Modal Analysis Research Articles

Modal analysis and frequency matching study of subway bogie frame under ambient excitation

A wealth of practical cases indicates that the fatigue failure of subway bogies primarily stems from the modal resonance of the structure. If the modal characteristics of the entire vehicle, including equipment and bogies, are mismatched, rail vehicles may experience abnormal vibrations and noise. Therefore, it is imperative to conduct modal analysis and matching design for subway vehicle bogies to ensure smooth operation, reduce structural vibrations and noise, and enhance vehicle safety and ride comfort. Modal identification methods under the ambient l excitations during vehicle operation were employed to identify the modal parameters of the bogie structure before and after wheel reprofiling and under different load conditions. According to the test results, wheel reprofiling has minimal impact on the modal parameters of the structure, but with an increase in load, the modal frequencies of each order generally increase. This is associated with boundary constraint states, such as the increased stiffness of the bogie air spring with an increase in vehicle load. By comparing the test results with simulation analysis results of the bogie structure under free and constrained states, it is evident that simulating realistic boundary constraint conditions is crucial to ensure the accuracy of the finite element model. Based on frequency isolation criteria and vibration isolation theory, a frequency planning basis for the bogie structure was established. The study found that as the vehicle load increases, changes in the boundary conditions of the bogie affecting the elastic modal frequencies of the structure may have a certain impact on matching design, and may even better comply with the requirements of frequency management equations. This provides a new direction for subsequent scholars researching modal matching design.

Nonlinear characteristics and radial-bending-torsional vibration of a blade with breathing crack

Rotor failures due to cracked blades are frequently observed in rotating machinery. The identification of cracking state of rotating blade based on vibration characteristics has garnered a lot of attention. However, nonlinear characteristics and vibration combining in radial, bending and torsional directions of a rotating blade induced by the crack breathing is yet not clear. This paper proposes a radial-bending-torsional dynamic model of rotating blade with breathing crack. A time-varying integration method is proposed for determining the crack state based on the strain energy release rate. The crack breathing behavior is described by Boolean operation and the numerical integration are applied to open or close the crack. The model is validated through modal analysis, vibration responses and contact state of crack surface. Frequency veering is changed between the 2nd flap and 1st edgewise frequency due to the existence of crack. Strong nonlinear behaviors are found in the radial and torsional vibrations because of the crack breathing. Nonlinearities are also found in the combined vibrations between the radial-bending and the bending-torsional directions. Radial and torsional vibration amplitude levels can be used as an indication of blade crack failure, but the applicability depends on the absolute response decided by the aerodynamic excitation and resonant vibration. These findings can serve as guidance in crack identification and cracking state monitoring of rotating blades.

Dynamic and modal analysis of nearly incompressible structures with stabilised displacement-volumetric strain formulations

This paper presents a dynamic formulation for the simulation of nearly incompressible structures using a mixed finite element method with equal-order interpolation pairs. Specifically, the nodal unknowns are the displacement and the volumetric strain component, something that makes possible the reconstruction of the complete stain at the integration point level and thus enables the use of strain-driven constitutive laws. Furthermore, we also discuss the resulting eigenvalue problem and how it can be applied for the modal analysis of linear elastic solids. The article puts special emphasis on the stabilisation technique used, which becomes crucial in the resolution of the generalised eigenvalue problem. In particular, we prove that using a variational multiscale method assuming the sub-grid scales to lie in the finite element space orthogonal to that of the approximation, namely the Orthogonal Sub-Grid Scales (OSGS), results in a convenient linear and symmetric generalised eigenvalue problem. The correctness, convergence and performance of the method are proven by solving a series of two- and three-dimensional examples.

Wind-induced response of saddle membrane structure under typhoon wind field by weather research and forecasting model and computational fluid dynamics

Currently, the research on wind-induced response of membrane structures focuses on the normal wind field, and there is little research on typhoon with greater disaster. In this paper, the wind-induced response of saddle membrane structures under typhoon is studied by numerical simulation. Firstly, the wind field information of typhoon is simulated according to the Weather Research and Forecasting model, and the information is used as the inlet boundary condition of Computational Fluid Dynamics. The vibration modal analysis is carried out, considering the influence of wind field intensity, wind direction angle, rise-span ratio, and pretension on the displacement of the membrane. The results show that the probability density curve of wind-induced response has a certain skewness. The saddle membrane structure has the largest vibration amplitude of the membrane at 0° wind direction angle, and the most unfavorable wind pressure value of the membrane is negative. In reducing the displacement of the membrane, the effect of reducing the wind-induced vibration response by increasing the rise-span ratio of the structure is better than that of the pretension. This paper reveals that the law of wind-induced response can provide a theoretical basis for the design of membrane structures against typhoons.

