Modal Test Results Research Articles

A scaled derivative-based DMDc method for modelling multiple-input multiple-output mechanical systems

Dynamic mode decomposition with control (DMDc) is a powerful data-driven method for modelling dynamical systems with inputs and outputs. However, the inability to identify oscillations and the high sensitivity to noise limit the application of standard DMDc in structural dynamics. To address this challenge, this paper proposes a novel method called scaled derivative-based DMDc (sd-DMDc) to construct a discrete state-space model for mechanical systems using noisy data. This method requires only the displacement and excitation data, computes the scaled derivatives of displacement to extend the system states, and integrates the extended forward-backward strategy. Two crucial parameters are defined and optimized by minimizing the response error. The sd-DMDc algorithm is first verified through numerical simulations of a multiple-input multiple-output (MIMO) cantilever plate. The results indicate that sd-DMDc exhibits superior modelling accuracy across various noise levels and measurement points compared to the delay-DMDc method. It has also been proved that sd-DMDc can accurately identify dynamical systems from partial observations. Subsequently, vibration experiments are conducted on a MIMO cantilever plate. The sd-DMDc method is further verified using experimental data, and the conclusions align with those drawn from simulation studies. The sd-DMDc algorithm demonstrates great modelling accuracy, surpassing that of delay-DMDc, especially for partial observations. In addition, the model given by sd-DMDc can extract the modal parameters of the plate, which are consistent with the modal test results.

Contact Stiffness Identification Method for Joint Surface and the Effect of Contact Stiffness on the Dynamic Response of the Cable Bracket

The cable bracket is one of the crucial components of high-speed Electric Multiple Units (EMUs), which is fixed to the axle box by bolts to support the cable. As an important parameter of the joint surface, contact stiffness significantly affects the dynamic response and service life of the cable bracket. However, it is difficult to directly measure the contact stiffness of the joint surface. As a result, an identification method is proposed in this investigation to identify the contact stiffness. A finite element model incorporating both normal and tangential stiffness parameters is developed. According to the finite element model and modal testing results, an improved particle swarm optimization algorithm is employed to identify the contact stiffness of the joint surface. The effect of the contact stiffness on the vibrations of the cable bracket is investigated. The findings indicate that pre-tightening torque significantly influences the contact stiffness of the cable bracket. The contact stiffness has a great effect on the vibrations of the cable bracket. Optimal contact stiffness notably reduces vibrations of the cable bracket, thereby extending its service life.

Investigation on the dominant mechanism of chatter in high-load robot milling process based on theoretical and experimental analysis

Chatter has always been a key problem restricting the improvement of robotic milling quality and efficiency. To avoid chatter, it is necessary to determine what is the dominant chatter mechanism (mode coupling or regenerative) of the robot milling system. Therefore, this paper focus on the dominant chatter mechanism in high-load (600kg) robot milling. The modal test results show that the dynamic flexibility of spindle-tool structure mode in high-load robot is significantly higher than that of the body structure mode, which is significantly different from the low-load robot in other studies. The mode coupling chatter stability prediction models are established based on eigenvalue method and zeroth order approximation, and the predicted stability boundaries are compared with the experimental results. The results show that only high-frequency chatter exists in the high speed region (1000-8000rpm), and no low frequency chatter occurs. The low-frequency chatter around the robot body mode is found in the low-speed region (400-1000rpm), but the mode coupling chatter theory could not explain the chatter varies periodically with the spindle speed. However, the stability boundary predicted by the regenerative chatter theory also changes periodically with the spindle speed. This indicates that the milling chatter dominant mechanism of high load robot is regenerative chatter. This study analyzes the milling chatter dominant mechanism of high-load robot through theoretical and experimental verification, which can provide theoretical support for high-load robot milling chatter control.

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

A recursive calculation method of vibration displacements using blade tip timing in angular domain

