Differences In Mode Shapes Research Articles

Integrated Optical Diagnostics Of Cyclopentane Sprays To Characterize Transcritical Phase Transitions

This research investigates spray phase transitions under subcritical and transcritical conditions relevant to high-pressure combustion systems. Using advanced optical diagnostic techniques, including shadowgraphy (SH), Mie scattering (MS), and infrared radiation (IR) measurements, the study focuses on cyclopentane sprays in a high-pressure, high-temperature chamber filled with gaseous nitrogen. Three cases are studied to understand spray behavior under varying injection conditions. SH and MS analyses reveal significant differences across the cases. As the chamber temperature increases, the liquid core length shortens, indicating enhanced vaporization. This is particularly evident in the MS images, where step-like transitions in the axial distribution highlight abrupt phase changes from liquid to gas in subcritical conditions. Such transitions are absent under supercritical conditions, suggesting a smoother phase transition process. IR measurements provide additional insights into the spray dynamics, especially under transcritical conditions. The IR images display complex downstream (at x/D > 125) signal patterns with bimodal distributions. The application of inverse Abel deconvolution highlights negative intensities near the spray axis downstream, indicative of regions near the pseudo-critical temperature. This phenomenon, characterized by blocked background radiation due to critical opalescence, offers indirect evidence of the pseudo-critical temperature and the associated phase transition dynamics. Dynamic Mode Decomposition (DMD) analysis identifies dominant frequencies around 4.5 kHz, corresponding to injection pressure fluctuations. This correlation suggests that injection pressure variations significantly influence spray fluctuations. Differences in mode shapes among the cases are also observed; lateral fluctuations near the injector nozzle exit are present in Cases 1 and 2 but not in Case 3. Axial fluctuations beyond a certain length are consistent in all cases. The lateral fluctuations are related to the chamber pressure and the potential large-scale vortex formation or cavitation in the nozzle. The combined use of SH, MS, and IR methodologies provides a comprehensive understanding of transcritical spray dynamics, emphasizing the effectiveness of combining multiple optical diagnostic techniques. These findings will improve numerical simulations and contribute to the development of more efficient high-pressure combustion systems. The research underscores the complexity of phase transitions in sprays and the critical role of precise diagnostics in the advancement of combustion technology.

Saturation of flames to multiple inputs at one frequency

Existing experimental results show that swirling flames in annular combustors respond with a different gain to acoustic azimuthal modes rotating in either the clockwise or anti-clockwise direction. The ratio $R$ of these two gains is introduced, with $R=1$ being the conventional case of flames responding the same to the two forcing directions. To allow a difference in response to the different directions ( $R\neq 1$ ), a multiple-input single-output azimuthal flame describing function is successfully implemented in a quaternion valued low-order model of an annular combustion chamber in the current work. Theoretical studies have explored this kind of symmetry breaking between the two acoustic wave directions in the past, but it has not been backed by experimental data. One of the main features of the new model proposed in this work is the potential difference in mode shapes between the acoustic and the heat release rate modes, which has recently been observed experimentally. This results in a gain-dependent equation for the nature of the mode, which has a significant influence on the fixed points of the system. For example, one of the spinning solutions and the standing solution can disappear through a saddle node bifurcation as the parameters are varied. The presence of only a single direction for the spinning solution matches experimental observations better than the conventional models, and the proposed model is shown to qualitatively describe experimental measurements well.

Finite Element Model Updating of Steel Arch Bridge Based on First-Order Mode Test Data

In order to obtain an accurate finite element model of a steel arch bridge, a first-order modal finite element model updating method is proposed by using the measured first-order modal data of the bridge. Using the measured acceleration time history data under random excitation and the first-order mode updating method, the stiffness matrix of the finite element model is updated, and the first-order frequencies and first-order mode shapes before and after updating of the model are compared and analyzed. The state space method is used to compare and analyze the dynamic response and the reliability of the structure before and after the updating of the model. The results show that the difference of the first-order frequencies between the updated finite element model and the measured result is about 0.001, and the difference of the first-order mode shapes is less than 0.197, which meets the needs of engineering. Dynamic response values of the updated structural model are much larger than those of the structural model before updating. The theoretical model is different from the dynamic response of actual structure, so it is necessary to update the theoretical model. The finite element model updating method can provide a reliable analytical way for bridge structural health monitoring, state evaluation, and damage identification.