Natural frequency informed finite element modal analysis method for estimating elastic properties of solid materials

Natural frequency informed finite element modal analysis method for estimating elastic properties of solid materials

A comprehensive study of optical resonances in metals, dielectrics, and excitonic materials in double interface structures

From an optical perspective, depending on the relationship between the real (n) and imaginary (k) parts of its refractive index, three broad categories of materials can be distinguished: metals (k ≫ n), dielectrics (n ≫ k), and materials in which n ≈ k (termed here excitonic materials). The modes and optical resonances that appear in a thin film bounded by two dielectrics with similar refractive index, what we call here a double interface structure, have been widely studied in the case of metals, but not for dielectrics, or materials with n ≈ k. In this work, we propose a new approach, based on employing the phase matching condition to correlate the resonances that appear in the wavelength versus incident angle color maps of the reflected power with the modal analysis of the cross section of the structure. This analysis is performed, using an attenuated total reflection (ATR) setup, for thin film materials that belong to each of the mentioned categories: a metal (gold, Au), a dielectric (titanium dioxide, TiO2), and a material with n ≈ k (chromium, Cr). The theoretical analysis is supported with experimental results. It is demonstrated that this method enables to identify any resonance at any wavelength or incident angle, being valid for all three types of materials. Therefore, it is considered the suggested approach will help the research in these materials and in the double interface structure in the optics and photonics field.

A Frequency Domain Fitting Algorithm Method for Automotive Suspension Structure under Colored Noise

The suspension of a car has different structural forms but usually consists of springs, shock absorbers, guiding mechanisms, etc. As a vehicle moves, the terrain often induces a multifaceted non-white noise vibration within the vehicle. Research on this type of vibration often uses the operational modal analysis (OMA) method, due to its advantages of not requiring knowledge of excitation signals. The disadvantage is that it can only analyze systems under white noise excitation, otherwise it will bring errors. So, this paper proposes a frequency domain fitting algorithm (FDFA) based on colored noise excitation. Initially, an exposition on the foundational principles of the FDFA technique was provided, followed by a demonstration of the modal identification approach. Subsequently, a simulation scenario involving a cantilever beam, akin to a suspension system, was chosen for examination in three instances, revealing that the frequency discrepancies are under 2.94%, and for damping coefficients, they are less than 2.76%. In conclusion, the paper’s introduced FDFA technique, along with the frequency–spatial domain decomposition (FSDD) approach, were employed to determine the modal characteristics of aluminum cantilever beams subjected to four distinct colored noise stimulations. The findings indicate that when utilizing the FDFA technique, the error in modal frequency is kept below 2.5%, while the error for the damping ratio does not exceed 15%. Compared with FSDD, the accuracy was improved.

An insight on local defect resonance based on modal decomposition analysis: A two-dimensional case

The resonance behaviors of defects, specifically local defect resonance (LDR), are useful for defect detection in structures. However, there is a lack of intuitive elucidation regarding the underlying mechanisms governing defect resonance. This study aims to analyze the LDR of a horizontal crack in a plate activated by Lamb waves using the modal decomposition method (MDM). The MDM involves an approximate decomposition of the wavefield into finite constituent Lamb wave modes, including propagating, non-propagating, and inhomogeneous modes. The amplitude of each mode is determined according to the continuous boundary conditions of displacement and stress between the damaged zone and the intact zone. Analytical results reveal specific frequencies at which the damaged zone exhibits significantly stronger vibrations than the intact zone, indicating the emergence of LDR. The corresponding wavefields exhibit various resonance patterns, encompassing both in-plane LDR and out-of-plane LDR types. In contrast to finite element simulations and experimental observations, the MDM unveils the dominant constituents of resonance patterns: out-of-plane LDR results from the combination of reflected and transmitted A0 and A1 modes within the damaged zone, while in-plane LDR is formed by the superposition of reflected and transmitted A0, A1, and S0 modes.

