Vibration Model Research Articles

A Novel Physics-Informed Hybrid Modeling Method for Dynamic Vibration Response Simulation of Rotor–Bearing System

For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples at the cost of computational complexity. Moreover, single data-driven modeling methods may be more accurate, employing larger numbers of measured samples and reducing computational complexity, but these methods are affected by the insufficient and imbalanced samples in engineering applications. This paper proposes a physics-informed hybrid modeling method for simulating the dynamic responses of rotor–bearing systems to vibration under different rotor speeds and bearing health statuses. Firstly, a three-dimensional model of a rolling bearing and its supporting force are introduced, and a physics-based dynamic vibration model that couples flexible rotors and rigid bearings is constructed using multibody dynamics simulation. Secondly, combining the simulation vibration data obtained using the physics-based model with measured vibration data, algorithms are designed to learn vibration generation and data mapping networks in series connection to form a physics-informed hybrid model, which can quickly and accurately output the vibration responses of a rotor–bearing system. Finally, a case study on the single-span rotor platform is provided. By comparing the signal output by the proposed physics-informed hybrid modeling method with the measured signal in the time and frequency domains, the effectiveness of proposed method under both constant- and variable-speed operating conditions are illustrated.

Methods of periodically non-stationary random processes for vibrations monitoring of rolling bearing with damaged outer race

The vibrations of a rolling bearing with a damaged outer race are analyzed using a method based on periodically non-stationary random processes (PNRPs). PNRPs can be considered as a particular case of poly-periodically non-stationary random processes (PPNRs), which describe the interactions of vibration stochastic rhythms with different periods that are determined based on the characteristic bearing frequencies. A PNRP model for these vibrations is verified using methods for discovering the first- and second-order periodicities. By applying the least squares technique, it is shown that the mean function and variance are time periodic functions, and their basic frequencies are determined. This enables us to calculate the amplitude spectra for the deterministic oscillations and the time changes in the power for the stochastic part. It is shown that the dependencies of the Fourier coefficients for the covariance function on lag have the forms of slowly damped groups. Vibration covariance structures are compared for different fault widths; it is found that high-frequency modulations of the PNRP carrier modulations are narrow-band, and Rice representations are used to model them. The PRNP model of vibrations is then represented in the form of a superposition of the stationary high-frequency components that are jointly periodically non-stationary. The mutual periodical non-stationarity of these components results in variance time changes. Band-pass filtering of the vibration signal is conducted, and the influence of the filter bandwidth on the number and values of the amplitude of the variance harmonics is analyzed. It is shown that PNRP methods for time series processing enable fault detection in cases where the squared envelope and other familiar techniques are ineffective.

On vibration response of heavy hammer self-falling pile driver in uneven unsaturated soil – Experimental and analytical study

The goal of this study is to determine the scope of the impact of pile driving construction vibration on surrounding residential houses and buildings during engineering construction. Firstly, introducing the gradient factor of unsaturated soil, proposed a model for non-uniform variation of pores with depth. Secondly, Consider the coupling between the model and soil skeleton density, relative fluid density, relative gas density, pore fluid, pore gas, and shear modulus. Finally, coupling the pile with the driving depth and propose a pile driving vibration model for non-uniform unsaturated soil. Proposed a new method for solving coupled equations using Hankel transform. Moreover, the analytical solution of this study was validated through on-site experiments. Results show that, deeper the pile is inserted into the soil, the greater the peak vertical velocity at different measuring points. The vibration of the pile is strongest at the last 1 m into the soil. When close to the vibration source, the amplitude values in the three directions are: maximum in vertical direction, followed by horizontal and radial direction, and minimum in horizontal and tangential direction. When pile driving construction is carried out outside the range of vibration influence, the seismic damage generated is equivalent to the seismic intensity below V (excluding V). The rate amplitude calculated by the model established in this study is closer to the measured value. Therefore, using the model established in this work can more accurately evaluate the impact of pile driving vibration during the construction process of highways and high-speed railways.