Pattern Matching-Based Structural Damage Identification Using Mode Shape Difference Ratio with Limited Sensors

In order to rapidly identify structural damage, a pattern matching-based structural damage identification using mode shape difference ratio with limited sensors is proposed. The mode shape difference ratio is proposed as the damage indicator for pattern matching. The natural frequencies and mode shapes of the structure under different damage scenarios are obtained by the numerical simulation with finite element software. Using the simulation results, the damage pattern library based on mode shape difference ratio matrix is constructed. Afterwards, for the real structure to be test, the response power spectrum ratio is calculated with the measured acceleration responses. Then the mode shape difference ratio matrix of real structure is constructed using the power spectrum ratio of the measured responses with limited sensors. With the reciprocal of correlation coefficient difference (ROCCD) used as the pattern matching approach, the actual structural damage pattern is matched with the pattern in the damage pattern library. The pattern in the library corresponding to the maximum value of ROCCD is considered to be the damage condition of the structure. Finally, the numerical simulation and experiment of a four-layer interlayer shear model are investigated. The results show that the proposed method well determines the damage location and severity of the structure, and possesses excellent practicability.

Grid-like Vibration Measurements on Power Transformer Tank during Open-Circuit and Short-Circuit Tests

In this work, the vibrations on the surfaces of the tank wall, stiffeners, and the cover of a 5 MVA transformer experimental model were measured during open-circuit and short-circuit transformer tests. Vibration measurements of a transformer tank side were conducted at discrete points using two different voltage sources in no-load test. Using interpolation functions, the RMS values of acceleration and vibration velocity are visualized and compared for each considered measurement configuration (no-load and load tests and two different excitation sources). Significant differences in mode shapes and amplitudes of vibrations at different frequencies are observed. The maximum RMS values of acceleration, velocity and displacement in the open-circuit test are 0.36 m/s2, 0.31 mm/s, and 0.42 µm, respectively. The maximum values in short-circuit test are 0.74 m/s2, 1.14 mm/s, and 1.8 µm, respectively. In the short-circuit test, the frequency component of 100 Hz is dominant. In the open-circuit test, the first few 100 Hz harmonics are significant (100 Hz, 200 Hz, and 300 Hz). In addition to the visualization of RMS values during the open-circuit and short-circuit tests, animations of the vibrations are created. Fourier analysis and phase comparison between frequency components are also used to show vibration animations at dominant frequencies in the spectrum (100 Hz harmonics). The visualization of the vibrations at the tank wall surfaces is transferred into 3D space in such a way that all 15 surfaces are mapped to the spatial coordinates of the surfaces so that a 3D model of the acceleration, vibration velocity, and displacement of the transformer tank is shown.

Damage identification for a beam structure based on a PVDF piezoelectric film combined sensor

The structural strain curvature mode is widely used in structural health monitoring because of its high sensitivity to local changes and accurate damage localization capability. In this research, a combined polyvinylidene fluoride (PVDF) sensor was designed and manufactured based on measurement characteristics of the PVDF sensor. The designed sensor can directly measure the response signal of the strain difference in the structure. According to the central difference principle, the measured value is deduced and used to obtain the local strain curvature of the structure, and the strain curvature modal parameters of the structure are identified with the operating modal identification method. Taking the strain curvature mode shape difference as the damage index, the damage recognition results of the single-chip PVDF sensor and the combined PVDF sensor are compared by performing single damage, multiple damage and damage range experiments on a beam structure. The experimental results show that the combined PVDF sensor proposed in this study is more sensitive to local minor damage.

Circular cross section waveguides processed by multi-foci-shaped femtosecond pulses.

We developed a simple multi-foci-shaped femtosecond pulsed (MFSFP) method for processing circular cross section waveguides in transparent materials. With this flexible processing method, the focus energy distribution can be designed freely and arbitrarily, and single-mode waveguides with cross section circularity better than 96.0% were achieved. The mode shape difference (1.93%) of circular waveguides is smaller than the difference (7.01%) of normal elliptical waveguides. The coupling abilities of the two kinds of waveguides were investigated with three-dimensional (3D) directional couplers in both experiments and theoretical simulations. The coupling coefficient difference of circular waveguides in vertical and horizontal coupling directions was ∼0.01mm-1, which was smaller than 0.33mm-1 of normal waveguides. The circular symmetric waveguides will play an important role in large-scale high-intensity 3D photonic integrated circuits.

