A Multilevel Hierarchical Parallel Algorithm for Large-Scale Finite Element Modal Analysis

The strict and high-standard requirements for the safety and stability ofmajor engineering systems make it a tough challenge for large-scale finite element modal analysis.At the same time,realizing the systematic analysis of the entire large structure of these engineering systems is extremely meaningful in practice.This article proposes a multilevel hierarchical parallel algorithm for large-scale finite element modal analysis to reduce the parallel computational efficiency loss when using heterogeneous multicore distributed storage computers in solving large-scale finite element modal analysis.Based on two-level partitioning and four-transformation strategies,the proposed algorithm not only improves the memory access rate through the sparsely distributed storage of a large amount of data but also reduces the solution time by reducing the scale of the generalized characteristic equation(GCEs).Moreover,a multilevel hierarchical parallelization approach is introduced during the computational procedure to enable the separation of the communication of inter-nodes,intra-nodes,heterogeneous core groups(HCGs),and inside HCGs through mapping computing tasks to various hardware layers.This method can efficiently achieve load balancing at different layers and significantly improve the communication rate through hierarchical communication.Therefore,it can enhance the efficiency of parallel computing of large-scale finite element modal analysis by fully exploiting the architecture characteristics of heterogeneous multicore clusters.Finally,typical numerical experiments were used to validate the correctness and efficiency of the proposedmethod.Then a parallel modal analysis example of the cross-river tunnel with over ten million degrees of freedom(DOFs)was performed,and ten-thousand core processors were applied to verify the feasibility of the algorithm.

Study of Axial Vibration of a Motor-Compressor System Using Operational Modal Analysis

A case study of excessive vibration on a motor-compressor system is presented in this paper.After barely two months of operation,the reciprocating compressor motor’s routine monitoring revealed excessive axial vibration amplitude.For this reason,the Operational Modal Analysis(OMA)was carried out in order to identify the pri-mary cause.According to the investigation,one of the harmonic components which was 18 times the motor’s running speed matched with a resonance frequency of 112 Hz.According to OMA study,the motor was vibrating in torsional motion because the compressor’s load had stimulated the entire motor-compressor unit at this reso-nance frequency.The analysis also demonstrates the bulging effect of the motor shaft’s axial vibration on the motor’s endplate.

An operational modal analysis method in frequency and spatial domain

A frequency and spatial domain decomposition method （FSDD） for operational modal analysis （OMA） is presented in this paper, which is an extension of the complex mode indicator function （CMIF） method for experimental modal analysis （EMA）. The theoretical background of the FSDD method is clarified, Singular value decomposition is adopted to separate the signal space from the noise space. Finally, an enhanced power spectrum density （PSD） is proposed to obtain more accurate modal parameters by curve fitting in the frequency domain. Moreover, a simulation case and an application case are used to validate this method.

Finite Element Modeling and Modal Analysis of Complicated Structure with Bolted Joints

A contact bolt model is proposed as a new modeling technique to investigate the complex structure with bolted joints for modal analysis and compared with the coupled bolt model, and the test results are given. Among these models, the coupled bolt model provides the best accurate responses compared with the experimental results. The contact bolt model shows the best effectiveness and usefulness in view of operational time. The bolt models proposed in this study are adopted for a dynamic characteristic analysis of a large diesel engine consisting of several parts which are connected by many bolts. The dynamic behavior of the entire engine structure was investigated by experiment. The coupled bolt model and the contact bolt model were applied to model the assembly of engine with high preload. The experimental results are in good agreement with the finite element method （FEM） results. Compared with the other models, the contact bolt model presented in this paper is more effective and useful in view of operational time and experience of analysts.

Modal analysis of coupled vibration of belt drive systems

The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm. The characteristic equation of the system is derived from the governing equation. Numerical results demenstrate the effects of the transport speed and the initial tension on natural frequencies.

CALCULATING RESPONSE SPECTRAL MOMENTS BY COMPLEX MODAL ANALYSIS

Response spectral moments are useful for system reliability analysis.Usually,spectral mo- ments are calculated by the frequency domain method.Based on the time domain modal analysis of random vibrations,the authors present a new method for calculating response spectral moments through response correlation functions.The method can be applied to both classical and non-classical damping cases and to three kinds of random excitations,i.e.,white noise,band-limited white noise, and filtered white noise.