Traveling-wave vibration modelling for thin-walled gear with ring damper

The harmful resonances of the thin-walled gears for aviation high-speed gear transmission systems, especially the traveling-wave vibration (TWV), frequently occur under complex excitations. The ring damper is an excellent and widely used damping technology for TWV reduction. However, lacking the TWV predictive method, there are few theoretical bases for the damper optimization. In this paper, firstly, assuming that the external input energy, the gear damping energy dissipation, and the ring damper energy dissipation form an energy balance, a novel model of TWV response based on energy dissipation (TRED) is proposed for the thin-walled gear with ring damper. Secondly, to solve the complex nonlinear TRED model, using the Rayleigh damping theory, the discrete expression of TRED model is innovatively given instead of traditional equation solving methods. Considering that the TRED model is established based on the vibrational displacement, a method for the conversion of gear vibration strain and displacement is given under different TWV directions and vibration strain measurements, and the solving method is proposed for the TRED model based on the above established theories. Finally, to validate the TRED model and its solutions, the speed-up experiments are conducted, and the experimental results are compared with the TRED prediction. Results show that the experimental and theoretical results are consistent, and the maximum predictive error is 8.7 %, which validates the feasibility of the proposed theories and methods.

On the nonlinear dynamics of a multi-scale flexoelectric cylindrical shell

The flexoelectric property shows the relationship between the strain gradient and the electric polarization and has a significant effect on static and dynamic responses of structures at small scales such as micro and nano. Nowadays, experimental studies for intelligent/composite ultra-small mechanical systems are complex, challenging, and in most cases still impossible, especially for nonlinear dynamic behavior analysis. For the first time, this study presents an advanced and complex generalized model for the nonlinear vibrations of a piezo-flexoelectric mechanical system based on a cylindrical shell. It should be noted, that the formulated boundary value problem is generalized, well-posed, and can be applied to the system at micro and nano scales. Hamilton's variational principle as well as assumptions of the first-order shear deformation theory (FSDT) and reformulated flexoelectric theory were used to derive equations of motion of the multi-scale intelligent shell system. To introduce nonlinear effects, von-Kármán strains are applied. Appropriate classical and non-classical mechanical/electric boundary conditions as well as higher-order forces and moments are determined to fully close the formulated problem. The Galerkin method combined with the GDQM, supported by the displacement control strategy and the weighted residual method, have been used to discretize and solve the nonlinear governing equations of the shell with different boundary conditions. Good convergence between the current results and the results from previous studies for simpler cases of the shell was proved. Furthermore, the results showed that geometric ratios of the structure, gradation of material properties, thickness of the flexoelectric layers, and the size effect parameter significantly influence the nonlinear frequency of the structure under the direct flexoelectric effect.

Research on Transformer Omnidirectional Partial Discharge Ultrasound Sensing Method Combining F-P Cavity and FBG.

To achieve omnidirectional sensitive detection of partial discharge (PD) in transformers and to avoid missing PD signals, a fiber optic omnidirectional sensing method for PD in transformers combined with the fiber Bragg grating (FBG) and Fabry-Perot (F-P) cavity is proposed. The fiber optic omnidirectional sensor for PD as a triangular prism was developed. The hollow structure of the probe was used to insert a single-mode fiber to form an F-P cavity. In addition, the three sides of the probe were used to form a diaphragm-type FBG sensing structure. The ultrasound sensitization diaphragm was designed based on the frequency characteristics of PD in the transformer and the vibration model of the diaphragm in the liquid environment. The fiber optic sensing system for PD was built and the performance test was conducted. The results show that the resonant frequency of the FBG acoustic diaphragm is around 20 kHz and that of the F-P cavity acoustic diaphragm is 94 kHz. The sensitivity of the developed fiber optic sensor is higher than that of the piezoelectric transducer (PZT). The lower limit of PD detection is 68.72 pC for the FBG sensing part and 47.97 pC for the F-P cavity sensing part. The directional testing of the sensor and its testing within a transformer simulation model indicate that the proposed sensor achieves higher detection sensitivity of PD in all directions. The omnidirectional partial discharge ultrasound sensing method proposed in this paper is expected to reduce the missed detection rate of PD.

