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The main principle of vibration-based damage detection in structures is to interpret the changes in dynamic properties of the structure as indicators of damage. In this study, the mode shape damage index (MSDI) method was used to identify discrete damages in plate-like structures. This damage index is based on the difference between modified modal displacements in the undamaged and damaged state of the structure. In order to assess the advantages and limitations of the proposed algorithm, we performed experimental modal analysis on a reinforced concrete (RC) plate under 10 different damage cases. The MSDI values were calculated through considering single and/or multiple damage locations, different levels of damage, and boundary conditions. The experimental results confirmed that the MSDI method can be used to detect the existence of damage, identify single and/or multiple damage locations, and estimate damage severity in the case of single discrete damage.

The electromechanical dynamic patterns of the power system, which normally refer to electromechanical oscillation dominant modes, mode shapes, participation factors and coherent groups, are important for the study of power system dynamic behaviours. Different from the existing measurement‐based methods which mainly estimate one or two facts of dominant modes, mode shapes or coherent groups, a holistic data‐driven estimation approach is developed to estimate all the four electromechanical dynamic patterns from the measurements systematically and estimate the participation factors from measurements. In the developed approach, the multichannel continuous wavelet transform is firstly employed to dominant modes and mode shapes estimation. Besides, the estimated mode shapes are used to calculate the left eigenvalue vectors of the dominant modes. With the estimated mode shapes and left eigenvalue vectors, the participation factors are solved and coherent groups are separated. Finally, the proposed data‐driven approach is evaluated by the 16‐machine, 68‐bus test system and China Southern Power Grid. The results validate that the proposed data‐driven approach can accurately estimate all the four electromechanical dynamic patterns from synchrophasor measurements in a single way.

Quadcopter is a mechatronic device that has four arms and each arm having a D.C. motor with a propeller. These four propellers provide the thrust to quadcopter, furthermore difference in the angular speed of these propellers is responsible for roll, pitch and yaw motion. The propeller of the quadcopter is subjected to the dynamic loading and vibration during the flight. The present study investigates the vibration characteristics of quadcopter propeller. To investigate the vibration behaviour, three different type of material are analyzed for result comparison. The solid model of propeller was designed in Creo 2.0 and Ansys 16.2 was used for analysis. Modal analysis was performed to find the First 6 natural fundamental frequencies and their mode shape. The frequency variation describes the failure and safe region through colour couture scale under different loading condition. The obtained results are compared and validated with the previous studies.

Conducting surveys of multi-storey buildings is a laborious task, because large volumes of visual and instrumental research should be carried out. Reduction of labor costs with an increase in the reliability of information about the state of damage and technical condition is an actual scientific and practical task. One of the ways to solve it is to use non-destructive vibration diagnostic methods. The purpose of carrying out diagnostics with the use of vibration based damage detection methods is to search for damages in structural elements that can cause the deviation of the dynamic parameters of a structure from calculated ones. Determination of the dynamic parameters of the structure, in particular natural frequencies and mode shapes of mechanical systems, is one of the most important tasks that allows obtaining integral information about the state of a structure. This article presents the results of calculations for the localization of slabs defects in a multi-storey building with a transverse crack, span L = 4.5 (m), height H = 0.2 (m), with prestressed reinforcement d = 0.05 (m). Vibration based Damage Index method was used to localize the defect. During the study, reliable localization values of the defect area of the slab were obtained, this indicates that the vibration method for determining the damage index with a sufficient degree of accuracy allowed predicting the site of damage to the structure.

The stress mode shapes are highly sensitive to the local state of the structure, e.g., holes, cracks, and grooves. In this paper, two new defect indices based on stress mode shapes are developed to locate single or multiple local structural defects with different severity levels on the marine propeller blade edge. A stress modal analysis was performed on the intact model of the blade and the different models of the defective blade. The first four stress mode shapes along the propeller blade edge were calculated for every model of the blade. The new defect indices called modal stress flexibility change and defect index based on stress modal energy were calculated for each stress mode shape. Firstly, the ability of the two new defect indices calculated for each mode to locate a single defect was investigated. Secondly, the effectiveness of the defect indices calculated from the combination of the first four stress mode shapes is investigated for single and multiple defect localization considering different severity levels. Through the numerical investigation, the modal stress flexibility and defect index based on stress modal energy are promising to locate single or multiple defects in real structures such as marine propeller blades.