Blade tip timing (BTT) is a non-contact measurement technique that can be used to monitor blade vibration in turbomachinery. The raw data measured by BTT is the arrival time of all blades at the same stage. However, most blade vibration monitoring methods based on BTT require the use of blade vibration displacements, which are derived from the raw arrival time data, the blade rotation radius and speed. Conventional BTT methods calculate blade tip displacements by comparing the measured arrival time with the ideal arrival time. The ideal arrival time is obtained by assuming that the rotational speed is constant in a revolution, which is inconsistent with the fact, especially when the rotational speed changes rapidly. In this paper, a recursive calculation method called recursive BTT is proposed to reduce the influence of rotational speed fluctuation on the accuracy of blade tip displacement calculation. Recursive BTT calculates the displacements in the angular domain instead of the time domain. A recursive formula is constructed in the angular domain to calculate the blade vibration displacement by using the angle between the vibrating blades. Compared with the conventional BTT method, which relies on the once-per-revolution (OPR) signal, recursive BTT makes full use of the arrival time of all blades at the same stage to calculate the displacements. The advantage of recursive BTT is illustrated through a simulation, a laboratory test and a full-scale aeroengine test. To evaluate the reliability of the calculated displacements, strain signals are resampled to compare with the calculated displacements in the laboratory test. In the full-scale aeroengine test, due to the lack of strain signals, BTT displacements are used to track the blade natural frequency to qualitatively indicate the influence of displacements on blade vibration monitoring. The results of finite element analysis and modal test are used for verification in the full-scale aeroengine test. Simulation and experimental results demonstrate that compared with existing methods, recursive BTT is robust for calculating blade vibration displacements.

A distortion model test method of the casing string system considering FSI

To solve the problem of prototype test’s high cost and difficulty of the casing string system in shale gas horizontal wells, this paper proposes a large-scale distortion model test method for the casing string system. Firstly, the elastic centralizer is simplified as elastic support, and the dynamic model of casing string system is established by finite element method. Then, the test platform of casing string system is designed and built. The modal test results show that the maximum error of the first five natural frequencies between the numerical calculation and the test results is 5.12 %, which verifies the correctness of the dynamic model of casing string system. On this basis, the distortion model’s constant power similarity law (CPSL) and power function similarity law (PFSL) are obtained by the dimensional analysis method and the least square method. The CPSL and PFSL are used to predict the vibration characteristics of the prototype casing string system by distortion models with different scaling ratios. The calculation and analysis show that the prediction accuracy of the PFSL is higher than CPSL’s with the same scaling ratio, and the PFSL can accurately predict natural frequency of the prototype casing string system within a large-scale distortion range and greatly reduce the test cost.

Investigation of the profile of the blade considering machining vibration based on finite element analysis

Abstract Vibration is a problem that is easy to occur in the manufacturing process of thin-walled parts such as blades. Through the analysis of modal test results, the role of tool response and blade response in machining vibration is analyzed. With the aid of finite element simulation, the effects of damping ratio, cutting force peak, and force exciting position on the amplitude of response displacement are studied. The profile error caused by the machining vibration is simulated and the peak value of the response displacement amplitude is experimentally verified.

Optimization Design of Straw-Crushing Residual Film Recycling Machine Frame Based on Sensitivity and Grey Correlation Degree

This paper takes the frame as the research object and explores the vibration characteristics of the frame to address the vibration problem of a 1-MSD straw-crushing and residual film recycling machine in the field operation process, and an accurate identification of the modal parameters of the frame is carried out to solve the resonance problem of the machine, which can achieve cost reduction and increase income to a certain extent. The first six natural frequencies of the frame are extracted by finite element modal identification and modal tests, respectively. The rationality of the modal test results is verified using the comprehensive modal and frequency response confidences. The maximum frequency error of modal frequency results of the two methods is only 6.61%, which provides a theoretical basis for the optimal design of the frame. In order to further analyze the resonance problem of the machine, the external excitation frequency of the machine during normal operation in the field is solved and compared with the first six natural frequencies of the frame. The results show that the first natural frequency of the frame (18.89 Hz) is close to the external excitation generated by the stripping roller (16.67 Hz). The first natural frequency and the volume of the frame are set as the optimization objectives, and the optimal optimization scheme is obtained by using the Optistruct solver, sensitivity method, and grey correlation method. The results indicate the first-order natural frequency of the optimized frame is 21.89 Hz, an increase of 15.882%, which is much higher than the excitation frequency of 16.67 Hz, and resonance can be avoided. The corresponding frame volume is 9.975 × 107 mm3, and the volume reduction is 3.46%; the optimized frame has good dynamic performance, which avoids the resonance of the machine and conforms to the lightweight design criteria of agricultural machinery structures. The research results can provide some theoretical reference for this kind of machine in solving the resonance problem and carrying out related vibration characteristics research.