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical structure and neglect feedback action of joint controller. In order to study the effects of joint controller on the modal analysis of rotational flexible manipulator, a closed-loop analytical modal analysis method is proposed. Firstly, two exact boundary constraints, namely servo feedback constraint and bending moment constraint, are derived to solve the vibration partial differential equation. It is found that the stiffness and damping gains of joint controller are both included in the boundary conditions, which lead to an unconventional secular term. Secondly, analytical algorithm based on Ritz approach is developed by using Laplace transform and complex modal approach to obtain the natural frequencies and mode shapes. And then, the numerical simulations are performed and the computational results show that joint controller has pronounced influence on the modal parameters： joint controller stiffness reduces the natural frequency, while joint controller damping makes the shape phase non-zero. Furthermore, the validity of the presented conclusion is confirmed through experimental studies. These findings are expected to improve the performance of dynamics simulation systems and model-based controllers.

Modal Analysis of Thread off Failure of Oil Round Thread Casing Connection

The dynamic modal model analysis of the oil casing connection is done by finite element method (FEM), and the first nature frequency, the second nature frequency, the vibration mode shape and the time domain of the node displacement and the element stress variation in the thread connection are gotten. The Von.Mises stresses of the connection in the static and dynamic state are also studied. The results of calculation and analysis show: (1) because the maximum of static stress is at the coupling thread end of connection, the connection begins to thread off at the coupling thread end, which is in accord with the results of the thread off experiment in laboratory; (2) because the first nature frequency is very high, the probability of casing connection to be damaged from vibration is little; (3) the shock dynamic load makes casing connection begin to thread off at the tube thread end.

OPERATIONAL MODAL ANALYSIS SCHEMES USING CORRELATION TECHNIQUE

For some large-scale engineering structures in operating conditions, modal param- eters estimation must base itself on response-only data. This problem has received a considerable amount of attention in the past few years. It is well known that the cross-correlation function between the measured responses is a sum of complex exponential functions of the same form as the impulse response function of the original system. So this paper presents a time-domain operating modal identifcation global scheme and a frequency-domain scheme from output-only by cou- pling the cross-correlation function with conventional modal parameter estimation. The outlined techniques are applied to an airplane model to estimate modal parameters from response-only data.

Vibration Modal Analysis of Compressor Blade based on ANSYS

Compressor is an important part of aero engine. In the environment of high temperature and high pressure,compressor blade will suffer from several physical and chemical processes,such as centrifugal force,aerodynamic force vibration and oxidation. These processes will lead compressor blade to fatigue fracture,and at the same time,make negative effects on the engine’ s overall performance. Based on the software ANSYS15. 0,we made strength analysis and modal analysis of compressor blade in this paper. As a result,we got its natural frequencies,relevant modal parameters and vibration mode cloud pictures. After analyzing the influence that centrifugal force made on modal parameters,we predicted the expected damage of the blade. Eventually the analysis results will provide the basis for overall performance evaluation,structural crack detection,fatigue life estimation and strength calculation of aircraft engine compressor.

Modal Analysis of Drilling Machine Derrick

In this paper, the finite element analysis software (ANSYS) is applied to the modal analysis of a ZJ30/1700CZ's drilling machine derrick under a natural condition and a loaded condition, respectively. The preceding nine step natural frequencies and the corresponding mode shapes of the derrick are calculated. By means of the comparison of the natural frequency of the derrick with the design work frequency of the drilling machine and the analysis of the step mode shape of the derrick, the drilling machine derrick structure design is proved to be correct.

MODAL ANALYSIS OF A CHASSIS FRAME OF A HEAVY LECTRA HAUL

The chassis frame of a heavy lectra haul is analysed by both modal experiment method and finite element method (FEM ) . The first ten order modal parameters of the chassis frame have been obtained satisfactorily. These parameters have important reference value in designing the chassis frame properly and provide a necessary basis for the fault diagnostics of the truck.

