In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

Clutch system is an important element in the vehicle powertrain. It transmits the rotation from the crankshaft to the gearbox input shaft and filters axial and torsional vibrations providing from engine or induced by friction. This paper discusses axial dynamic behavior of automotive clutch for manual transmission. For this study, a tridimensional finite element model of clutch system is developed to simulate a clutch shaker test. First, an impact hammer test is performed to identify vibration properties of each clutch component. A pre-stressed modal analysis is then carried out to determine mode shapes and its associated natural frequencies of the clutch assembly. Shaker and simulation results are eventually compared to validate the clutch model. This latter offers for the design phase, a tool to avoid natural vibrations or to vibrate at specified frequencies.

In this study, dynamic behaviour of trapezoidal and sinusoidal corrugated plates which are widely used in the fields of space, aviation, automotive, construction and shipbuilding have been analyzed. 330 different surface models varying according to corrugation height and number have been created for these plates which have various manufacturing parameters. At this stage, the number of analyses is 660. These models have been analyzed for different boundary conditions and modal analyses to obtain natural frequencies and mode shapes have been conducted using finite element method. In addition, changes in the trapezoidal cross-section profile have also been investigated by analyzing 38 different plates with varying cross-section profiles. Examining these results, the effects of corrugation height and number on natural frequencies and mode shapes have been determined. As a result of the study a total of 368 drawings were prepared and 736 analyses were performed. Besides, the theoretical results have been verified using the experimental modal analysis technique for some selected models which are being manufactured in the market.

An approach is proposed to identify the modal properties of a subsystem made up of an arbitrary chosen inner module of embedded space equipment. An experimental modal analysis was carried out along the equipment transverse direction with references taken onto its outer housing. In parallel, a numerical model using the finite element (FE) method was developed to correlate with the measured results. A static Guyan reduction has led to a set of master degrees of freedom in which the experimental mode shapes were expanded. An updating technique consisting in minimizing the dynamic residual induced by the FE model and the measurements has been investigated. A last verification has consisted in solving the numeric model composed of the new mass and stiffness matrices obtained by means of a minimization of the error in the constitutive equation method.

The Modal Strain Energy Method (MSEM) is widely used in practice for the prediction of damping levels in structures. MSEM is based on a fundamental assumption that the damped and the undamped mode shapes of a structure are identical. Therefore, when MSEM is to be used, it is essential to ensure that this assumption is an acceptable assumption. However, detailed information on the accuracy of the method as a function of the system parameters including modal (or mode shape) complexity is quite limited. In this paper, the performance of MSEM is assessed in terms of the damping levels of the structure, proportionality of damping distribution and/or the modal complexity. To do so, an effective finite element based MSE approach is proposed first. Then, a proportionally damped structure with different damping levels is modeled and the performance of MSEM is assessed as a function of the structural damping level. After that, a non-proportionally damped structure is studied in order to examine the performance of the method with respect to mode shape complexity. In all cases, a more accurate reference method, based on complex eigenvalue approach, is used for comparison purposes. Furthermore, a few definitions of mode shape complexity are utilized in order to quantify the mode shape complexity. The results show that as long as the mode shapes are real or close to being real, MSEM can predict the damping levels as well as the natural frequencies of a damped structure with good accuracy. However, the accuracy that can be achieved with MSEM decreases as mode shape complexity increases.

Of the multitude of available control techniques, modal control is a favourite amongst structural dynamicists because of its representation in modal coordinates. The term modal control is used to describe a wide variety of control techniques which find their origin in a description of the system through the main coordinates, defined by the modes of vibration of the system. This approach stems from the consideration that the response of a mechanical system to a disturbance is the sum of the independent responses of its vibrational modes. This motivates the desire to design a control that does not alter these mode shapes, but allows to change the natural frequency and the damping of each mode. In active vibration control the purpose is to increase the damping of modes interested in the vibratory phenomenon. The paper shows how stability, spillover effects, system controllability and sensors and actuators position are all linked to the analysis of the controlled system damping matrix and to the possibility that the forces introduced by the control is non-dissipative. Theoretical aspects are supported by numerical simulations.

