Modal Frequencies Research Articles

Application of a Modal Parameter Identification Method Based on Variational Mode Decomposition in Flight Flutter Testing

Signals of flight flutter testing exhibit non-stationary characteristics, closely spaced modes, and low signal-to-noise ratio, presenting challenges in data processing. In recent years, the variational mode decomposition (VMD) method has emerged as a promising approach to mitigate mode mixing and exhibit robust noise resistance. Therefore, a novel time-frequency domain modal parameter identification method based on VMD is proposed to process impulse response signals in flight flutter testing. The modal frequency and damping ratio are determined through a three-step process: VMD analysis, Hilbert transform, and least square fitting. The efficacy of the proposed method in identifying closely spaced modes and resisting noise is validated through a numerical example. Furthermore, this method is applied to analyze two types of pulse excitation signals in actual flight flutter testing: one induced by the pilot’s shaking stick and the other induced by small rocket excitation. The obtained modal parameters are compared with those from ground vibration tests and specialized software, respectively, to showcase the effectiveness and superiority of the proposed method.

Modal analysis of honeycomb panel satellite structure based on MSC Apex

Modal analysis plays an important role in the process of Satellite structure development. In this paper, the honeycomb sandwich plate and the satellite structure are taken as the research objects, and the corresponding finite element models are established. The analysis results of the actual modeling of honeycomb plate and the equivalent modeling of sandwich sandwich plate are obtained, and the fundamental frequency deviation of the whole satellite structure is discussed when the equivalent correction coefficient γ of honeycomb plate is different. The results show that the maximum relative error of the modal frequency between the equivalent method of sandwich sandwich plate and the actual modeling is 2.8%. Therefore, the equivalent method can be applied to large-scale finite element analysis and calculation, and the calculation efficiency can be improved. When the value of γ is 0.4∼0.6, the vibration modes of the whole satellite structure are basically consistent, and the maximum fundamental frequency difference is 10%. The results can evaluate the accuracy of the sandwich sandwich plate equivalent method for satellite mechanical analysis.

Design of active vibration isolation system for satellite optical load based on Stewart platform

According to the requirements of hyperstatic environment of a satellite optical load during in orbit operation, the Stewart active vibration isolation platform was designed, and its dynamic equation was established by Newton Euler method. The virtual prototype model was established in ADAMS, and the accuracy of the model was verified by comparing the numerical solution and simulation solution of the modal frequency of the platform; On this basis, the dynamic model is decoupled into six SISO systems, and the optimal controller is designed for each subsystem. Finally, the whole system is simulated by ADAMS/MATLAB, and the displacement response curves of the load before and after control are obtained. The simulation results show that the Stewart active vibration isolation platform can effectively suppress the vibration.

Marine shaft optimization using surrogate models and multi-objective optimization

This paper aims to obtain an application software using Ansys software in which a static, dynamic, and modal analysis for the power transmission of ships is presented. The objective functions of this research are maximum static stress, maximum dynamic stress, shaft mass, and modal shaft frequency analysis. A complete, comprehensive, and generalizable model for metal shaft types is presented. Then, using the kriging response surface and multi-objective genetic algorithm (NSGA II), these goals are optimized simultaneously. In this research, the optimization parameters are geometric parameters of the shaft design, including the position of the supports and the inner and outer diameters of the shaft. As a result of this optimization, the shaft's maximum static and dynamic stresses are reduced by 36% and 42%, respectively. The shaft's mass, which is one of the most critical factors during the shaft and its vibrations, is reduced by about 9%. In this regard, the first natural frequency of the optimized shaft increased by about 28.5% compared to the initial shaft.