Comparison Between Modal Analysis and Impedance-based Methods for Analysing Stability of Unbalanced Microgrids with Grid-forming Electronic Power Converters

Stability in unbalanced power systems has deserved little attention in the literature.Given the importance of this scenario in distribution systems with distributed generation,this paper revisits modal analysis techniques for stability studies in power systems,and explains how to tackle unbalanced power systems with voltage-dependent loads.The procedure is described in detail and applied to a low-voltage(LV)simple case study with two grid-forming electronic power converters and unbalanced loads.Results are then compared with those obtained with the popular impedance-based method.While the latter is easier to implement using simulation or field data,the former requires complete information of the system,but gives a better insight into the problem.Since both methods are based on a small-signal approximation of the system,they provide similar results,but they discern different information.A larger second case study based on an LV CIGRE distribution system is also analysed.Results are obtained using a detailed Simulink model of the microgrids with electronic power converters.

Noise robustness of an operational modal-based structural damage-detection scheme using impact-synchronous modal analysis

Data-driven damage-detection schemes are usually unsupervised machine-learning models in practice,as these do not require any training.Vibration-based features are commonly used in these schemes but often require several other parameters to accurately correlate with damage,as they may not globally represent the model,making them less sensitive to damage.Modal data,such as frequency response functions(FRFs)and principal component analysis(PCA)reduced FRFs(PCA-FRFs),inherits the dynamic characteristics of the structure,and it changes when damage occurs,thus showing sensitivity to damage.However,noise from the environment or external sources such as wind,operating machines,or the in-service system itself,can reduce the modal data's sensitivity to damage if not handled properly,which affects damage-detection accuracy.This study proposes a noise-robust operational modal-based structural damage-detection scheme that uses impact-synchronous modal analysis(ISMA)to generate clean,static-like FRFs for damage diagnosis.ISMA allows modal data collection without requiring shutdown conditions,and its denoising feature aids in generating clean,static-like FRFs for damage diagnosis.Our results showed that the FRFs obtained through ISMA under noise conditions have frequency response assurance criterion(FRAC)and cross signature assurance criterion(CSAC)scores greater than 0.9 when compared with FRFs obtained through experimental modal analysis(EMA)under static conditions;this validates the denoising feature of ISMA.When the denoised FRFs are reduced to PCA-FRFs and used in an unsupervised learning-based damage-detection scheme,zero false alarms occur.

Modal Analysis and Vortex Trajectory Description for Tip Leakage Flow of a Transonic Turbine Cascade

Tip leakage vortex(TLV),which develops from the clearance between the turbine blade and casing,has been studied for decades.Nevertheless,some associated phenomena,such as its unsteady behaviors,are still not well understood.In the present work,an unsteady simulation of a transonic turbine cascade was conducted by using a validated unsteady Reynolds averaged Navier-Stokes(URANS)technique with the k-ωshear stress transport(SST)turbulence model.Typical three-dimensional vortical topology in the tip region of this transonic turbine blade was depicted based on the vortex and shock wave identification.Afterwards,quantitative descriptions of TLV transient parameters,including core position,radius,intensity,wandering motion amplitude and their statistical analysis were also provided via an ellipse fitting method.Combined with the turbulent parameters in the tip region,it is recognized that the breakdown of TLV does not occur upstream of the trailing edge,and the TLV wandering,especially the spanwise motion is a dominant unsteady feature as migrating downstream.To mathematically extract underlying flow features of tip leakage flow(TLF),two data-driven modal analysis techniques,namely proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD),are presented to complement one another to reveal underlying flow feature.Observation of modes distribution allowed qualitative identification of shockwaves,vortical cluster and corresponding transient interaction.Results of POD show that the dominant unsteady structures in the tip region exhibit various morphology with moving downstream.In the front part near the leading edge,the oscillation of separation bubble and bifurcation of passage vortex paly a dominant role;while in the middle part of the tip region,the corresponding factors are the wandering of TLV and unsteady interaction between shock waves and TLF/TLV.In the vicinity of the trailing edge,the instability induced by the mixing of large-scale vortices serves as the main factor in the context of flow unsteadiness.Both the POD and DMD methods can decompose the dominant frequency of TLV evolution and its harmonic frequencies;however,the DMD method presents a superiority in segregating the high-frequency components and their corresponding unsteady structures.