An approach to seismic damage detection and evaluation in RC bridge piers through vibration data

A timely post-earthquake damage evaluation in existing bridges is fundamental for an efficient emergency management. Structural Health Monitoring (SHM) systems can allow a fast damage assessment; however, a lack of methods for the SHM data interpretation is recognised. The present paper proposes an approach for the probabilistic seismic damage detection and quantification in ductile bridge piers from vibration-based SHM data by comparing time variations of modal properties. To this aim, the selected modal properties are natural frequencies and mode-shapes, expressed in terms of CoMAC and ECoMAC indices. Experimental results of quasi-static cyclic tests and output-only modal identification tests are adopted to calibrate a reliable finite element model able to predict the variations in fundamental modal properties of ductile RC piers due to seismic damage. The calibrated model is used to perform probabilistic analyses to derive probability distributions for the variation of the considered modal-based features of piers at different seismic damage levels. The approach provides fragility models to support a timely assessment of serviceability levels in monitored assets in the immediate aftermath of an earthquake by monitoring the variation of natural frequencies. Conversely, CoMAC and ECoMAC resulted slightly sensitive to seismic damage for the investigated piers portfolio.

Modeling and free vibration analysis of bolted composite flanged cylindrical-cylindrical shells under partial bolt loosening conditions

The bolted composite coupled cylindrical shell is a common substructure in modern engineering, which may encounter the issue of local loosening conditions during service. Meanwhile, the influence of flanges on the structural vibration characteristics is often overlooked in dynamic numerical analysis. In this paper, a semi-analytical dynamic model for the bolted composite flanged cylindrical-cylindrical shell structure under arbitrary connection conditions is established, and the free vibration characteristics of locally loose structures are emphatically studied. In the model, the annular plate modeling method is developed to achieve the simulation of the flange part. To fully reflect the connection characteristics of the bolted joint, a spring surface model and the corresponding parameter determination method based on fractal contact theory are developed. The equations of motion of the structure are obtained utilizing the Lagrange equations. The accuracy of the model and its predictive ability for the vibration characteristics of the bolted composite flanged cylindrical-cylindrical shell under local loosening conditions are fully demonstrated through numerous comparisons with experimental results from other literature and modal test results obtained under various working conditions. Furthermore, the influence of the number and degree of loosening bolts on the free vibration characteristics of the structure and the coupling phenomenon between different modes are discussed. The research in this paper is expected to provide references for the design of bolted composite flanged cylindrical shell structures and the monitoring of bolt connection defects.

Modelling of Multi-Storey Cross-Laminated Timber Buildings for Vibration Serviceability

In this study, the vibration serviceability of multi-storey timber buildings is addressed. The core of this study pertains to the preparation of a comprehensive finite element model to predict modal properties for an accurate vibration serviceability checking. To that end, findings obtained from studying three multi-storey timber buildings are summarized and discussed. Two of the buildings (of seven and eight storeys) consist entirely of cross-laminated timber (CLT), while the third is a five-storey hybrid CLT-concrete building. Thanks to the detailed finite element models and modal testing results, one has the capability to conduct sensitivity analyses, classical and Bayesian model updating, and uncertainty quantifications. With these methodologies, influential modelling parameters as well as the sources of modelling error were identified. This allowed for conclusions to be drawn about the in-plane shear stiffness of the constructed walls (whose higher value causes the natural frequencies to increase by up to 25%), the soil deformability (which may cause the natural frequencies to drop by up to 20%), and the perpendicular-to-the-grain deformation of floor slabs (which may lead to an overestimation of a fundamental frequency by up to 8%).

Deep learning-based vibration stress and fatigue-life prediction of a battery-pack system

The primary concerns of the automotive industry are structural integrity and battery-pack system (BPS) reliability. To ascertain the appropriate thickness of critical BPS components (e.g., the long bracket, crossbeam, and bottom shell), engineers are required to perform several simulations of finite element (FE) analysis. This procedure is laborious and requires a significant amount of time. This study introduces a very effective approach for predicting vibration-induced stress and fatigue life, intending to enhance dependability in the design process. Firstly, a three-layer lithium battery model is utilized to investigate the impact of vibration on the maximal Mises stress at various states of charge. This information is used to model the BPS, including the batteries. The nonlinear FE model of the BPS is validated using the modal test results. Secondly, a sensitivity analysis is performed to ascertain the impact of component thickness on the maximum Mises stress. For vibration simulations, multiple design variables are selected to collect data. Next, the nonlinear relationship between inputs (thicknesses of critical components) and outputs (maximum Mises stress and minimum fatigue life) is described using a deep learning (DL) modeling framework with forward and backward propagation. Finally, the accuracy of the DL model is assessed by measuring error functions and comparing its performance to six commonly employed methods. Furthermore, the inclusion of Gaussian noise is employed to assess the model’s robustness and ability to generalize. Additionally, the establishment of fatigue-life and stress boundaries serves to offer designers valuable insights. The results indicate that the proposed method for predicting vibration stress and fatigue life is highly efficient and cost-effective, making it useful for the design of a robust and reliable BPS.