Optimal Parameters for Tuned Mass Dampers and Examination of Equal Modal Frequency and Damping Criteria

Optimal Parameters for Tuned Mass Dampers and Examination of Equal Modal Frequency and Damping Criteria

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

Model updating of a shear‐wall tall building using various vibration monitoring data: Accuracy and robustness

SummaryAcceleration measurements are often used for model updating of civil engineering structures, especially in the case of seismic monitoring. It is yet unclear if accelerations alone would generate an accurate and robust finite‐element (FE) model. This study examines this notion and analyzes the possibility of using other vibration monitoring data for model updating of shear‐wall tall buildings. This study compares the accuracy and robustness of the FE models being optimized via accelerations, roof displacement, wall rotations, interstory drift ratios, and the linear combination of these measurements. A numerical case study is analyzed using Timoshenko beams for modeling the lateral vibration of a benchmark 42‐story building under seismic excitations. Results show that the acceleration response of the examined building is mostly governed by its higher vibration modes. Depending on the characteristics of ground motions, using accelerations alone may generate an FE model biased towards higher‐order modes without effectively capturing the lower‐order modes. For instance, the first modal frequency of the updated FE model could be 12.0% lower than the true value, and the reconstructed displacement and rotation responses are noticeably inaccurate. Employing multi‐source monitoring data for model updating, for example, the combinations of roof displacement and acceleration measurements, could reduce the normalized root‐mean‐square errors in displacements by more than 70%. This study also quantifies the robustness of the FE model under various measurement noise levels and 50 pairs of earthquake records. Finally, the effects of multi‐source data on FE model updating are validated via experiments on a 7‐story shear wall building. Analysis reveals that a more accurate and robust FE model can be determined via a combination of accelerations and top displacement than via acceleration alone.

Model refinements with experimental validation in piezoelectric plate actuators

The axisymmetric vibration analysis of circular plates with piezoelectric layers and step changes in plate thickness is conducted. For the chosen configurations, it is necessary to solve a coupled system of differential equations for extensional and flexural vibration to obtain accurate modal results. The adopted computational approach is based upon the classical transfer matrix method. Instead of employing analytical solutions in the form of e.g. Bessel functions, matrix exponentials of the system matrix are directly computed in the transfer matrices for finding highly accurate solutions. The developed approach has enabled the complete quantitative modal analysis in piezoelectric actuators. The procedure is firstly verified against available analytical results for natural frequencies and modes shapes in circular homogeneous plates, and by using finite element simulations for plates with asymmetric step changes in thickness. Ultimately, the developed approach is validated against experimental results of relevance to applications in piezoelectric synthetic jet actuation. The obtained numerical results for modal parameters and frequency response functions are in excellent agreement with the available analytical results, and with previous and newly presented in the paper experimental data, when considering the inherent uncertainty in parameter values. Based on extensive experimental results, realistic damping is introduced in the model of piezoelectric plate actuators. Importantly, it is shown that solutions of high accuracy can be obtained by a more general coordinate system than that traditionally linked to the plate neutral plane(s).

Quantum-informed plasmonics for strong coupling: the role of electron spill-out

The effect of nonlocality on the optical response of metals lies at the forefront of research in nanoscale physics and, in particular, quantum plasmonics. In alkali metals, nonlocality manifests predominantly as electron density spill-out at the metal boundary, and as surface-enabled Landau damping. For an accurate description of plasmonic modes, these effects need be taken into account in the theoretical modeling of the material. The resulting modal frequency shifts and broadening become particularly relevant when dealing with the strong interaction between plasmons and excitons, where hybrid modes emerge and the way they are affected can reflect modifications of the coupling strength. Both nonlocal phenomena can be incorporated in the classical local theory by applying a surface-response formalism embodied by the Feibelman parameters. Here, we implement local surface-response corrections in Mie theory to study the optical response of spherical plasmonic–excitonic composites in core–shell configurations. We investigate sodium, a jellium metal dominated by spill-out, for which it has been anticipated that nonlocal corrections should lead to an observable change in the coupling strength, appearing as a modification of the width of the mode splitting. We show that, contrary to expectations, the influence of nonlocality on the anticrossing is minimal, thus validating the accuracy of the local response approximation in strong-coupling photonics.