AN IMPROVED MODAL ANALYSIS FOR THREE-DIMENSIONAL PROBLEMS USING FACE-BASED SMOOTHED FINITE ELEMENT METHOD

In this work, we further extended the face-based smoothed finite element method （FS-FEM） for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smoothed Calerkin weak form which employs smoothed strains obtained using the gradient smoothing operation on face-based smoothing domains. This strain smoothing operation can provide softening effect to the system stiffness and make the FSFEM provide more accurate eigenfrequency prediction than the FEM does. Numerical studies have verified this attractive property of FS-FEM as well as its ability and effectiveness on providing reliable eigenfrequency and eigenmode prediction in practical engineering application.

Modal analysis of AC quadrupole magnet system for CSNS/RCS

The quadrupole magnet of the China Spallation Neutron Source （CSNS） Rapid-cycling Synchrotron （RCS） is operated at a 25 Hz sinusoidal alternating current which causes severe vibration. The vibration will influence the long-term safety and reliable operation of the quadrupole magnet. By taking the quadrupole magnet and girder as specific model system, a method for analyzing and studying the dynamic characteristic of the system is put forward by combining theoretical calculation with experimental testing. The theoretical modal analysis results coincide with the experimental testing results. It shows that the dynamic characteristic parameters of the structure can be obtained by modal analysis which will provide a theoretical basis for the further study and the magnet girder optimal design of CSNS/PtCS.

Research on vibration reduction test and frame modal analysis of rice transplanter based on vibration evaluation

The chassis of rice transplanter tends to vibrate severely in the severe working environment,causing a severe effect on the operational performance and driving comfort.In order to avoid this situation,this paper constructs a vibration evaluation system of the rice transplanter and carries out experimental analysis.According to the optimal acceleration sensor placement scheme,a test platform system was designed.Taking the high-speed transplanter chassis as the research object,this study carried out the experiments modal analysis and optimization on the chassis.The three-dimensional model of the transplanting machine chassis established by SolidWorks was imported into ANSYS Workbench for finite element modal simulation analysis.Comparing the two modal analyses,it is found that the results data of the two analysis methods were very close.After optimization,the length x1,the section width x2 and the thickness of the hollow beam x3 of the main load-bearing beam of the frame were as follows:x1=1641.5 mm,x2=26.7 mm,x3=5 mm,respectively.The maximum overshoot of the low-level system was reduced by 28.57%.It has been verified that the vibration of the whole machine has been effectively reduced.

Seismic bearing capacity of strip footing on partially saturated soil using modal response analysis

The present study proposes a novel and simplified methodology to assess the seismic bearing capacity(SBC) of a shallow strip footing by incorporating strength non-linearity arising due to partial saturation of a soil matrix. Furthermore, developed methodology incorporates the modal response analysis of soil layers to assess SBC. A constant matric suction distribution profile has been considered throughout the depth of the soil. The Van Genuchten equation and corresponding fitting parameters have been considered to quantify matric suction in the analysis. SBC has been obtained for three different geomaterials;viz. sand, fly ash and clay, based on their predominant grain size and diverse soil water characteristics curve(SWCC) attributes. Variation of SBC with different modes of vibration and damping ratio are reported for ranges of matric suction pertinent to the geomaterials considered in the study. The relative significance of matric suction on SBC has been reported for suction values within the transition zone of each geomaterial. It is observed that the SBC of sand is drastically reduced, with matric suction reaching beyond the residual suction value. The SBC of fly ash remains constant beyond the residual suction value, whereas the SBC of clay shows an increasing trend toward the practical range of matric suction values.

An iterative approach for modal analysis of solid rocket motor incorporating frequency dependent modulus

The modulus of viscoelastic materials varies with excitation frequency.However,during modal analysis of frequency dependent materials,a material evaluation frequency is necessary because stiffness cannot be modified during eigenfrequency procedure.As a result,only those vibration modes are accurate,of which eigenfrequency is close to the material evaluation frequency.In order to obtain vibration modes of solid rocket motor(SRM) using material modulus based on frequency which is the same as the eigenfrequency,an iterative approach was proposed.Results of the iterative technique show that frequency modes obtained from the method are in complete agreement with the eigenfrequency and material evaluation frequency.