Exact Solution of the Raman Response Function of Chalcogenide Fiber and Its Influence on the Mid-Infrared Supercontinuum

We fabricated a core-cladding Ge–Sb–Se glass fiber with a Ge12.5Sb15Se72.5 core and Ge15Sb10Se75 cladding, achieved a supercontinuum spectrum spanning from 2 μm to 9 μm by pumping the Ge–Sb–Se fiber with a core diameter of 11 μm using a femtosecond laser pump at 3.8 μm, and numerically simulated the supercontinuum generation using the generalized nonlinear Schrödinger equation. In particular, we investigate the effect of the different Raman response functions that were calculated using the traditional single Lorentzian model and a multiple vibrational mode model on the evolution of the supercontinuum by comparing the supercontinua obtained from simulation and experimental results. We demonstrate that the Raman response function generated by the multiple vibrational mode model captures the actual response behavior of the material, and the supercontinuum generated using this model has more accuracy. To the best of our knowledge, this is the first reported study on supercontinuum generation in Ge–Sb–Se fiber utilizing a Raman response function calculated using the multiple vibrational mode model. This significant advancement enables more accurate simulation of supercontinuum generation in fibers with a multi-peaked structured Raman gain spectrum and holds great potential for optimizing the performance of various mid-infrared supercontinuum sources.

MATHEMATICAL MODEL OF TORSIONAL OSCILLATIONS DRILLING COLUMN WITH FLEXIBLE COUPLING IN COMPOSITION

A generalized mathematical model of the torsional vibrations of the drilling columnis proposed, the composition of which includes support-centering elements, an elastic coupling, and a screw drilling motor. The portable movement of the drilling columnis taken to be a steady rotational movement with a given angular velocity and the relative movement is taken to be oscillations disturbed by the bit. The model allows you to determine the relative and transfer components of the angle of rotation, torque and tangential stress in the cross sections of the column.

Actual measurement on vibration propagation of embankment and cut road

Institute of Noise Control Engineering of Japan (INCE/J) proposed a prediction model of road traffic vibration "INCE/J RTV Model 2003". The scope of this prediction model is only for flat roads. Prediction of Road Traffic Vibration subcommittee is trying to expand the scope of application. This paper discussed expand the scope for embankment and cut road with actual measurement. Regarding whether the prediction formula for flat roads can be applied to embankment and cutting roads, It is compared with the actual measurement result of a runnning truck on the cutting road. It also describes inpact tests of ground vibration propagation on cut roads.

Stability Analysis of Graphite Circumferential Seal Considering Perturbation

With the rapid development of aviation engine technology, the performance requirements for sealing systems under harsh operating conditions are also increasing. This article focuses on the graphite circumferential sealing system of an aircraft engine, and analyzes the structure and stress of the graphite circumferential sealing system under the influence of sealing runway vortex, sealing gas, and structural and operating parameters. The graphite circumferential sealing system is simplified as a radial vibration model of spring damping mass, and the dynamic equation of the graphite circumferential sealing system under coupled disturbance is established. Based on the theory of motion stability, the state space equation and equilibrium point of the sealing system under decoupled disturbances were solved, and the displacement response, axis trajectory, and other dynamic behaviors of the sealing ring and sealing runway were obtained through numerical simulation. The operation state and stability law of the graphite circumferential sealing system under disturbances were analyzed. The research results provide guidance for the optimization design of graphite circumferential sealing systems. Keywords: graphite circumferential seal, perturbation, dynamic characteristics, seal

A coupled vibration model of double-rod in cross flow for grid-to-rod fretting wear analysis

In Pressurized Water Reactors, most of the failed fuel rods are often observed at the periphery of the fuel assembly, especially near the core baffle. The rod vibration-induced fretting wear is a significant failure mechanism strongly correlated with the coolant and support conditions. This paper presents a coupled vibration model of double-rod to predict the grid-to-rod fretting (GTRF) wear. A motion-dependent fluid force model is used to simulate the coolant cross flow, the gap constraints with asymmetric stiffness between spring and dimple on the vibration form, and the fretting wear are discussed. The results show the effect of the coupled vibration on the deterioration of wear, providing a sound theoretical explanation of some failure phenomena observed in the previous experiment. Exploratively, we analyze the impact of the baffle jet on the GTRF wear, which indicates that the high-velocity cross-flow will significantly affect the vibration forms while sharply changing the wear behavior.