Development of nonlinear flat shell element with nonlinear thickness variation for highly flexible wind turbine blade

Large deformation from continuously varied thicknesses on existing and wind turbine blade shell structures is investigated. Various structure models having complicated outer shapes and thickness variations are considered and validated in this paper. A co-rotational method is developed to analyze geometric nonlinearity with a triangular shell structure. The updated stiffness matrix from interpolated thickness function and integral formulation is suggested to consider complicated geometry and thickness variation. Moreover, the co-rotational flat shell element based on the updated stiffness matrix is developed to analyze various nonlinear shell structures, which are the main feature of this research. The numerical analysis for structure deformations show well matched trends in static load analysis. Furthermore, the deformation of a simplified flexible wind turbine blade having tapered geometry and various thickness cases is adopted as a practical case. Moreover, modal analysis for composite beam structure is performed to verify the dynamic problems. The structural behaviors of the nonlinear thickness shell are validated against the solid and the shell models in commercial software, ABAQUS.

Effects of simulated space conditions on CD4+ T cells: a multi modal analysis.

The immune system is an intricate network of cellular components that safeguards against pathogens and aberrant cells, with CD4+ T cells playing a central role in this process. Human space travel presents unique health challenges, such as heavy ion ionizing radiation, microgravity, and psychological stress, which can collectively impede immune function. The aim of this research was to examine the consequences of simulated space stressors on CD4+ T cell activation, cytokine production, and gene expression. CD4+ T cells were obtained from healthy individuals and subjected to Fe ion particle radiation, Photon irradiation, simulated microgravity, and hydrocortisone, either individually or in different combinations. Cytokine levels for Th1 and Th2 cells were determined using multiplex Luminex assays, and RNA sequencing was used to investigate gene expression patterns and identify essential genes and pathways impacted by these stressors. Simulated microgravity exposure resulted in an apparent Th1 to Th2 shift, evidenced on the level of cytokine secretion as well as altered gene expression. RNA sequencing analysis showed that several gene pathways were altered, particularly in response to Fe ions irradiation and simulated microgravity exposures. Individually, each space stressor caused differential gene expression, while the combination of stressors revealed complex interactions. The research findings underscore the substantial influence of the space exposome on immune function, particularly in the regulation of T cell responses. Future work should focus expanding the limited knowledge in this field. Comprehending these modifications will be essential for devising effective strategies to safeguard the health of astronauts during extended space missions. The effects of simulated space stressors on CD4+ T cell function are substantial, implying that space travel poses a potential threat to immune health. Additional research is necessary to investigate the intricate relationship between space stressors and to develop effective countermeasures to mitigate these consequences.

Flow-induced vibration of turbo-expander impellers for industrial waste heat recovery: An analysis based on two-way fluid structure interaction

In the effort to conserve energy and reduce emissions, waste heat recovery for power generation offers a significant advantage by enabling energy recycling. The turbo-expander, a critical component within expansion power generation systems, plays a pivotal role. However, flow during various operation can generate vibrations that negatively affect operational efficiency and trigger safety hazards. Therefore, studying the flow-induced vibration of the turbo-expander is of significant value. We apply computational fluid dynamics (CFD) and transient structural mechanics to examine the flow-induced vibration characteristics of the turbo-expander influenced by stator-rotor interaction using a two-way fluid structure interaction (FSI) strategy. The flow field modeling and calculation approach discussed here is validated through actual operating data from a prototype. Subsequent stages involve coupling the steady-state flow field with the structural field and performing pre-stress modal analysis on the impeller. In the end, we integrate flow-induced excitation from flow field calculations with the transient structural field to calculate the impeller’s flow-induced vibration at the expansion end of the turbo-expander. Our analysis reveals that guide vane frequency (3267 Hz), its harmonic frequencies, and pre-stress modal frequency (1465 Hz) prominently manifest in pressure pulsation and the dynamic response of the turbo-expander impeller under the influence of stator-rotor interaction.

Computational biomechanics for a standing human body: Modal analysis and simulation.

We develop computational mechanical modeling and methods for the analysis and simulation of the motions of a human body. This type of work is crucial in many aspects of human life, ranging from comfort in riding, the motion of aged persons, sports performance and injuries, and many ergonomic issues. A prevailing approach for human motion studies is through lumped parameter models containing discrete masses for the parts of the human body with empirically determined spring, mass, damping coefficients. Such models have been effective to some extent; however, a much more faithful modeling method is to model the human body as it is, namely, as a continuum. We present this approach, and for comparison, we choose two digital CAD models of mannequins for a standing human body, one from the versatile software package LS-DYNA and another from open resources with some of our own adaptations. Our basic view in this paper is to regard human motion as a perturbation and vibration from an equilibrium position which is upright standing. A linear elastodynamic model is chosen for modal analysis, but a full nonlinear viscoelastoplastic extension is possible for full-body simulation. The motion and vibration of these two mannequin models is analyzed by modal analysis, where the normal vibration modes are determined. LS-DYNA is used as the supercomputing and simulation platform. Four sets of low-frequency modes are tabulated, discussed, visualized, and compared. Higher frequency modes are also selectively displayed. We have found that these modes of motion and vibration form intrinsic basic modes of biomechanical motion of the human body. This view is supported by our finding of the upright walking motion as a low-frequency mode in modal analysis. Such a "walking mode" shows the in-phase and out-of-phase movements between the legs and arms on the left and right sides of a human body, implying that this walking motion is spontaneous, likely not requiring any directives from the brain. Dynamic motions of CAD mannequins are also simulated by drop tests for comparisons and the validity of the models is discussed through Fourier frequency analysis. All computed modes of motion are collected in several sets of video animations for ease of visualization. Samples of LS-DYNA computer codes are also included for possible use by other researchers.