The current state of the problem of numerical investigation of metal structure refusal based on dynamic monitoring

The article considers the critical role of long-term dynamic monitoring of building structures in ensuring their safety and stability. The importance of studying the structural behavior of truss structures after local failures is emphasized, which is key to the development of effective monitoring methods. The value of vertical deflections and modal frequencies as indicators of the general behavior of structures is pointed out, as well as the high costs associated with traditional monitoring methods requiring a large number of sensors. It is also emphasized that modern engineering practice does not have universal monitoring methods that would take into account all the features of construction structures, especially spatial structures with a complex design and a variety of elements. Authors calls for the development of new approaches and technologies to improve risk monitoring and management, which can prevent catastrophic consequences, as was the case with Viadotto Polchevera and other structural collapses. Attention is also drawn to current research that uses dynamic monitoring to inform the design of civil structures, including updating finite element models based on measured in-service performance. It is highlighted that long-term monitoring can provide valuable information about structural behavior, which allows for a better assessment of the condition of the structure and the prediction of potential defects. It is emphasized that a local failure can lead to the progressive destruction of the entire structure, which makes monitoring extremely important to prevent such incidents. The article concludes with conclusions about the need to establish management and maintenance procedures to maximize the life cycle of structures and obtain optimal return on investment.

Developing and Testing High-Performance SHM Sensors Mounting Low-Noise MEMS Accelerometers.

Recently, there has been increased interest in adopting novel sensing technologies for continuously monitoring structural systems. In this respect, micro-electrical mechanical system (MEMS) sensors are widely used in several applications, including structural health monitoring (SHM), in which accelerometric samples are acquired to perform modal analysis. Thanks to their significantly lower cost, ease of installation in the structure, and lower power consumption, they enable extensive, pervasive, and battery-less monitoring systems. This paper presents an innovative high-performance device for SHM applications, based on a low-noise triaxial MEMS accelerometer, providing a guideline and insightful results about the opportunities and capabilities of these devices. Sensor nodes have been designed, developed, and calibrated to meet structural vibration monitoring and modal identification requirements. These components include a protocol for reliable command dissemination through network and data collection, and improvements to software components for data pipelining, jitter control, and high-frequency sampling. Devices were tested in the lab using shaker excitation. Results demonstrate that MEMS-based accelerometers are a feasible solution to replace expensive piezo-based accelerometers. Deploying MEMS is promising to minimize sensor node energy consumption. Time and frequency domain analyses show that MEMS can correctly detect modal frequencies, which are useful parameters for damage detection. The acquired data from the test bed were used to examine the functioning of the network, data transmission, and data quality. The proposed architecture has been successfully deployed in a real case study to monitor the structural health of the Marcus Aurelius Exedra Hall within the Capitoline Museum of Rome. The performance robustness was demonstrated, and the results showed that the wired sensor network provides dense and accurate vibration data for structural continuous monitoring.

Output-only identification of time-varying structural modal parameters under thermal environment

Obtaining the input load presents a significant challenge for system identification problems with time-varying characteristics in aerospace engineering. Therefore, the modal parameter is determined through output-only identification techniques. Considering rapid time-varying characteristics in thermal environment, a Recursive Subspace Method (RSM) is used to enhance the precision of identifying modal parameters. A three-degree-of-freedom system with time-varying stiffness is first investigated to validate the identification method. The effect of noise on the robustness of the algorithm is discussed. Then, the experimental investigation is undertaken considering a composite beam under a time-varying thermal environment though the thermal-vibration experimental system. Experimental results indicate that the change of structural modal frequencies under variable temperature environment is mainly affected by the thermal stress induced in the structure. Comparing the experimental and simulation result, the output-only identification approach has good efficiency and convergence for time-varying system.