Gear transmissions in general and spur gears in particular exhibit a different dynamic behavior depending on the level of the transmitted load. This fact justifies the interest in the study of the role of the load in gear dynamics not only in the context of design, vibration and noise control but also for condition monitoring. This task requires the development of advanced models achieving a compromise between accuracy and computation time. In this work, gear and bearing non-linearities associated with the contact among teeth and roller elements have been included, taking into account the flexibility of gears, shafts and bearings. Besides, parametric excitations coming both from gear and bearing supports, as well as clearance, were also considered. Gear contact force calculations are carried out following a hybrid approach which combines both analytical and numerical tools. This lets to achieve accurate results with an acceptable computational effort and thus dynamic analysis becomes feasible. This approach was improved and the calculation speeded up from the point of view of computational time. This was performed by using a pre-calculated value for gear tooth stiffness as a function of load and the angular position when it operates under stationary conditions. On the other hand, bearings were formulated just as deflections of Hertzian type. This means that bending and shearing of races and rolling elements are neglected. However, the variation in the number of loaded rolling elements as a function of the load and the angular position was taken into account. Shaft flexibilities were added to gear and bearing models to define a simple transmission that was used to study the vibratory behavior under different levels of applied torque. In a preliminary study, this model was linearized for several loads, obtaining the corresponding frequencies and mode-shapes in order to assess their variation with this parameter. Finally, dynamic simulations were carried out, showing the modifications undergone by the orbits, meshing contact forces and transmitted bearing forces.

With the increase of ship size and speed, shipboard vibration becomes a great concern in the design and construction of the vessels. Excessive ship vibration is to be avoided for passenger comfort and crew habitability. In addition to undesired effects on humans, excessive ship vibration may result in the fatigue failure of local structural members or malfunction of machinery and equipment. The propeller induces fluctuating pressures on the surface of the hull, which induce vibration in the hull structure. These pressure pulses acting on the ship hull surface above the propeller as the predominant factor for vibrations of ship structures are taken as excitation forces for forced vibration analysis. Ship structures are complex and may be analyzed after idealization of the structure. Several simplifying assumptions are made in the finite element idealization of the hull structure. In this study, a three-dimensional finite element model representing the entire ship hull, including the deckhouse and machinery propulsion system, has been developed using a solid modeling software for local and global vibration analyses. Vibration analysis has been studied under two conditions which are free-free (dry) and in-water (wet). Wet analysis has been implemented using acoustic elements. The total damping associated with overall ship hull structure vibration has been considered as a combination of the several damping components. As the result of global ship free vibration analysis, global natural frequencies and mode shapes have been determined. Besides, responses of local ship structures have been determined as the result of propeller induced forced vibration analysis.

This paper addresses the optimal shape design of segmented spatial sensors and actuators that excite selected mode shapes and perform modal filtering. In MEMS filters, the input signal is converted to external electrostatic forces and in order to perform the desired filtering, the electrodes need to be shaped such that they excite only a desired part of the dynamics. These electrodes are usually designed according to some simplified theoretical identities, often representing lumped models, where in practice, Micro electromechanical structures dynamics are governed by a three dimensional continuum. An optimization scheme that shapes these electrodes to achieve optimal filtering is developed in this paper. The method provides a trimming methodology that can be performed on a real device and it illustrates the need for suitable modeling. Several simulated examples examine the effectiveness of the proposed optimization methods.

Computational model updating techniques have been developed in the past for adjusting selected parameters of large order finite element models in order to make the models compatible with experimental data. Numerical optimization procedures are applied for minimizing the differences of analytical and experimental data, for example, natural frequencies, mode shapes and/or frequency response functions. Since long these techniques have also been investigated with regard to their ability to localize and quantify structural damage. The success of such an approach is mainly governed by the quality of the damage model and its ability to describe the structural property changes due to damage in a physical meaningful way. The change of such parameters identified from test data taken continuously or temporarily over the time may serve as a feature for structural health monitoring. It is well known that low frequency vibration test data or static response data are not very well suited for detecting and quantifying localized small size damage. Exploitable results can only be expected if high spatial resolution of the response data is available. Time domain response data from impact tests carry high frequency information which usually is lost when experimental modal data are utilized for damage identification. Even so only little literature was found addressing the utilization of experimental time histories for model updating in conjunction with damage identification. The theoretical background and examples for using both types of experimental data, high resolution modal data as well as time domain data with high frequency content will be presented in the paper. These data are used in conjunction with a new technique of localizing and quantifying the damage parameters using the test data and the models of the damaged and the undamaged structure simultaneously (“multi model updating”) which is regarded as an attempt to reduce the effects of the unavoidable non-uniqueness of structural damage models.

This paper presents a study conducted to estimate the remaining theoretical life of one type of 400 kV latticed steel towers installed on a power transmission line in Venezuela. The study focused on determining the structural behavior and vibration characteristics of suspension towers on the fore mentioned line, considering material loss of their structural members due to atmospheric corrosion, in different design conditions. For this purpose, a commercially available FEM code was used to build models to perform structural and modal analysis of the chosen type of tower, in order to determine load effects in the structure (stress and deformation), natural frequencies and mode shapes in each of the different design states. Then, a simple methodology engineered as part of this study leads to prediction of the tower’s service life based on an allowable state of stress and deformation in the tower (direct and vibration-induced) affected by different reliability factors and taking into account corrosion effects and corrosion rates in a particular environment along the transmission line.