Theoretical analysis for free vibration of submerged conical motor stator

The conical rim-driven motor stator is a structure with variable thickness and non-standard boundaries, which can be treated as an orthotropic conical shell. To prevent resonance and reduce electromagnetic noise, a modal analysis of the stator is necessary. This paper presents an analytical model for the free vibration of the conical stator in both onshore and underwater environments. Due to the relatively large thickness of the motor stator, the first-order shear deformation theory (FSDT) is employed. The fluid loading is calculated by discretizing the conical shell into a series of narrow cylindrical shells featuring diverse radii and thickness. The resulting equations are solved employing the transfer matrix method (TMM), which is capable of different types of boundary conditions (BCs). The convergence and accuracy of the proposed method are validated through a comparative analysis involving numerical simulations and outcomes derived from the thin shell theory. The importance of considering shear deformation and rotatory inertia in determining the natural frequency of motor stators is demonstrated. Finally, the impact of fluid loading on the vibration behavior of stators with various geometric parameters and boundary conditions are investigated and discussed. The proposed model presents a precise and convenient approach for analyzing the free vibration of submerged conical motor stators, and can be extended to conventional cylindrical motor stators through appropriate degradation procedures.

Variation characteristics of key dynamic measurement signals of anchor bolts with different anchorage qualities under pull-out loads

Pull-out load and the cement-sand ratio (CSR) can affect the non-destructive testing (NDT) results of anchor bolts. Therefore, in this article, NDT experiments were conducted on both fully and defectively grouted anchor bolts, and variation patterns of key dynamic testing signal parameters were analyzed. A longitudinal vibration model of defectively grouted anchor bolts considering dynamic and static damping was proposed, and simulated NDT of anchor bolts with varying qualities. The results indicated that grouting defects resulted in an increase in wave velocity, along with a decrease in the fundamental frequency and dynamic stiffness of anchor bolts. When grouting defects and pull-out load acted concurrently, the fundamental frequency, and dynamic stiffness of the defectively grouted anchor bolts were consistently smaller than those of fully grouted ones during the initial loading phase. With pull-out load increasing, wave velocity decreased first, then increased; fundamental frequency increased, followed by a decrease; dynamic stiffness rose. When the CSR of defectively grouted anchor bolts was reduced, wave velocity decreased, fundamental frequency increased slightly, and a substantial increase in dynamic stiffness was observed. Pull-out loads were more sensitive to anchor bolt key dynamic signals than defects and CSR. Simulated validation demonstrated the reliability of the proposed theory.

Sparse optimal control of Timoshenko's beam using a locking‐free finite element approximation

AbstractThis paper addresses the optimal control problem with sparse controls of a Timoshenko beam, its numerical approximation using the finite element method, and the numerical solution via nonsmooth methods. Incorporating sparsity‐promoting terms in the cost function is practically useful for beam vibration models and results in the localization of the control action that facilitates the placement of actuators or control devices. We consider two types of sparsity‐inducing penalizers: the ‐norm and the ‐penalizer, which measures function support. We analyze discretized problems utilizing linear finite elements with a locking‐free scheme to approximate the states and adjoint states. We confirm that this approximation has the looking‐free property required to achieve a linear convergence linear order of approximation for control case and depending on the set of switching points in the controls. This is similar to the purely ‐norm penalized optimal control, where the order of approximation is independent of the thickness of the beam.

Tunable conversion of electromagnetically induced transparency to electromagnetically induced absorption based on vanadium dioxide metastructure

Metastructure analogs of electromagnetically induced transparency (EIT) show great potential in telecommunications, light storage, and slow light, owing to the unremitting research of our predecessors. Research on electromagnetically induced absorption (EIA) has also been accelerating in recent years. However, few researchers have studied the switch between the EIT and EIA. This paper proposes a tunable conversion of EIT to EIA in the terahertz (THz) band, by employing vanadium dioxide (VO2), a phase change material. With the incidence of the electromagnetic wave, the split-ring resonator is coupled with a double U-shaped resonator when VO2 is set in the dielectric state, and destructive interference appears, resulting in EIT. The cross-shaped resonator works when VO2 functions in the metallic state, which allows coherence enhancement, and the EIA phenomenon can be observed. Moreover, the value of the maximum transmission coefficient reaches 0.837 at 0.570 THz with maximum group delay reaching up to 4.45 ps through calculation, proving the slow light effect of EIT. In the metallic state of VO2, the maximum absorption value arrives at 0.826 at 0.571 THz. The consistency of the simulation results is further confirmed by verifying the dual spring vibration model.