Numerical study on lead–bismuth cross-flow induced vibration in the elastic tube bundle

The physical properties of liquid lead–bismuth eutectic fluid are quite different from that of water or air. It needs to be verified whether the cross-flow vibration mechanism and the empirical prediction model of fluidelastic instability in conventional media are applicable to lead–bismuth. In this work, for an in-line elastic tube bundle with pitch ratio P/D = 1.5, the flow excitation of lead–bismuth at 200 °C is studied and compared with that of water in uncoupled flow field. Then, two cases of lead–bismuth flow-induced vibration with different mass-damping parameters are simulated and studied by fully coupled numerical simulation considering fluid viscous damping. The tube bundle experiences the process from turbulence-induced vibration in low flow velocity to fluidelastic instability in high velocity. The results of flow excitation show that the pressure coefficient distribution of the front row tube in lead–bismuth is basically consistent with that in water, while the inconsistency of the pressure coefficient distribution for the back row tube is caused by the bi-stable deflective flow. The results of lead–bismuth flow-induced vibration show that, in fluidelastic instability, the vibration of tube bundle and the vortex shed from tube bundle are dominated by the frequency close to the first wet modal frequency of tube bundle. The different deflective directions of lead–bismuth and water, caused by bi-stable characters, have less effect on the onset of fluidelastic instability. The instability points of lead–bismuth agree with the experimental results of other media and the Connors prediction model considering fluid viscous damping. The prediction model is suggested to predict the onset of fluidelastic instability induced by lead–bismuth cross-flow in the tube bundle.

Mode Shape-Based Damage Detection of Twin Skewed Bridges Based on OMA and FE Model Updating

A comparative study of the dynamic behavior of twin single-span bridges was carried out based on operational modal analysis and a linear finite element model updating with the aim of finding a potential damage indicator. The bridges are skewed, 30 m long and with prestressed concrete girders as the main support structure, but one of them were collided and suffered damage in two of its I-shape girders. Ambient vibration tests were conducted by deploying 14 uniaxial accelerometers along the sidewalks, experimental modal parameters were identified using the COVariance-driven Stochastic Subspace Identification method (SSI-COV). Six vertical modes were clearly identified for each structure. Additionally, some extra modes with non-proportional damping were identified. It was found that the modal frequencies are sensitive to the support conditions and the overall stiffness of the bridge but not to the localized girder damage, which, on the contrary, is reflected in the discrepancy in the fundamental bending mode shape amplitude between the lateral sides of the bridge, and a so-called Continuous Symmetry Measure adopted as a symmetry index seems to be a good damage indicator for this type of straight-alignment simply supported bridges, given the symmetric nature of the bending mode shapes and the asymmetric nature of the damage.

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

Response spectrum-based analysis of airborne radar random vibration and multi-point control improvement

During the flight of a UAV (unmanned aerial vehicle), the LiDAR device undergoes random vibrations due to the changing flight attitude and wind speed conditions of the UAV. It is important to control the frequency and amplitude of the vibrations within a reasonable range by means of a damping structure. As the vibrations caused by various factors during flight are random and non-linear, this paper innovates the analysis principle and damping control means for the random vibrations of airborne optoelectronic devices. The response spectrum analysis theory is used to establish the shock response spectrum, and an optimised and improved recursive digital filtering method is used to fit the frequencies of random vibration to the synthetic shock response. Considering the uncertainty of the vibration excitation signal, a virtual excitation method is used for the first time to simulate the random vibration to which the radar may be subjected in the air, and to simplify the calculation steps. The shock plate structure is designed using a multi-point control method to innovate a passive response to the random excitation. Finally, a modal analysis of the synthesised impact response was carried out. It is verified that the first six modal frequencies are controlled within 220 Hz, realising the frequency reduction. The amplitude of the three x, y, and z directions is controlled to within 0.5 mm, thus achieving vibration damping.

Explicit solution framework and new insights of 3-DOF linear flutter considering various frequency relationships