Online Monitoring Dynamic Characteristics in Thin-Walled Structure Milling: A Physics-Constrained Bayesian Updating Approach

Accurate estimation of modal parameters of thin-walled structures during the milling process is crucial since it determines the accuracy of deformation and vibration prediction and then the feasibility of selected machining parameters. However, time-varying dynamic characteristic due to material removal brings a great challenge in the pursuit. This article presents an online monitoring strategy for the estimation of modal parameters of thin-walled structures with measured cutting forces and single acceleration signal. The detailed physical constraints are presented, and the analytical form of the modal shape of thin-wall structures is derived. A Bayesian filter framework with slack variables is established for updating the modal parameters by simultaneously considering the physical constraints and the measured signals. Validation experiments are conducted on two kinds of thin-walled structures with different structures. The results of the proposed method are compared with the results of the standard modal test at certain stages. It indicates that the proposed approach is effective for accurately online monitoring of the spatiotemporally varying modal parameters in milling of thin-walled structures.

Modal analysis of tracking photovoltaic support system

The tracking photovoltaic support system is a distinctive structure that adjusts its inclination to maximize energy yield and exhibits significant aeroelastic behavior, akin to long-span bridges and aircraft wings. Given the unique mechanical properties and aerodynamic effects of this system, wind loads play a crucial role in its design, as does a deep understanding of wind-induced dynamic effects. In this study, field instrumentation was used to assess the vibrational characteristics of a selected tracking photovoltaic support system. Using ANSYS software, a modal analysis and finite element model of the structure were developed and validated by comparing measured data with model predictions. Key findings are as follows. Dynamic characteristics of tracking photovoltaic support systems obtained through field modal testing at various inclinations, revealing three torsional modes within the 2.9–5.0 Hz frequency range, accompanied by relatively small modal damping ratios ranging from 1.07 % to 2.99 %. Additionally, we propose a finite element analysis method for modal analysis of tracking photovoltaic support systems, which yielded four torsional modes within the 2.8–7.0 Hz frequency range. The first three modes of this analysis closely align with field modal test results. The accuracy and applicability of the model were confirmed through a comparison of its predictions with the results of field modal testing on the tracking photovoltaic support system.

Validation of a railway rolling noise model on a system with slab track and resilient wheels

This study investigates rolling noise emissions using an analytical model of the Seattle Sound Transit Light Rail system developed using Train Noise Expert (TNE) software. Measurements of track frequency response, decay rate, rail and wheel roughness were used to determine model input parameters. Wheel modal test results were used to characterize the wheels. Wayside noise and track vibration measurements during revenue service train passbys were used to experimentally validate the model. The average difference between measured and predicted overall passby LAeq noise at a position immediately adjacent to the track was 0.1 dBA (average from four scenarios, i.e. two surface track sites with two train types). Inspection of the predicted versus measured noise spectra indicates the model does not exactly match the measured spectrum in every frequency band, however the correlation with overall spectrum shape is good in the frequency bands that contribute most to the overall A-weighted level. It is concluded that the model provides an accurate representation of the most relevant physical rolling noise factors and is reliable with resilient wheels and light rail vehicles on ballast and slab track.

Structural Integrity Assessment of Concrete Sleepers by Modal Test Technique.

Concrete sleepers used in railway engineering are subject to damage, such as cracks and breakage. Damaged concrete sleepers undergo changes to their material and structural properties, including response, mode shape, and natural frequency. Therefore, we have proposed modal testing in this study to quantitatively evaluate the structural integrity of concrete sleepers. The results of modal testing were compared with those of numerical analysis and visual inspection. In addition, an impact hammer test was conducted to evaluate the structural performance of damaged concrete sleepers. The results show that natural-frequency analysis using the modal-testing technique can usefully complement visual inspection for structural performance evaluation in the field.

Improving the Properties of Gray Cast Iron by Laser Surface Modification.