Measuring Crack-type Damage Features in Thin-walled Composite Beams using De-noising and a 2D Continuous Wavelet Transform of Mode Shapes

A new method is described, allowing to locate and also measure the length and orientation of crack-type damage features in thin-walled composite beams (TWCB), a capability not previously reported. The method is based on a modal-analysis technique and is shown to work on a hollow composite beam, going beyond previous work limited to simple beams and plates. The method is shown to be capable to function down to signal-to-noise ratios (SNR) of about 15, corresponding to far noisier conditions than in most previous work. This capability is achieved by a combination of wavelet de-noising and the use of a 2D Continuous Wavelet Transform (CWT), applied to two modal analysis metrics, COMAC and Mode Shape Differences (MSD). The length and orientation of the crack can be determined accurately using a 2D curve fitting approach. Using either COMAC or MSD produces reliable results, but MSD is found to be somewhat more noise-tolerant. The new method is believed to be useful for the measurement of damage features in a variety of thin-walled composite beams such as aircraft wings and wind turbine blades, among others.

PREDICTION OF DYNAMIC PARAMETERS OF STRUCTURES BASED ON MODAL ANALYSIS USING FDD

Dynamic behavior and system identification are important topic in monitoring and maintaining existing infrastructures. System identification using Frequency Domain Decomposition (FDD) is an operational modal analysis (OMA) in frequency domain used on experiment of shear frame model with random vibration method is validated by comparing output of FDD data using acceleration input from simulated model with output of FDD using acceleration result of experimental model. The result of acceleration data is recorded using USB accelerometer X16-1D then calibrated and analyzed using Matlab programs, data_procces.m and solve FDD_eksperiment.m to estimate the modal parameter of model structure. Compared with parameter modal of simulation model, FDD method with input simulated acceleration resulted in difference of 1.757% in first frequency and 0.462% in second frequency. Meanwhile for FDD method using acceleration of experimental model, resulted in difference of 6.3126% in first frequency and 7.7327% in second frequency. FFD method is fairly accurate in predicting the frequency of structure, but for difference of mode shapes in experimental is very big compared to simulated model therefore it can be concluded that, this modal parameter is cannot be detected in experimental model.

Multi-strategy structural damage detection based on included angle of vectors and sparse regularization

Recently, many structural damage detection (SDD) methods have been proposed to monitor the safety of structures. As an important modal parameter, mode shape has been widely used in SDD, and the difference of vectors was adopted based on sensitivity analysis and mode shapes in the existing studies. However, amplitudes of mode shapes in different measured points are relative values. Therefore, the difference of mode shapes will be influenced by their amplitudes, and the SDD results may be inaccurate. Focus on this deficiency, a multi-strategy SDD method is proposed based on the included angle of vectors and sparse regularization in this study. Firstly, inspired by modal assurance criterion (MAC), a relationship between mode shapes and changes in damage coefficients is established based on the included angle of vectors. Then, frequencies are introduced for multi-strategy SDD by a weighted coefficient. Meanwhile, sparse regularization is applied to improve the ill-posedness of the SDD problem. As a result, a novel convex optimization problem is proposed for effective SDD. To evaluate the effectiveness of the proposed method, numerical simulations in a planar truss and experimental studies in a six-story aluminum alloy frame in laboratory are conducted. The identified results indicate that the proposed method can effectively reduce the influence of noises, and it has good ability in locating structural damages and quantifying damage degrees.

Exact Damage Identification of Plate-Like Structure using Mode Shapes

In this paper, Mode Shape Based Damaged Detection Technique (MSBDT) has been applied for plate-like structures to recognize the damage location and quantify the damage length. Two alternative approaches are exclusively used to extract damage indexes through mode shapes of undamaged plate (i.e. reference data) and damaged plate. The absolute difference of mode shapes used in first approach and mode shape curvatures used in second approach of undamaged and damaged plates. Healthy Aluminium plate was tested in the laboratory for accurate material properties and considered three different damage cases by changing the crack orientation and location for successfully implementation of above approaches. In order to make certain the sensitivity of the proposed approaches, natural frequencies and corresponding mode shapes for first six modes in transverse direction of a plate are obtained by Finite Element Modal Analysis (FEMA) in ANSYS 18.1 and validated by Experimental Modal Analysis (EMA) in virtual instrumentation environment using LabView software.