Surface acoustic waves in porous soils with two-layered infiltration

Abstract Two stage mathematical and computer models based on the finite element solution of Richards’ equation for water infiltration in two-layered fluid-saturated soil and modal analysis using a semi-analytical approach for vertically stratified soils are presented and briefly described. Dispersion curves of surface waves in the layered poroelastic half-space are computed and studied. The features of porous water infiltration effect on the characteristics of surface elastic waves are discussed.

Effects of electrochemical machining on high-cycle fatigue of Inconel 718 blades

Blades made from Inconel718 (IN718) are generally machined using electrochemical machining (ECM), and the high-cycle fatigue (HCF) of such blades significantly impacts the service life of aeroengines. In this study, modal analysis was performed to obtain the blade modal shape and stress distribution at first-order frequency, after which blades were machined at different current densities (9.5A/cm2, 18.2A/cm2, 34A/cm2, 46.7A/cm2, 61.2A/cm2, 70.1A/cm2) and then subjected to detailed surface-integrity analysis and fatigue tests. No surface defects (e.g., intergranular corrosion, recast layers) were observed, the microhardness was unchanged, and new residual stress was not found to be introduced to the machined surfaces. The machined surfaces were uneven and contained micro-pits, and high current density contributed to better surface quality. At a constant load of 520 MPa, the blade machined at 70.1A/cm2 had the best fatigue life of 1.4×106. The blades fractured because of micro-pits, and as the surface quality of the blades improved, so did their fatigue performance. Therefore, the fatigue failure mechanism characterized in this work provides a reference for the HCF behavior of blades machined by ECM.

Research on the influence of applying counterweight on the deflection and stability of cantilever beam of machine tool

Abstract The deflection and stability of the cantilever beam of the machine tool are important factors that affect the machining accuracy of the machine tool. Because of the space size, it needs to be weighted within a limited size. By designing different weighting schemes, the static analysis and modal analysis are carried out by finite element analysis software, and the influence law of the deflection and stress of the beam is obtained, so the appropriate weighting scheme is selected. Through the analysis of different schemes, it is known that the deflection of the beam is the smallest under the action of the arm of 900mm and the force of 1000N, and the machine tool structure is more compact, which is the key component of the subsequent machine tool.

Experimental and numerical analyses on the modal behaviour of an aluminium alloy sheet

Abstract The study of modal behaviour for vehicle body panels represents a field of interest for automotive engineering, having a major influence on automotive comfort, with respect to vehicle noise, vibration and harshness, but also concerning the durability of vehicle body. The investigation of natural frequencies and vibration mode shapes is crucial in the design phase, because essential information can be obtained concerning the behaviour of the components in dynamic conditions. The current paper focuses on the investigation of vibration modes and frequency response function on an aluminium alloy sheet. The aim of the paper is to perform the study of modal behaviour both experimentally and theoretically, through measurements using the impact hammer method and respectively through finite element analysis. The CAD model of the aluminium alloy sheet has been developed in Catia V5 environment in view of elaborating the finite element model, which has been used for investigation of modal behaviour, taking into account the case of free vibrations. Through the modal finite element analysis performed in Ansys Workbench, the natural frequencies of the aluminium alloy sheet, as well as the corresponding mode shapes have been obtained. Experiments have been performed on an aluminium alloy sheet, mounted on an elastic support with low natural frequency. The impact hammer method has been used for obtaining the natural frequencies, through frequency analysis of accelerations measured with two piezoelectric accelerometers mounted on the aluminium alloy sheet. The frequency response function has been computed from the response acceleration measured on the aluminium alloy sheet and the impact force measured using the force transducer of the impact hammer. Virtual instruments have been developed in LabVIEW environment for data acquisition, time domain and frequency analysis, as well as for determining the frequency response function using the measured signals. The natural frequencies obtained from the finite element analyses have been compared to the results of measurements and very good similarities have been ascertained. The experimental investigation of modal behaviour contributed to the validation of the finite element model, but further research is required to investigate the possibilities of improving the modal behaviour of the aluminium alloy sheet.