Laser surface modification is a widely used technology to improve the properties of functional surfaces. In this study, the properties of gray cast iron are modified by laser surface modification, and the influence of laser quenching on the properties of cast iron in terms of frictional vibration and noise, friction and wear, internal structure, residual stress, hardness, and corrosion resistance is investigated. The experimental results show that, after high-power laser quenching, the frictional vibrations and noise of most gray cast iron specimens are decreased, but the coefficients of friction against a bearing steel counterface are increased and more stable. The surface and sub-surface hardness of all laser-quenched cast iron specimens is significantly increased. The residual stresses on the surface of the cast iron specimens are significantly increased and changed from tensile to compressive residual stresses. Experimental modal testing results show that the modal damping ratios of the laser-treated specimens are increased significantly, although their modal frequencies are not significantly changed. In addition, through the metallographic observation, XRD (X-ray diffraction) analysis, and TEM (transmission electron microscopy) observation, it is found that the microstructures of the cast iron specimen after high-power laser modification become fine-grained, and the pearlite and ferrite in the matrix become fine martensite, which leads to the improvement of the dynamical, tribological, and chemical properties of cast iron after laser modification.

Structural safety assessment oriented modal experiments on Renyihe Bridge using vehicle excitations

High order modal parameters which are sensitive to local damages can be employed as useful structural health indicators for effective structural safety assessments of in-service long-span bridges. As a promising method to measure high order modal parameters of the full-scale bridge, the modal experiment using vehicle excitations draws the attention of engineering circle recently. However, this experimental method is currently subjected to a drawback which limits its usage, i.e., the weight and the location of the running vehicles adversely affect the accuracy of modal test results. To this end, a practical approach relying on finite-element (FE) model updating is proposed in this article to compensate for the deviation of the test results due to the adverse effects of running vehicles. The proposed method first uses the measurement change in the low order modal frequency to identify the equivalent vehicle weight on the bridge and updates the FE model, and then uses the updated FE model to predict the measurement change in the high order modal frequency and compensates for the measured high order modal frequency for use. Under the engineering background of Renyihe Bridge, a long-span concrete rigid-frame continuous highway bridge, the new approach to improve the accuracy of modal experiments using vehicle excitations has been presented. The results suggest that the bridge’s compensated 11th order modal frequencies measured on location for different cases are very close to each other, and they vary in the small range [3.80 Hz, 4.05 Hz]. The accuracies of these compensated modal experimental results are therefore validated by each other, and the method proposed for the improvement of the modal experiment using vehicle excitations based on FE model updating is thereby validated.

A Study On Flight Vibration Environmental Test of Unmanned Aerial Vehicle using Dual Electric Vibration Exciters

Analysis of dynamic characteristics and flight vibration test for unmanned aerial vehicles was studied by using dummy test body. The FEM model for dummy test body was supplemented by results of modal and random vibration test. The free end boundary condition to simulate flight environments was made by test setup using bungee cable. Prior to the flight vibration test using a dual electric vibration exciters, the test procedure to calculate quantitative vibration level was studied by using military specification. The actual test was successfully done by using the analysis and pretest results. From the analysis results, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test and to get the response of any point which could not be measured by the test. The results of this study will much contribute to the Test and Evaluation of unmanned aerial vehicles.

Dynamic performance of co-cured composite structure with sandwich damping film

In this paper, a research on theoretical analysis and finite element simulation of the damping sandwich composite plate with fixed support condition is carried out, and the dynamic characteristics of composite plates are explored by modal experiments. The vibration equilibrium equation of damping sandwich composite plate with fixed support condition is derived by combining first-order shear deformation theory, variational principle, and Hamilton principle. A set of modal basis functions satisfying the fixed support condition are established. The analytical solution is obtained via Galerkin weighted residual theory. The influence of structural parameters on the free vibration characteristics of the sandwich composite plates is investigated based on the mutual verification of theoretical calculation, numerical simulation, and modal test results. When the damping layer (0.2 mm) is located on the surface of the skin (2 mm), the first-order mode frequency and first-order loss factor are 196.66 Hz and 0.01, respectively. When the damping layer is in the neutral layer, the first-order mode frequency and first-order loss factor are 189.99 Hz and 0.14, respectively. Compared with the damping layer in the skin, the first-order mode frequency is reduced by 3.39%, while the first-order loss factor is 14 times higher. The results show that the damping performance of the structure is optimal when the damping layer is located in the neutral layer, and the structural stiffness is higher when the damping layer is close to the skin. The work provides theoretical guidance for the development and application of lightweight composite structures with large damping and high stiffness.