Damage detection in flexible structures is a research field and an industrial favorite. If damages in structures, air crafts and ships are not detected and repaired, they will possibly collapse. Damage detection in flexible structures using vibration signals and in particular Modal test data is the most suitable method. This method is in fact an NOT technique. In this we will present an analytical method for damage detection in .undamped flexible structures using Modal data (natural frequencies. and mode shapes). Reviewing past theories, eigenvalue and igenmode, sensitivity equations are used to derive a system of equations .relating the shifts in natural frequencies/mode-shapes to elemental physical parameters. Damage detection is then carried out by solving the extracted system of equations. Also, Modal expansion and Nelson method are examined and the better method of solving for eigenmode perturbation is chosen. It is recommended that in solving for repeated eigenmode perturbation with generalized inverse techniques, orthogonally condition between theoretical mode shapes must be satisfied. The presented mathematical relations are applicable for trusses, beams and frames but the principles of the theory is general. Finally an experimental investigation is carried out and the position of a crack in a frame with this theory detected.

A new damage detection (crack locating) approach for pipe is introduced based on sensitivity analysis. The method is also validated by Modal test results. As far as the applications concern, pipes are mostly slender structural members, therefore the Euler-Bernoulli beam theory is adopted here in the pipe Finite Element model. The damage is modeled by a stiffness reduction of the element (within the FE model) containing the crack. The minor variation of the mass matrix due to crack is neglected. Expressions relating the sensitivity of Modal frequencies to the changes of stiffness (and mass) matrices are presented. Using this method, the crack is connected to the changes of natural frequencies with a simple relation. This relation then forms the basis of inverse solution to find a pipe crack from changes of few Modal frequencies. First, the direct problem is formulated. A typical case with numerical simulation is presented. Then, the inverse problem is solved for-the same case presented in the direct simulation. Finally, the experiments conducted on a pipe (undamaged and damaged) instrumented for Modal testing is fully reported. The computational method is verified. The experimental results confirm the validity and applicability of the method for crack detection in slender pipes.

Dynamic behavior of a structure is significantly affected by the properties of its joints. This effect is more important in light weight structures with low damping such as airspace structures. In this paper two models for joint inteiface are presented and their properties are identified using Modal testing results. In the identification procedure the characteristic equation of motion is used to obtain joint parameters. A good correlation between identified model and the Modal testing results is obtained.

In this study, damage detection methods of cable stayed bridges were investigated. Cable stayed bridges are flexible structures; meanwhile they are sensitive to vibrations due to their complicated and multiple vibrations modes; therefore, damage detection methods based on vibration data in cable-stayed bridges has become a challenging issue. In the present study, finite element model of Bill Emerson, Missouri cable stayed bridge was simulated in order to achieve a precise finite element model to simulate the damage scenarios in bridge and the study of them. General process includes four damage detection indices based on the Modal data (mode shapes and natural frequencies) achieved by modelling structure and simulated damages and in each case the results of damage detection were presented by indices. These methods are: Enhanced Coordinate Modal Assurance Criterion (ECOMAC), Mode Shape Curvature (MSC), Modal Flexibility Index (MFI), Damage Index (DI). Some of the methods were applied in damage detection of the pervious structures and bridges. In this paper, correlative study of these methods were performed based on different damage scenarios as well as study of challenges such as different levels of random noise in the input data, incomplete Modal data and low damage intensity in detection of damage in cable-stayed bridge and then, performance of the methods were assessed.

Damages or cracks change the natural frequencies and the mode shapes of the structures. Therefore, the Modal parameters could be used in damage detection or structural health monitoring techniques. Based on the knowledge of the authors, most researches in this field have been focused on one-dimensional problems, e. g. beams, trusses, columns, and frames. It seems that the main reason for the lack of comprehensive researches is the huge computational cost for two or three-dimensional problems involved with the finite-element modeling. In order to reduce the costs, two distinct techniques have been utilized here. Firstly, instead of using the genetic algorithm method, the particle swarm optimization (PSO) technique has been applied for finding the best solution. Secondly, instead of applying the fine meshes for calculation of the Modal parameters in the finite-element modeling, the course meshes are used. In this paper, the combination of the frequencies and the mode shapes as an objective function has been applied in the optimization procedure for damage detection of two-dimensional plane stress type problems. For this purpose, the finite-element computer program has been developed in MATLAB environment for the required calculations. The results show that non-gradient-based optimization techniques such as GA and PSO have been successfully detected the existence, location and the intensities of the pre-defined damage scenarios.

