixed numerical‐experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and the experimentally measured frequencies. The numerical frequencies are calculated by employing a finite‐element model for beam with introduced damage. Further, by using the response surface approach, a relationship (second‐order polynomial function) between the modal frequencies and the damage extent is constructed. The damage extent is obtained by solving the minimization problem. Santrauka Tyrimo metu buvo ieškomos sijines konstrukcijos pažeidimo frezuojant vietos, apimtis ir pažeidimo dydis pagal atlikto vibraciju eksperimento dinamines charakteristikas. Pažeidimo padetis ir apimtis buvo nustatomi pagal išlinkio formos virpesiu kvadrato dydi. Pažeidimo dydis buvo nustatomas skaitiniu‐eksperimentiniu metodu, taikant modalinius dažnius. Šio metodo efektyvumas ir patikimumas parodytas tiriant dvi aliuminio sijas, kurios buvo pažeistos frezos vienoje vietoje ir kurios buvo pažeistos skirtingose vietose.

On a modal damping identification model for non-classically damped linear building structures subjected to earthquakes

A simple modal damping identification model developed by the present authors for classically damped linear building frames is extended here to the non-classically damped case. The modal damping values are obtained with the aid of the frequency domain modulus of the roof-to-basement transfer function and the resonant frequencies of the structure (peaks of the transfer function) as well as the modal participation factors and mode shapes of the undamped structure. The assumption is made that the modulus of the transfer function of the non-classically damped structure matches the one of the classically damped structure in a discrete manner, i.e., at the resonant frequencies of that function modulus. This proposed approximate identification method is applied to a number of plane building frames with and without pronounced non-classical damping under different with respect to their frequency content earthquakes and its limitations and range of applicability are assessed with respect to the accuracy of both the identified damping ratios and that of the seismic structural response obtained by classical mode superposition and use of those identified modal damping ratios.

SlightEffect of damping on the propensity of squeal instability: An experimental investigation

Friction induced vibrations in automotive brakes is recognized as a major problem in industry. Squeal is a difficult subject because of its unpredictability caused by a not completely understood sensitivity to variation of the system parameters. In the literature several analytical and numerical studies deal with the relationship between damping and system propensity to have instability. These studies highlight the existence of a nonintuitive effect of damping distribution on modal coupling that gives rise to the unstable vibrations. The complexity of commercial brakes and the difficulties to identify the values of modal damping in brake assemblies lead to the necessity to rely on experimental analysis using simplified test rigs. This paper presents an experimental investigation of the relationship between the distribution of modal damping and the propensity to develop squeal in a beam-on-disk setup, which reliably reproduces squeal events with easy control and measurement of the damping of the disk and the beam, respectively. The experiments highlight the key role played by the modal damping distribution on squeal: A nonuniform repartition of the modal damping causes an increase of the squeal propensity.

Overview of Vibrational Structural Health Monitoring with Representative Case Studies

In the field of nondestructive evaluation and damage detection, there is continued interest in the utilization of vibrational techniques. Structural damage will result in permanent changes in the distribution of structural stiffness. These changes may be detected through structural monitoring. Because of the direct relationship of stiffness, mass, and damping of a multi-degree-of-freedom system to the natural frequencies, mode shapes, and modal damping values, many studies have been directed at using these dynamic properties for the purpose of structural health monitoring. The use of vibrational monitoring is a developing field of structural analysis and is capable of assisting in both detecting and locating structural damage. Vibrational data have been shown to be most useful when used in conjunction with other monitoring systems if a remote and robust damage detection scheme is desired. This paper includes a literature review that summarizes the basic approaches to vibrational monitoring, suggested guidelines for sensor selection and monitoring, and concludes with three example case studies.

DYNAMIC RESPONSES OF A TWO-SPAN BEAM SUBJECTED TO HIGH SPEED 2DOF SPRUNG VEHICLES

The deflection, bending moment, shear force and acceleration-time histories of a two-span beam subjected to moving sprung vehicles are presented. The vehicle model is a 2DOF system with a constant velocity. The two-span beam with a rough surface is used as structure model. The beam is defined in modal domain by natural frequencies, mode shapes and modal damping values. The rough surface is modeled by filtered white noise. The equations of motion for the coupled vehicle-structure system are formulated, for non-dimensionalized variables in the system equation. The first-order linear stochastic differential equations are solved, and the effects of the span passage rate and other important parameters are studied.

