Modal Parameters Research Articles

A Resonance-Avoiding Modal Balancing Method for Multimodal Balancing of High-Speed Flexible Rotors

Abstract Conventional balancing methods for high-speed flexible rotors typically necessitate costly and potentially hazardous balancing tests conducted near their critical speeds. This paper first demonstrates the feasibility of achieving multi-mode balancing using measurements taken below the first critical speed, based on traditional modal balancing methods and rotor modal parameters. However, while theoretically viable, this approach is highly susceptible to measurement noise, complicating its practical implementation. To address this issue, we propose an innovative resonance-avoiding modal balancing (RAMB) method specifically designed for multi-mode balancing. In RAMB, balancing is performed mode by mode in a forward manner, effectively integrating the correction weights of lower modes into the balancing equation. This strategy eliminates the need to operate the rotor at unbalanced critical speeds, enhancing the effectiveness of multi-mode balancing while ensuring measurement safety. The effectiveness of both the conventional method and the RAMB approach is validated through numerical simulations and experimental tests as well. The results show that RAMB significantly enhances the vibration suppression over the entire operating speed range while avoiding resonance measurements and exhibits comparable robustness to noise, confirming the validity and superiority of the proposed balancing method

Research on damage identification of simply supported bridge based on effect size method for vehicle-bridge coupled vibration

Abstract This paper presents a novel bridge damage identification method employing Cohen's d as an effect size indicator, predicated on the detection of bridge damage through the coupled vibration between a vehicle and the bridge. By analyzing the dynamic response of the bridge as a vehicle passes over, this method effectively extracts the modal parameters of the bridge and facilitates the identification of bridge damage. Numerical models of the bridge under various damage conditions, including no damage, mid-span damage, and damage at the 1/4 and 3/4 span locations, have been constructed to substantiate the efficacy and precision of the effect size as a damage indicator. Furthermore, to address the challenge of accurately identifying damage at boundaries, which is often confounded by boundary effects, a boundary subdivision method has been defined for the detection of boundary damage. Through the implementation of a real-bridge test based on indirect measurement technology, the self-vibration frequency of the bridge was successfully extracted. This empirical data was then compared and analyzed against results from ANSYS numerical simulations, thereby validating the practicality and accuracy of the proposed method. In the final analysis, the influence of random traffic flow on the bridge damage identification results was examined. The findings indicate that the vibrations in simply supported beam bridges are intensified due to the impact of random traffic flow, which aids in enhancing the accuracy of damage identification. The introduction of this method provides a new quantitative tool for bridge health monitoring, enabling the rapid and accurate identification of bridge damage without interrupting traffic. It holds significant value for engineering applications in bridge maintenance and safety assessment.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Dynamic Testing and Finite Element Model Adjustment of the Ancient Wooden Structure Under Traffic Excitation

In situ dynamic testing is conducted to study the dynamic characteristics of the wooden structure of the North House main hall. The velocity response signals on the measurement points are obtained and analyzed using the self-interaction spectral method and stochastic subspace method, yielding natural frequencies, mode shapes, and damping ratios. This study reveals that the natural frequencies and damping ratios are highly consistent between the two methods. Therefore, to eliminate errors, the average of the results from both modal identification methods is taken as the final measured modal parameters of the structure. The natural frequencies of the first and second order in the X direction were 2.097 Hz and 3.845 Hz and in the Y direction were 3.955 Hz and 5.701 Hz. The modal frequency in the Y direction of the structure exceeds that in the X direction. Concurrently, a three-dimensional finite element model was established using ANSYS 2021R1, considering the semi-rigid properties of mortise–tenon connections, and validated based on in situ dynamic testing. The sensitivity analysis indicates adjustments to parameters such as beam–column elastic modulus, tenon–mortise joint stiffness, and roof mass for finite element model refinement. Modal parameter calculations from the corrected finite element model closely approximate the measured modal results, with maximum errors of 9.41% for the first two frequencies, both within 10% of the measured resonant frequencies. The adjusted finite element model closely matches the experimental results, serving as a benchmark model for the wooden structure of North House main hall. The validation confirms the rationality of the benchmark finite element model, providing valuable insights into ancient timber structures along transportation routes.