Application of two-dimensional wavelet transform to detect damage in steel plate structures

Wavelet Transforms (WT) have been receiving an increasing attention for the detection of damage in structures based on vibration response. The existence of the problem of boundary distortion in WT may lead to unreliable results at and around the boundaries of the structure. Previous studies have applied methods such as signal extension, zero padding and windowing to avoid border distortion. However, these methods try to avoid border distortion by distorting/reducing the original signal to prevent the distortion at the boundaries of the signal from occurring, thus altering the original signal and leading to unreliable damage identification. In this study, a WT-based method is proposed to solve boundary distortion problem. To achieve this, the mode shape difference of a structure is applied for WT decomposition. By using mode shape difference, the problem of border distortion is solved by reducing the effect of sudden change in stiffness that occurs at boundaries. A two-dimensional Continuous Wavelet Transform (CWT) is applied to decompose the difference between the damaged and the undamaged first mode shape signal. The damaged mode shape is subtracted from the undamaged mode shape to obtain the difference, and the difference is decomposed to detect and locate the damage. This method is demonstrated via numerical and experimental examples of a square steel plate. The reliability of the method is demonstrated through different damage intensities and locations. The numerical study involves applying a square plate model with two boundaries formats: all four sides fixed, and two opposite sides fixed and free. The mode shape and mode shape difference are decomposed and the coefficients of the two are compared to show the advantage of this method. The experimental example was applied to a square steel plate with all four sides fixed to verify the efficiency of the method. The numerical results showed that the problem of boundary distortion is resolved by using the mode shape difference and damage at all locations are detected, while applying mode shape provided unreliable results for both numerical models even at 25% severity. The sensitivity of the proposed method to noise is investigated by introducing various levels of signal to noise ratios and showed the detection of damage with 5% severity when mode shape difference was applied in presence of noise.

Mode shape curvature squares method for crack detection in railway prestressed concrete sleepers

This unprecedented study aims to demonstrate the potential to locate crack damage and severity in full-scale railway prestressed concrete sleepers. The dynamic mode shape curvature squares method has been utilised. This approach adopts structural deflection shapes extracted from experimental modal analysis using an impact excitation. The railway concrete sleepers are exposed to the first crack and 1.5 times above the first-crack loads using experimental setup in accordance with the British Standard (for benchmarking purpose). It is found that the first cracking of the sleepers has caused non-significant stiffness reduction of the structural component evidenced from the fact that the natural frequency shifts are only few percent and no visible differences in deflection mode shapes are observed. In addition, the mode shape curvature alone cannot indicate the crack establishment in the railway sleepers. However, a relatively sparse wireframe for deflection shapes enable the plausible density of sensor grids that can be further analysed for damage detection. In this paper, the curvature square approach has been developed to quantify and locate the damage in the railway sleepers. The standardized damage index distributions and subsequent thresholding with different levels of confidence of damage localization have been firstly developed to enhance the accuracy of crack localization. It is found that accurate locations of cracks mostly in the mid span of the sleepers can be reasonably detected in accordance with the actual crack measurements from the experimental data. The novel insight into this approach can enhance the new development of on-board technology for railway sleeper crack detection using operational modal signals.

Damage identification in plate using wavelet transform and artificial neural network

Detection of damage at early stage is necessary to prevent catastrophic collapse of civil structure. The quantification of small damage has however, not received the much needed attention from researchers. Amongst various non-destructive methods studied by researchers to identify structural defects are Wavelet Transform (WT) and Artificial Neural Network (ANN). In this paper, a technique is proposed to quantify damage by combining WT and ANN. The study is divided into two phases. The first phase involves detection and location of damage in a plate numerical model by WT decomposition of the mode shape difference. Due to difficulties in obtaining higher mode shapes in practice, the difference of the first mode shapes of the damaged and undamaged plates are applied. After obtaining the damage location, the coordinates of the damage location and the mean values of the obtained WT moduli are applied as input to the designed neural network. The output of the ANN is the severity of damage in the plate model. This method is demonstrated by using a numerical square steel model with all the four sides fixed. The results indicate the ease of the method and that reliable damage identification can be obtained by combining ANN and WT.

Optimal sensor distance for damage detection considering wavelet sensitivity and uncertainties

Wavelet Transform (WT) is an efficient signal processing tool used extensively to detect damage in various types of structures. It is capable of describing signals in both time and frequency domains. However, improper sensor distance may result to false detection of damage, thus affecting the reliability of the method. A small sensor distance leads to large number of sensors, thus increases the financial cost and causes higher computational time, while large sensor distance may provide inadequate data for accurate damage detection. In this paper, the optimum sensor placement for damage detection is investigated by considering the effect of noise and sensitivity of WT. This involves using Continuous Wavelet Transform (CWT) to decompose the mode shape difference of a plate numerical model. Different measurement distances and different levels of uncertainties are added to the mode shape data to evaluate the optimum sensor distance that provide the best damage detection result. A numerical plate model with all four sides fixed is used as an example. The results indicate that increase of noise reduced the detectability of damage. It is also observed that excessive sensor distance increment significantly effects damage detectability.