A shear beam finite element for the damping analysis of tubular laminated composite beams

The paper presents a three-dimensional beam element developed for predicting the damping of composite blades with hollow laminated cross-sections. The unified theoretical framework for synthesizing the equivalent damping properties of a tubular composite blade section is outlined. Building upon the damping mechanics, a damped three-dimensional shear beam finite element is developed, which explicitly provides damping, stiffness and mass matrices. A methodology for analyzing the damped free-vibration response of tubular beams is formulated, and modal frequencies and modal damping values are predicted. Application examples illustrate the ability of the beam element to predict the modal damping and modal frequencies of hollow blades of various uniform circular, elliptical and box sections. The results further quantify the ability of the element to capture the strong effect of skin laminations, as well as the contribution of shear to the modal damping of the beam.

The Dynamic Equation and Simulation of a Linkage Mechanism Fabricated from Three-Dimensional Braided Composite Materials

The work in this paper is concerned with a four-bar linkage mechanism with links fabricated from three-dimensional braided composite materials. The dynamic equation of the mechanism is established by finite element method (FEM), it includes composite materials parameters and structural parameters of the mechanism. The mass matrix of the beam element is obtained in light of the mass distribution characteristics of the composite materials. According to the 3-dimensional microstructure characters of the three-dimensional braided composite materials, the anisotropic beam element is considered to be made up of four parts, and then the stiffness matrix of the beam element is derived from the constitutive equations of each part and the relation between the strain distribution of each part and the node displacement of the beam element. Based on the damping element model and the expression of dissipation energy of the 3-dimentional braided composite materials, each modal damping value of the mechanism is calculated and the damping matrix of the mechanism is established. The dynamic responses and natural frequency of the mechanism are obtained by simulation, respectively. The work presented in the paper provides theoretical basis to a certain extent for the further research on nonlinear vibration characteristics and optimum design of this kind of mechanism.

Field performance of an FRP slab bridge

Fiber reinforced polymer (FRP) composite decks are new to bridge applications and hence not much literature exists on their in-service performance. The in-service performance, and impact and dynamic characteristics of the first fiber reinforced polymer composite bridge superstructure built in New York State in late 1998 are documented in this paper. Test data indicate that the superstructure and the shear-key are structurally performing well. The average impact factor was about 0.3. Observed low strains and deflections, compared to those predicted at the design stages, show room for optimization of the deck design to make these more cost-effective in the future. Higher modal damping values were observed and reflect the vibration absorbing capacity of FRPs. Several delaminations were found during visual inspections and the wearing surface was replaced once. For future applicability of FRPs for bridge deck applications, these issues affecting the long-term durability should be resolved.

High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams

A high-order discrete-layer theory and a finite element are presented for predicting the damping of laminated composite sandwich beams. The new layerwise laminate theory involves quadratic and cubic terms for approximation of the in-plane displacement in each discrete layer, while interlaminar shear stress continuity is imposed through the thickness. Integrated damping mechanics are formulated and both laminate and structural stiffness, mass and damping matrices are formed. A finite element method and a beam element are further developed for predicting the free vibration response, including modal frequencies, modal loss factors and through-thickness mode shapes. Numerical results and evaluations of the present model are shown. Modal frequencies and damping of sandwich composite beams are measured and correlated with predicted values. Finally, parametric studies illustrate the effect of core thickness and face lamination on modal damping and frequency values.

Seismic response analysis of highway overcrossings including soil–structure interaction

AbstractThis paper presents a systematic procedure for the seismic response analysis of highway overcrossings. The study employs an elementary stick model and a more sophisticated finite element formulation to compute response quantities. All dynamic stiffnesses of approach embankments and pile groups are approximated with frequency‐independent springs and dashpots that have been established elsewhere. A real eigenvalue analysis confirms the one‐to‐one correspondence between modal characteristics obtained with the three‐dimensional finite element solutions and the result of the simpler stick‐model idealization. A complex eigenvalue analysis yields modal damping values in the first six modes of interest and shows that modal damping ratios assume values much higher than those used by Caltrans. The validity of the proposed method is examined by comparing the computed time response quantities with records from the Meloland Road and Painter Street overcrossings located in southern and northern California, respectively. The proposed procedure allows for inexpensive parametric analysis that examines the importance of considering soil–structure interaction at the end abutments and centre bent. Results and recommendations presented by past investigations are revisited and integrated in comprehensive tables that improve our understanding of the dynamic characteristics and behaviour of freeway overcrossings. The study concludes with a step‐by‐step methodology that allows for a simple, yet dependable dynamic analysis of freeway overcrossings, that involves a stick model and frequency‐independent springs and dashpots. Copyright © 2002 John Wiley & Sons, Ltd.