Full-field Modal Analysis of a Tensegrity Column Using a Three-dimensional Scanning Laser Doppler Vibrometer with a Mirror

Abstract Tensegrity structures become important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on their dynamic analyses mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study proposes a non-contact approach for experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer is used with a mirror for extending its field of view to measure full-field vibration of a novel three-strut metal tensegrity column with free boundaries. Tensions and axial stiffnesses of its cable members are determined using natural frequencies of their transverse and longitudinal modes, respectively, to build its theoretical model for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and theoretical mode shapes are used to identify their paired modes. Modal parameters of the first 15 elastic modes of the tensegrity column identified from the experiment, including those of the overall structure and its cable members, can be classified into five mode groups depending on their types. Modes paired between experimental and theoretical results have MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The proposed non-contact 3D vibration measurement approach allows accurate estimation of 3D full-field modal parameters of the tensegrity column.

Modal Parameter Identification of Electric Spindles Based on Covariance-Driven Stochastic Subspace

Electric spindles are a critical component of numerically controlled machine tools that directly affect machining precision and efficiency. The accurate identification of the modal parameters of an electric spindle is essential for optimizing design, enhancing dynamic performance, and facilitating fault diagnosis. This study proposes a covariance-driven stochastic subspace identification (SSI-cov) method integrated with a simulated annealing (SA) strategy and fuzzy C-means (FCM) clustering algorithm to achieve the automated identification of modal parameters for electric spindles. Using both finite element simulations and experimental tests conducted at 22 °C, the first five natural frequencies of the electric spindle under free, constrained, and dynamic conditions were extracted. The experimental results demonstrated experiment errors of 0.17% to 0.33%, 1.05% to 3.27%, and 1.29% to 3.31% for the free, constrained, and dynamic states, respectively. Compared to the traditional SSI-cov method, the proposed SA-FCM method improved accuracy by 12.05% to 27.32% in the free state, 17.45% to 47.83% in the constrained state, and 25.45% to 49.12% in the dynamic state. The frequency identification errors were reduced to a range of 2.25 Hz to 20.81 Hz, significantly decreasing errors in higher-order modes and demonstrating the robustness of the algorithm. The proposed method required no manual intervention, and it could be utilized to accurately analyze the modal parameters of electric spindles under free, constrained, and dynamic conditions, providing a precise and reliable solution for the modal analysis of electric spindles in various dynamic states.

Prediction models for modal parameters of high-rise buildings based on the latest statistics of field measurements

Prediction models for modal parameters of high-rise buildings based on the latest statistics of field measurements

Review of Bridge Structure Damping Model and Identification Method

Damping is a fundamental characteristic of bridge structures, reflecting their ability to dissipate energy during vibration. In the design and maintenance of bridges, the damping ratio has a direct impact on the safety and service life of the structure, thus affecting its sustainability. Currently, there is no suitable theoretical method for estimating structural damping at the design stage. Therefore, the modal damping ratio of a completed or under-construction bridge can only be obtained through field dynamic tests to ensure compliance with design specifications. To summarize the latest research findings on bridge structure damping models and identification methods, and to advance the development of damping identification techniques, this paper provides an in-depth review from several perspectives: Firstly, it offers a comprehensive analysis of the theoretical framework for structural damping. Secondly, it summarizes the damping models proposed by researchers from various countries. Thirdly, it reviews the research progress on identifying the modal damping ratio of bridge structures using time domain, frequency domain, and time-frequency domain methods based on environmental excitation. It also summarizes the methods and current status of identifying the modal damping ratio using artificial excitation. Finally, the future prospects and conclusions are discussed from three aspects: damping theory, test and identification method and data processing. This research and summary provide a solid theoretical foundation for advancing bridge structural damping theory and identification methods and offer valuable references for bridge operation and maintenance, as well as damage identification. From the perspective of modal parameter identification, it provides a theoretical basis for the sustainable development of bridges.

Similarity analysis to enhance Transfer Learning for Damage Detection

Abstract One significant challenge in machine learning for Structural Health Monitoring (SHM) is reusing previously trained classifiers. A classifier might be suitable for one situation but not for another. Transfer learning techniques try to overcome this difficulty. In SHM, it is common to use the modal parameters as features; however, they are highly influenced by boundary conditions, geometry, and the level of structural damage. This work proposes an approach that performs a similarity analysis to select features before applying transfer learning, aiming at improving classification and damage detection. The reasoning is that a higher similarity leads to a more efficient transfer of learning and, consequently, a better classification. Transfer learning is conducted via the domain adaptation technique known as Transfer Component Analysis (TCA), and cases with low similarity are compared to those with high similarity. Two datasets are analyzed. The first consists of a beam under different boundary conditions, and data is generated through numerical simulations. The second derives from an experimental setup of bolted joints with loosening damage. The proposed strategy, which uses a cosine-type similarity, is shown to improve the transfer learning classification.