Clamp looseness detection using modal strain estimated from FBG based operational modal analysis

Clamps are widely used to fix and support the pipe in engineering community. Clamps looseness may further lead to the fatigue damage of the pipe, therefore the early detection of clamps looseness is very crucial. The robustness and the accuracy of damages detection have already been the greatest challenges in traditional methods in Structural Health Monitoring (SHM). Due to the higher sensitivity of Strain Mode Shape (SMS) to local damages and more effective performance of fiber Bragg grating (FBG) sensing technology for industrial and mechanical devices, present works focus on a new method to detect clamp looseness based on Strain Mode Shape Differences (SMSD) and FBG sensing technology. In order to estimate the SMSs online, a novel diagram of Operational Strain Modal Analysis (OSMA) with FBG sensing technology is also presented, in which a rational fraction composed by Forsythe Complex Orthogonal Polynomials (FCOP) is employed to fit the ‘Positive’ Strain Power Spectral Density (PSPSD) of a single output. Traditionally, the fitting of the all the outputs need to be conducted to obtain the SMSs, which increases the calculation cost. To further address this issue, an improved OSMA integrated with strain response transmissibility (SRT) is also proposed to calculate the SMSs by just fitting a single output. Firstly, the identified modal parameters based on the presented method is validated with simulation results. And then, the ability of the SMSD index is further investigated analytically and experimentally for clamp looseness detection under different locations and degrees, the results indicate that the clamp looseness can be detected by the SMSD index.

Optimisation of free vibration analysis on structural plates of fibre reinforced laminated composites

The present work deals with optimisation of free vibration of fibre reinforced composite rectangular plates. In this investigation, Eglass/epoxy and Jute/epoxy rectangular plates were fabricated using hand lay-up technique. Experimental mechanical testing was done as per ASTM standard for the plates and elastic properties such as Young's modulus, Poisson's ratio and shear modulus were carefully calculated from the test data. For the same specimens, elastic properties were derived using analytical method by rule of mixture and Chamis model. These data were fed into finite element analysis in ANSYS software to find the natural frequencies and mode shapes. Finite element analysis as the result of experimental mechanical testing and analytical model for both plates were compared and dynamic characteristics were discussed elaborately. The effects on aspect ratio (a/b = 3.75, 7.5) for both plates on natural frequency were studied experimentally using hammer method. Finally the cause for the difference in natural frequency and mode shapes were justified with available data.

Dynamic Behavior of A High-Rise Building Under Seismic Loads for Different Bearing Frame Types

Abstract Paper presents the results of dynamic behavior analysis of a high-rise building under seismic loads as part of the “base-foundation-building” system. Analysis covers different types of reinforced concrete construction with girder frame and non-girder frame. Using modal analysis, paper presents differences in mode shapes and frequencies caused by the presence or absence of girders. Paper also demonstrates variations in the stress-strain state for the vertical bearing structures under the seismic load for different frame types.

A New Two-Phase Method for Damage Detection in Skeletal Structures

One of the objective functions used in damage detection problems is the one in which the difference of natural frequencies and mode shapes for the actual and computed damage scenarios are compared simultaneously. Using this type of objective function, one can locate the damage and quantify its severity in a single step. In this paper, a new version of these objective functions is presented in order to decrease the burden of the calculations of the former methods. The presented method has two phases, in the first phase, the natural frequencies are calculated, and in the second phase, the mode shapes are evaluated. The second phase is performed only if the natural frequencies of the computed solution obtained from the first phase are equal to the natural frequencies of the considered scenario. Hence, the number of evaluating modes is considerably decreased. In order to demonstrate the efficiency of the new objective function, the accelerated water evaporation optimization algorithm is utilized for damage detection of three different skeletal structures using different scenarios. Additionally, the numbers of calculated fractions in each iteration of the single-phase and two-phase methods are compared, to show the reduction in the volume of the operations.

A Modified Support Vector Regression Approach for Failure Analysis in Beam-Like Structures

Natural frequency and mode shape differences play a vital role to distinguish between healthy and unhealthy structures. As per the proposed method, the unhealthy structure leads to crack identification in terms of the location and its severity. There are several methods defined in early stage of the research work, but multi-output least square support vector regression machine (MLS-SVR) is an easiest and quick tool in this field of application. MLS-SVR by its tendency can be used for data regression, which can be used to train the training data and test the testing data. The prospective effectiveness of the multi-output regression machine is to map two or more variables of input feature space to two or more variables of output feature space. In our research work, the natural frequencies of the beam structure are considered as input feature space and the crack depth and location are treated as output feature space. The research work initiated from theoretical approach and ended with a comparative statement with MLS-SVR, and it is found that MLS-SVR is one of the best methods for crack detection.