In this study, the torsional mode shapes of circular and non-circular functionally graded material shafts, focusing on triangular, rectangular, circular cross-sections are investigated. The shafts are composed of an aluminum-titanium (AlTi) alloy and various functionally graded materials, utilizing different mixing rules to create a gradient surface. The modal analysis is conducted using ANSYS Mechanical leading finite element analysis software to assess and visualize the vibrational characteristics of these shafts under torsional loading. Then, the same shafts made of isotropic material (pure Al) is prepared, and compared with respect to results. The objective is to understand the influence of FGMs compared to homogeneous and isotropic materials on the torsional behavior of shafts with non-circular geometries. By comparing the torsional mode shapes and frequencies, one can identify the distinct vibrational properties introduced by the gradient material composition. This comparison is highlight the potential advantages of FGM shafts in applications requiring tailored mechanical properties that traditional homogeneous materials cannot provide. The study also explores how the different cross-sectional shapes affect the torsional response, which is crucial for designing components subjected to twisting loads in aerospace, automotive, and construction industries. The results from ANSYS Mechanical are analyzed to extract the mode shapes and frequencies of torsional modes, providing a comprehensive understanding of how FG materials behave relative to isotropic counterparts under similar conditions. The study aims to show how the natural frequency and torsional mode shapes differ for a functionally graded material compared to isotropic material, may be useful for researchers working with applications where vibration behavior is crucial.

Steel rods are widely used in the areas of petroleum, chemical, architecture and transportation, steel rods with cracks will cause terrible accident and great losses when working in production practice. In view of traditional Non-destructive Testing (NDT) method can only realize static detection, this paper provide the method based on modal calculate analysis, including the choice of damage index and the judgment of damage degree and damage location for cracks of steel rods. The damage location is judged by the strain mode shape difference curve and the function expression of damage degrees and mutation degrees of curvature mode shapes is acquired by the method of least square fitting, which can achieve quantitative analysis of single crack of steel rods, this provide theoretical support and technical reference for experimental modal analysis and dynamic NDT.

This paper presents both deterministic and stochastic free vibration analyses of carbon nanotube (CNT)-reinforced multi-layered functionally graded material (FGM) cantilever plates. The reinforcement varies linearly following a power-law distribution. The governing equation is derived using the first-order shear deformation theory (FSDT), while the rule of mixtures is applied to determine the effective elastic modulus, mass density, and Poisson’s ratio of the CNT-reinforced FGM plate. A finite element-based Monte Carlo simulation (MCS) is employed for the stochastic analysis. The study begins with a validation of the finite element model by comparing the obtained results with existing literature. Subsequently, a parametric investigation is conducted, examining the effects of stochasticity percentage, power law index, plate thickness, volume fraction, temperature, and CNT size. Additionally, mode shapes for the first three vibration modes are plotted. The findings reveal that all these parameters significantly influence the first three natural frequencies.

The basis of rotor dynamic balancing procedures depends on the linearization hypothesis of the system. However, some dynamical characteristics of mechanical elements of rotor systems are nonlinear. To increase the balancing efficiency, an improved algorithm is proposed by applying the Nonlinear Normal Modes (NNMs) to the modal balancing procedure. To demonstrate the accuracy and effectiveness of the proposed method, a Jeffcott rotor with nonlinear restore force is balanced by both the NNMs method and the linear modal method for comparation. The simulations show that the balancing results by the NNMs method are significantly better than those by the linear modal method, regardless of levels of nonlinearity and eccentricity, by comparing the percentage reduction in vibration amplitude at critical frequencies, spectra of responses and resonance curves.

Curvature-based damage detection has been previously applied to identify damage in concrete structures, but little attention has been given to the capacity of this method to identify distributed damage in multiple damage zones. This study aims to apply for the first time an enhanced existing method based on modal curvature analysis combined with wavelet transform curvature (WTC) to identify zones and highlight the damage zones of a beam made of ultra-high-performance fiber-reinforced concrete (UHPFRC), a construction material that is emerging worldwide for its outstanding performance and durability. First, three beams with a 2 m span of UHPFRC material were cast, and damaged zones were created by sawing. A reference beam without cracks was also cast. The free vibration responses were measured by 12 accelerometers and calculated by operational modal analysis. Moreover, for the sake of comparison, a finite element model (FEM) was also applied to two identical beams to generate numerical acceleration without noise. Second, the modal curvature was calculated for different modes for both experimental and FEM-simulated acceleration after applying cubic spline interpolation. Finally, two damage identification methods were considered: (i) the damage index (DI), based on averaging the quadratic difference of the local curvature with respect to the reference beam, and (ii) the WTC method, applied to the quadratic difference of the local curvature with respect the reference beam. The results indicate that the developed coupled modal curvature WTC method can better identify the damaged zones of UHPFRC beams.