Different engineering structures, e.g., long-span bridges, bundled conductors, and cable-supported photovoltaic modules, exhibit various frequency relationships among different degrees of freedom (DOFs). Despite extensive research, the initiation mechanisms of flutter remain somewhat ambiguous for a 3-DOF system considering heaving-lateral-torsional motions, especially when frequencies are close among different DOFs. This study introduced an explicit eigenvalue solution framework for tackling the 3-DOF linear flutter problem by utilizing matrix perturbation methods, enabling the extraction of modal damping and frequency solutions for all possible frequency scenarios. These solutions explicitly clarified the influence mechanism of all flutter derivatives (aerodynamic damping and stiffness), structural frequencies, and mechanical dampings. Important flutter derivatives, flutter risk level, and sensitivity level to mechanical damping and to frequency detuning were summarized in a table for all frequency scenarios, providing a panoramic perspective on flutter instability and the coupling mechanism. Numerical studies were conducted on a thin plate, the Akashi Kaikyo Bridge, and an eight-bundled conductor to examine the proposed explicit solutions. The results showed that approaching frequencies can amplify the coupling effect among different DOFs by half an order, but this does not necessarily mean the system is more prone to flutter. A system where the torsional frequency approximates the heaving/lateral frequency is expected to face a higher flutter risk if given significant torsional-related aerodynamic stiffness (H3*, P3*). Evidently, this high risk exhibits insensitivity to mechanical damping and small frequency-detuning. Though usually ignored in bridge flutter analysis, drag force and lateral motion could exert noticeable influence in a minority of cases, e.g., more than 10 m/s decrease of critical wind speed for the Akashi Kaikyo Bridge at large angles of attack. The proposed explicit solution framework provides a systematic view and new insights into the flutter initiation mechanism, serving as a reference in the design and studies of various engineering structures with different frequencies and coupling features.

Effects of Concentrated Mass on the In-Plane Dynamic Behaviors of Two-Cable Networks with a Cross-Tie

This study proposes a two-cable network model, which includes a cross-tie and two concentrated masses installed at the connection points of cross-tie and cable. The characteristic equation of such a cable network system is formulated via the complex modal analysis method. Then, dynamics of a twin-cable network is discussed in details, and the effect of concentrated mass on the system modal frequencies, damping and mode shapes is investigated. Furthermore, a general two-cable network system is analyzed. Results show that the concentrated mass always reduces the modal frequency, as it causes an increase in the modal mass of the system. When installing a concentrated mass in a twin-cable network, the difference of vibration modes between the cables can be increased in the in-phase modes, thereby achieving the damping effect of the damping type cross-tie on these modes. For a twin-cable network with a viscous damper, a small concentrated mass can significantly increase the modal damping of the in-phase modes as long as the damping coefficient of the damper is properly set. Meanwhile, when there is a two-cable network with unequal length cables, the presence of concentrated masses may reduce differences in vibration modes between cables, thus leading to decreased damping of some modes.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.

Insight into the influence of frictional heat on the modal characteristics and interface temperature of frictionally damped turbine blades

The reciprocating relative motions of friction pairs introduce nonlinearities into the host structure, while also generating frictional heat, leading to a noticeable temperature rise at the contact interface. Consequently, the contact mechanics properties are not invariant but highly dependent on temperature. To elucidate the thermo-mechanical interaction mechanism in dry friction systems, we propose a novel multi-physical nonlinear modal analysis method called Thermo-Mechanical damped Nonlinear Normal Mode (TM-dNNM). This numerical method enables the determination of nonlinear modal characteristics considering thermo-mechanical coupling and the prediction of detailed temperature distribution on contact interface. The efficiency and convergence of the TM-dNNM are ensured through three key techniques: multi-physics reduced order modeling, analytical Jacobian matrix, and scaling adjustment. We apply the proposed numerical method to a typical turbine blade with a flat underplatform damper for engineering purposes. Results indicate that frictional heat significantly affects the nonlinear modal characteristics, exhibiting complex behavior such as softening/stiffening reversal and resonance amplitude backtracking. Neglecting the thermo-mechanical coupling can lead to a deviation of more than 13 Hz in the predicted modal frequency and an overestimation of the modal damping ratio by a factor of three. Interface temperature rises considerably at higher vibration levels, with the hotspot located near the lower left corner of the contact surface, where the average temperature exceeds 1180 ℃, approaching the melting point. By employing the TM-dNNM, designers can predict critical resonance amplitudes and identify potential local hotspots, thus helping prevent excessive temperature at the interface of frictionally damped turbine blades.