Tuned mass dampers ‐ evaluation of the effect on two real footbridges

AbstractPedestrian comfort, subtle design, minimizing the number of fixed supports of the footbridge or material saving. These are the key arguments for integrating tuned mass dampers into the bridge project. The goal is to protect people and structure from vibrations and damage. The following paper presents findings from the design, production and tuning of mass dampers, their optimization possibilities and benefits for bridge engineering. The validity of damper design was verified on two footbridges in the Czech Republic and Slovakia. It concerns the footbridge over the Svitava River in Bílovice nad Svitavou and the footbridge over the high‐speed road in Banská Bystrica. Dynamic tests including measurement were carried out on both bridges before and after the installation of the dampers. The dynamic monitoring of the compliance of modal parameters was conducted using operational modal analysis (OMA). The evaluation of the dynamic tests also includes the response to pedestrian effects (comfort criteria) and the determination of the logarithmic decrement of the damping.

Spatiotemporal Koopman decomposition of second mode instability from a hypersonic schlieren video

Data-driven modal analysis methods provide a powerful way to decompose data into a sum of modes. The spatiotemporal Koopman decomposition (STKD) enables the computation of modes defined by global frequencies and growth rates in various spatial dimensions and time. The method is an extension of the dynamic mode decomposition (DMD) and higher-order dynamic mode decomposition (HODMD) that represents the data as a sum of standing and traveling, possibly growing or decaying, waves. In this paper, the STKD with HODMD is applied to schlieren video highlighting second mode instability waves traveling down the length of a 3-degree half-angle cone and a 7-degree half-angle cone, both at a freestream Mach number of 6. The HODMD is able to compute dominant modes and frequencies that align with those from associated experimental measurements of unsteady pressure fluctuations, and whose mode shapes clearly show the intensifying wavepacket structure of the waves. The STKD algorithm is used to compute streamwise wavenumbers, spatial growth rates, and wave speeds. The spatial growth rates from the STKD and the magnitudes of the HODMD mode shapes are used to compute the N-factor for waves of several frequencies. Overall, the STKD with HODMD is shown to be a useful tool for extracting spatiotemporal disturbance growth from a schlieren video.

Systematic Experimental Evaluation of Aeroelastic Characteristics of a Highly Flexible Wing Demonstrator

This paper presents a comprehensive experimental analysis of the evolutionary modal characteristics of a highly flexible wing that exhibits bending–torsion coupling-driven instability. By implementing operational modal analysis on responses triggered by a combination of an external pulse-like stimulation and turbulence within the flow, this paper presents the airspeed-driven variations of the modal frequencies, damping ratios, and the underlying modal coupling behavior, leading to instability. This analysis is extended to varying the wing root pitch angles through which the effects of geometrical nonlinearity are exercised. Their effects are particularly noted on the hump feature of the airspeed-driven damping ratio locus of the mode responsible for instability. The decreasing critical damping ratio is shown to result in amplified turbulence-driven responses, which pose significant challenges to identification procedures by masking the visibility of other modes. Furthermore, through a novel technique used to analyze the modal coupling, the relative phase and magnitude properties of the coupled bending–torsion composition of the critical mode before and at flutter onset are evidenced experimentally. It is demonstrated that these relative participation measures provide a strong indication of the response content of the limit cycle oscillations that emerge after the flutter speed.

High efficiency and circular polarization in SATCOM phased arrays using tri-ridge apertures

A new antenna array architecture is proposed here to overcome a current bottleneck in phased arrays concerning the enhancement of radiation efficiency and avoidance of scan blindness. In contrast to the conventional approach of using patches with circular or square geometries that exploit 90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document} or 180∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document} rotational symmetry, this work proposes to use waveguide radiating elements based on 120∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document} symmetry. To implement such symmetry, the tri-ridge aperture is proposed, and its capability to scan widely within a broad frequency bandwidth is demonstrated. A modal analysis is performed to explain the physical phenomena underlying such superior performance. A successful experimental validation is provided by means of a monolithic prototype built in metal additive manufacturing. The measured results show, for the first time, that it is possible to achieve high radiation efficiency and circular polarization when scanning widely in a broad bandwidth. Such an accomplishment constitutes a major achievement in the field of active electronically steered phased arrays, and impacts significantly the capabilities and potential of modern radar and communication systems.