Vibration suppression of balls in different contact states during mirror milling of curved thin-walled parts based on magnetic follow-up support fixture

Milling of curved thin-walled parts is a critical step in the manufacturing of aircraft skins or rocket storage tanks. During the process of milling thin-walled parts using magnetic follow-up support fixture, the complex situation that the fixture balls in different contact states with the surface of the thin-walled parts occurs, leading to changes in the dynamic characteristics of the thin-walled parts, thereby causing machining vibration and even chatter, ultimately affecting machining quality. To this end, this paper focuses on the vibration of thin-walled parts under balls in different contact states. Firstly, the structure and function of the magnetic follow-up support fixture are illustrated. Then, a dynamical model of a mirror milling system that accurately reflects balls in different contact states is established using finite element technology, in order to explore the changing law of dynamic characteristics at milling points of thin-walled parts under balls in different contact states. To further investigate chatter under balls in different contact states of thin-walled parts, after obtaining modal parameters of the thin-walled parts through impact tests, three-dimensional stability lobe diagrams (3D-SLDs) of thin-walled parts under balls in different contact states are plotted using the full-discretization method, and chatter-free parameters are selected. Finally, the rationality of finite element analysis and stability analysis, as well as the practicality of the fixture, are verified through milling experiments. The experimental results show that after the fixture is applied, the dominant frequency of curved thin-walled parts can be increased by up to 6 times, its amplitude can be reduced by over 60 %, and the surface roughness can be reduced by up to 57.98 %.

Enhancing reliability in estimating modal parameters for automotive disk Brakes: A comprehensive approach using the Eigensystem Realization algorithm and additional criteria

This paper investigates the challenges in accurately identifying and assessing vibration characteristics in automotive disk brakes, which, due to their geometric symmetry, exhibit closely spaced vibration modes. Understanding the damping characteristics is crucial due to their significant impact on dynamic stability and the potential onset of brake squeal, as damping directly influences the stability threshold and its uneven distribution can destabilize the system. Therefore, this study primarily focuses on the identification of modal parameters with an emphasis on the damping of disk brakes. Traditional Experimental Modal Analysis (EMA) techniques, which rely heavily on Frequency Response Function (FRF) measurements, encounter challenges in distinguishing closely spaced modes, thereby affecting the reliability of parameter estimation, particularly damping. These algorithms are primarily based on FRF measurements and are of multi-input – single-output type (MISO). In comparison to Operational Modal Analyses (OMA) algorithms, which are widely used in civil engineering and are of the multi-input − multi-output type and contain statistical tools for assessing the uncertainty of the estimate, EMA provides limited possibilities to assess the quality of estimating parameters. The primary contribution of this work is demonstrating that the Eigensystem Realization Algorithm (ERA), supplemented with indicators such as Extended Modal Amplitude Coherence (EMAC), Modal Phase Collinearity (MPC), and the Consistent Mode Indicator (CMI), offers a robust tool for accurate damping estimation. Additionally, the application of ERA to data originally acquired for frequency-based methods, specifically the Rational Fraction Polynomial (RFP) method, allows for a direct comparison of these two EMA algorithms using the same dataset. The results demonstrate that the proposed identification process effectively distinguishes system modes from those influenced by noise, providing a pathway to optimize test data acquisition and improve the accuracy of modal parameter estimation, especially in systems with closely spaced modes. The method can also serve as a tool for optimizing the acquisition of test data to improve the estimation of modal parameters, by varying the positions of input (SIMO) or by transitioning to MIMO identification to enhance the observability and controllability of closely spaced modes of disk brake.