In this paper, an alternative approach in operational Modal analysis is presented, utilizing image processing technique and transmissibility functions. Imaging sensors do not impose additional mass on the structure due to their non-contact nature, while transmissibility functions, independent of excitation type, can directly extract mode shapes. The innovation of this research lies in combining these two techniques to record dynamic responses and identify Modal properties. To capture the temporal response history from video signals, the block-matching method with sub-pixel accuracy was employed. Validation was conducted by recording the response of the tip of a cantilevered steel beam subjected to impact excitation, using a high-speed camera and a laser vibrometer, simultaneously. The RMSE plots in the time domain and the PSD in the frequency domain indicate high accuracy of this method. Using this approach, the displacement time histories of various points on the structure were extracted from the video signals, and the Modal properties, including natural frequencies, damping ratios, and mode shapes, were identified using the transmissibility matrix method. The results obtained from the proposed method were compared with the stochastic subspace identification (SSI) method and analytical solutions. The findings reveal the accuracy of the Modal identification approach introduced in this article. The highest relative error in estimating the natural frequencies of the first and second modes, compared to the values from the laser method, are 0.19% and 0.13%, respectively, and in comparison to the analytical values, they are 0.34% and 1.5%, respectively.

This study tries to characterize national transportation modes to assess balancing and sustainability. Using a pioneer measure for sustainable development (SD), and based on the conformity of the growths of all sectors with transportation modes, the countries are comparatively studied. The proposed measure, elasticity, for each pair of variables indicates the extent to which the two variables have been changing consistently. Indeed the elasticity values are measures of" harmonic development" reflecting sustainability. The study database consisted of key aspects of transportation sustainability in the form of national variables including transportation, economic, social and environmental categories in the period 1980-1995. Having developed the elasticity of the social, environmental and economic variables with respect to those of Modal transportation, composite Modal sustainability indices were suggested. The composite indices were then integrated into a unique SD index utilizing the data Envelopment Analysis (DEA), and Concordance Analysis (CA) techniques. For comparative appraisal, country ranking and grouping based on DEA scores, as well as CA results were developed. The sustainability appraisal showed interesting patterns within and between group similarities and differences. The study confirmed the significance of Modal transportation balancing and sustainability challenges of the 21st century. The research focus is on its methodology. Thus, the data gathered from any other time period and geographical scope may be used for further analysis.

In this study, the variational mode decomposition (VMD) algorithm was used to identify the Modal characteristics of the structure using the decomposition of the acceleration responses recorded by the sensors. This algorithm has advantages over other signal decomposition methods that is resistant to the noise and sampling frequency. Also, the VMD algorithm extracts the natural frequencies of the structure concurrently. In addition, the damping ratios of the structure were estimated by fitting a linear function to the logarithmic diagram of the Modal response in the decaying amplitude and calculating the slope of this line. The efficiency and accuracy of this algorithm were investigated by decomposing the acceleration responses obtained from the sensors installed on a prestressed concrete bridge (PSCB) that is located under the load of passing vehicles. The VMD algorithm was used for signal processing in MATLAB to estimate the natural frequencies, damping ratios and mode shapes of the bridge and ARTeMIS was utilized to verify the results. In addition, the finite element modeling and Modal analysis of the bridge were performed in ABAQUS and the natural frequencies and mode shapes of the bridge were obtained. The results showed that the mode shapes estimated by the VMD algorithm were in good agreement with the finite element model and ARTeMIS. Also, the damping ratios estimated by this algorithm were obtained close to the damping value of the prestressed concrete bridge. The difference between the frequencies calculated by the VMD algorithm and ARTeMIS was about 1%, and the difference with the finite element model frequencies was close to 5%.