The aim of this paper is to produce modal data which can be used to synthesise assumed shapes for use in Rayleigh-Ritz approximations of the free vibrations of cantilevered swept plates. The modal data is generated via the use of the FEA technique to predict the natural frequencies and mode shapes of aluminium alloy plates of aspect ratio 2.0 and of swept angles varying from 0° to 20° in steps of 2°. The first fifty natural frequencies and mode shapes of swept cantilevered plates were calculated using ABAQUS FE programme which includes the ABAQUS/CAE pre-and post-processor. To classify each mode shape, the number of nodal lines i along the x-axis and the number of nodal lines j along the y-axis were defined. This definition worked fine for uniform rectangular plates of zero swept angles and also for the first few modes of the swept plates. But as the number of modes of the swept plates increased, this definition became difficult to apply. Similar mode shapes of the various swept angles were put into families and groups headed by the i and j definition of the uniform rectangular plate design. From this modal data, frequency charts, which showed the variation of the dimensionless natural frequencies of the swept plates with swept angle, were constructed. These charts can be used to deduce the types of modes of vibration, whether bending or torsion, of a vibrating swept plate and to synthesis accurately the assumed shapes for use in the prediction of the vibration characteristics of swept plates using the Rayleigh-Ritz approach.

As the vibration-based structural damage detection methods are easily affected by the environmental noise, a novel noise analysis method is proposed based on the statistics in this paper together with the Monte Carlo technique for assessing the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the commonly used random perturbation technique, the proposed technique is deduced directly by the Moore–Penrose generalized inverse of sensitivity matrix under the differential quotient rule of composite function. It can not only make the analysis process more effective but also analyze the noise influence on both frequencies and mode shapes in a similar way. Furthermore, an improved modal sensitivity based damage detection method is also proposed and compared with other two commonly used sensitivity-based methods in this paper. A one-story portal frame is adopted to evaluate the efficiency of both the proposed noise analysis technique and the improved modal sensitivity based method. The assessment results show that the proposed statistics-based noise analysis technique is effective and more suitable for the vibration-based damage identification. The improved modal sensitivity based method is more robust to noise than the other commonly used sensitivity-based methods.

This paper presents a new method for structural damage identification based on the finite element (FE) model updating techniques. First, an objective function is defined as minimizing the sum of differences between the experimental and analytical modal data (natural frequencies and mode shapes), which is set as a nonlinear least-squares problem with bound-constrains. The trust-region approach is then used to solve the minimization problem in order to make this optimization process more robust and reliable. In addition, the expansion and weighting of the original objective function are investigated so that the presented method can be well applied into the damage identification of more real structures. Finally, a numerical simulation model of two-story portal frame structure is adopted to evaluate the efficiency of the proposed technique when both the single and multiple damage cases are set up in the model. Some important issues are also discussed in this paper. The illustrated results show that the single and multiple damages on the two-story portal frame structure can be well identified by the proposed method.

Presented within this paper is the application of finite elements method combined with an evolutionary algorithm to the problem of damage detection in structural members using vibration data. The objective is to identify the position of the damage in structure, and to estimate the extent of the damage. To describe the damage, finite element method (FEM) is used here and the damage is modeled as a reduction in the stiffness of the associated element. Using this model, the effect of damage on the vibration characteristics of the structure is studied. The problem of damage detection is then formulated as an optimization problem. The decision variables are the position of damaged element and the extent of damage. The objective function is considered as the difference between measured natural frequencies and those obtained from FE model of the structure. Only natural frequencies are adopted here, because the measurement of mode shapes is usually accompanied by larger amount of error. The proposed damage detection approach is verified and assessed using a simulated cantilever Euler-Bernoulli beam.

Self-piercing riveting (SPR) has drawn more attention in recent years because it can join some advanced materials that are hard to weld, such as aluminum alloy sheets. In this paper, the free torsional vibration characteristics of single lap-jointed encastre SPR beam are investigated in detail. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of the single lap-jointed encastre SPR beam of different characteristics of sheets to be jointed. Numerical examples show that the torsional natural frequencies increase significantly as the Young’s modulus of the sheets increase, but almost no change corresponding to the change in Poisson’s ratio of the sheets to be joint. The mode shapes show that there are different deformations in the jointed section of SPR beam compared with the reference encastre beam without joint. These different deformations may cause different natural frequency values and different stress distributions.