Design theory for section model tests considering multimode coupling and imperfect modeshape similarity of full bridges

Section model tests are the most fundamental wind-tunnel technique widely employed in the design of flexible cable-supported bridges. To guarantee the accuracy of aeroelastic stability assessment, the dynamic behavior of a section model test should reflect the aeroelastic characteristics of the full bridge. Conventional method only employs the fundamental vertical and torsional modes for the design of dynamic parameters, typically ignoring multimode coupling effect and assuming perfect modeshape similarity. This paper introduces a novel theoretical framework that integrates multimode coupling and imperfect modeshape similarity into the design of a section model test. The framework establishes a direct equivalence between the complex modal parameters of the unstable mode in the multimode coupling system and the two degrees-of-freedom coupling system of the section model. It quantifies each mode's contribution to coupled flutter through a single parameter denoted as mode participation factor. Validation of this improved design theory is performed using numerical models of four representative cable-supported bridges, highlighting its effectiveness. The study also sheds light on the complexities of multimode aeroelastic coupling and the limitations of section model tests.

Research on the influence of cutter overhang length on robotic milling chatter stability

Serial industrial robots are widely in demand in the field of large-scale component processing and manufacturing. However, the structure characteristic of serial robots makes it easy to generate chatter during milling and the overhang length of milling cutter has an important influence on the stability of robotic milling. Milling cutter overhang length refers to the length from the tip of the cutter to the protrusion of the spindle, to study the influence of milling cutter overhang length on the stability behavior of robotic milling, the modal parameters of milling cutter under different overhang length were obtained by hammer experiment, and its dynamic characteristics were analyzed. The stability behavior for robotic milling under different cutter overhang lengths was analyzed by using the stability lobe diagrams, and the stability lobe diagrams were verified by robotic milling experiments. The results show that the rigidity and natural frequency of milling cutter decrease with the increase of overhang length. There is a big gap between the stability lobe diagrams and the actual machining state when the cutter overhang length is short, and the low frequency vibration is easy to occur in the robotic milling process when the spindle speed is low, which is most probably because that the absorbed vibration energy by the cutter has been transferred to the robot body before the milling cutter vibrates. When the cutter overhang is increased and the feed direction is along the y-axis of the robot global coordinate system, the stability lobe diagrams by considering the multi-mode coupling effect is more consistent with the actual milling state.

Determination of the Modal Parameters of the Historical Elevated Water Tank Using Experimental and Numerical Methods

Determining the modal parameters of historical buildings is crucial for understanding their dynamic behavior, which is essential for their preservation and safety for future generations. Experimental and numerical studies are commonly used to characterize modal properties such as natural frequencies and mode shapes. Experimental studies typically employ the operational modal analysis method, while numerical studies employ the finite element method. Vibration measurements of the structure under various environmental conditions, including wind and traffic, were used to determine the modal parameters. However, discrepancies often arise between modal parameters obtained from experimental research and those assessed by finite element models, primarily due to unknown factors like boundary conditions and material properties. The purpose of this study was to measure the vibrations of a historic elevated water tank a 150-year history under ambient conditions to determine its modal characteristics. Comparing the modal parameters obtained from numerical and experimental investigations revealed that the water tank's finite element model requires updating to align with the findings of the experimental modal study. Using the updated finite element model in future evaluations or assessments of the structure can lead to a better understanding of the behavior of the structure.

Modal analysis of key components of crusher based on digital simulation technology

The modal characteristics of the crusher rotor and shell constitute the crucial factors influencing vibration and noise. Based on the principle of simplification, the rotor component model was established. Through mesh optimization, the model accuracy and calculation efficiency can be ensured, and the calculation of natural frequency and modal shapes was completed based on ANSYS. To verify the accuracy of the finite element model, the modal test was carried out by the hammering method. Sensors were set in three different directions to obtain the frequency response function and the modal assurance criterion matrix mode confidence criterion. Using the same research method, the modal characteristics of the shell model were simulated and analyzed. The research results show that the modal parameters identified by the modal test are basically consistent with the simulation model. The natural frequencies of the rotor and the shell are quite different from the excitation frequency of the motor, and resonance problems will not occur when the crusher is proper functioning.

Automatic High-Resolution Operational Modal Identification of Thin-Walled Structures Supported by High-Frequency Optical Dynamic Measurements.

High-frequency optical dynamic measurement can realize multiple measurement points covering the whole surface of the thin-walled structure, which is very useful for obtaining high-resolution spatial information for damage localization. However, the noise and low calculation efficiency seriously hinder its application to real-time, online structural health monitoring. To this end, this paper proposes a novel high-resolution frequency domain decomposition (HRFDD) modal identification method, combining an optical system with an accelerometer for measuring high-accuracy vibration response and introducing a clustering algorithm for automated identification to improve efficiency. The experiments on the cantilever aluminum plate were carried out to evaluate the effectiveness of the proposed approach. Natural frequency and damping ratios were obtained by the least-squares complex frequency domain (LSCF) method to process the acceleration responses; the high-resolution mode shapes were acquired by the singular value decomposition (SVD) processing of global displacement data collected by high-speed cameras. Finally, the complete set of the first nine order modal parameters for the plate within the frequency range of 0 to 500 Hz has been determined, which is closely consistent with the results obtained from both experimental modal analysis and finite element analysis; the modal parameters could be automatically picked up by the DBSCAN algorithm. It provides an effective method for applying optical dynamic technology to real-time, online structural health monitoring, especially for obtaining high-resolution mode shapes.

Whale Optimization Algorithm for structural damage detection, localization, and quantification

This paper introduces an approach for vibration-based damage detection based on matrix updating aided by the Whale Optimization Algorithm (WOA). The methodology uses the Data-driven Stochastic Subspace Identification (SSI-DATA) technique to determine the modal parameters, which are compared with those obtained from both healthy and damaged conditions of the structure. The methodology’s efficacy is assessed through three distinct steps: numerical simulations, experimental data, and real-world data from a bridge. Initially, numerical analyses are conducted on a cantilever beam, a 10-bar truss, and a Warren truss subjected to environmental vibrations with varying damage cases and noise levels. Subsequently, experimental validations are performed on a test system and in the Z24 Bridge. Results from the computational simulations demonstrate the method’s promise to identify, locate, and quantify single and multiple damage cases, even amidst signal noise, variations in the first vibration mode as minimal as 0.015%, and complex structures with 54 elements. Moreover, the matrix updating method utilizing WOA showcased superior accuracy compared to existing techniques in the literature. In addition, the Z24 Bridge example validated the capability of the presented damage detection method to localize structural damage solely based on natural frequencies.

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Study on I/III mixed fracture characteristics of coal in different regions of China

The fracture mechanical property of coal rock constitutes an important mechanical constraint for hydraulic fracturing of coal reservoir, and its three-dimensional fracture characteristics hold great significance for coal-bed methane mining. In this study, non-invasive methods were employed to investigate the pore structure and permeability of coal, aiming to understand the gas storage, distribution, and mobility of coal from various regions. To assess the influence of geological stress on coal during coal-bed methane mining, a three-point bending test was conducted to determine the characteristics of coal I/III mixed fractures. The experimental results indicate that with the decrease of the modal mixing parameter Me, the fracture area expends, the fracture load Pf and fracture energy Ef increase, while the fracture toughness declines. The 3D fracture criterion is utilized to predict the toughness ratio of coal rock I/III mixed fracture. The 3D-MTS and 3D-MMTSN criteria offer the upper and lower limits of prediction respectively. The 3D-MTSED criterion proves to be a more appropriate fracture criterion for analyzing the 3D fracture.

Observation and Prediction of Instability due to RD Fluid Force in Rotating Machinery by Operational Modal Analysis

In recent years, as rotating machinery has become smaller and more efficient, various types of shaft vibration problems have arisen. Failure of rotating machinery may lead to major accidents and infrastructure shutdowns. Therefore, to prevent failures of rotating machinery, there is a growing need for the vibration analysis technology at the design stage and condition monitoring during operation stage. One of causes of the shaft vibration problems in rotating machinery is the rotordynamic (RD) fluid force acting on fluid elements such as journal bearings, seals, turbine blades, and so on. RD fluid force has a significant effect on the stability of rotating machinery and can destabilize the system. In recent years, operational modal analysis (OMA) methods, which identify modal parameters based on the measured data of a machine's operational condition, have been investigated in the condition monitoring. In this paper, the estimation of the modal parameters of rotating machinery using OMA from only the time history response of displacement data and, in particular, the prediction of the destabilization of rotating machinery caused by RD fluid force are investigated. As a result, the modal parameters are well estimated and, in particular, the destabilization of one mode due to RD fluid force is predicted and explained. The results are in good agreement with the results of the eigenvalue analysis of the original system, and the method is validated. Furthermore, the proposed method is applied to experimental data of the system destabilized by fluid force. The change in stability with rotational speed is observed, and the characteristics of the mode toward destabilization are confirmed. The results show the validity of OMA's predictions of destabilization in the experiments.