Implementation and analysis of viscoelastic damping in a 2D + 1D model of railway track vibrations

One of the most important technological challenges in the railway context nowadays is reducing the noise produced by the interaction between the train wheels and the track surface, that is the rolling noise. Introducing viscoelastic damping in the railway structure is one method to mitigate this rolling noise. In the paper, we investigate the impact of damping in the vibrational response of railway tracks using different viscoelastic models and parameters available in the literature. For this purpose, the main focus here is on developing an advanced numerical model in which viscoelastic models representing the rail foundation and/or pad are implemented in the framework of the Semi-Analytical Finite Element (SAFE) method. Linear or nonlinear viscoelastic models are considered, compared and effectively implemented for accelerance computation. The obtained numerical strategy leads to affordable and accurate predictions on dynamic features of the railway structure compared to classical methods.

On-line targeted metabolomics for real-time monitoring of relevant compounds in fermentation processes.

Fermentation monitoring is a powerful tool for bioprocess development and optimization. On-line metabolomics is a technology that is starting to gain attention as a bioprocess monitoring tool, allowing the direct measurement of many compounds in the fermentation broth at a very high time resolution. In this work, targeted on-line metabolomics was used to monitor 40 metabolites of interest during three Escherichia coli succinate production fermentation experiments every 5 min with a triple quadrupole mass spectrometer. This allowed capturing high-time resolution biological data that can provide critical information for process optimization. For nine of these metabolites, simple univariate regression models were used to model compound concentration from their on-line mass spectrometry peak area. These on-line metabolomics univariate models performed comparably to vibrational spectroscopy multivariate partial least squares regressions models reported in the literature, which typically are much more complex and time consuming to build. In conclusion, this work shows how on-line metabolomics can be used to directly monitor many bioprocess compounds of interest and obtain rich biological and bioprocess data.

Robust predictive compensation control for lateral magnetorheological semi-active suspension of high-speed trains with time delay

ABSTRACT Aiming at reducing the effect of time delay on the control performance of magnetorheological (MR) damper semi-active suspension, a control strategy with strong robustness to time delay is investigated in this study, including the force controller of MR damper, the robust controller and the predictive compensator. The force controller of MR damper is built based on the hyperbolic tangent function; the robust controller is built based on the simplified model of car body lateral vibration and is designed by μ-synthesis method considering the effect of time delay; then the Smith predictive model and the lateral velocity predictor are designed, which form the predictive compensator of semi-active controller to reduce the effect of time delay. To validate the effectiveness of the proposed control strategy, several conventional semi-active controllers are designed as comparative objects. The simulation results show that the proposed semi-active control strategy can maintain good performance when time delay is in the range of 0–100 ms and has better robustness to time delay compared with the conventional control strategy.

Vibration and bandgap characteristics analysis of multiple beams with arbitrary connection angles

Multi-coupled beam structures can be encountered in a wide range of engineering disciplines. Due to the possible periodicity of structures, it is important to investigate their vibration and bandgap characteristics. In this study, an accurate wave-based analytical model for the in-plane vibration of a multi-coupled beam structure with arbitrary coupling angles is developed. The reflection and transmission matrices corresponding to the incident waves arriving at the angular junctions from different directions are derived. By combining these reflection and transmission matrices, the free and forced vibrations of the multi-coupled angle beam structures can be analyzed systematically and concisely. The theoretical analysis results are in good agreement with those calculated from the FEM analysis results, which verifies the accuracy of the current method. Moreover, the analytical expression of the bandgap characteristics of infinite multi-coupled beam structures is formulated. The bandgap characteristics results of the infinite multi-coupled beam structures coincide well with the frequency response function (FRF) of the finite multi-coupled beam structures, which verifies the correctness of the analytical expression of bandgap analysis. Further results show that a low-frequency and wide bandgap can be obtained by choosing the appropriate lattice constants and junction angles, which has positive significance for the efficient design and vibration attenuation of multi-coupled beam structures in practical engineering.

The impacts of CO2 mineralization reaction on the physicochemical characteristics of fly ash: A study under different reaction conditions of the water-to-solid ratio and the pressure of CO2

Utilizing fly ash (FA) directly to mineralize CO2 and injecting carbon sequestration products into goafs of coal mines is a novel and promising technology. The impact mechanisms of CO2 direct mineralization reactions on the characteristics of key groups, physical phases, surface micromorphology, particle size and pore structure of FA are discussed systematically in detail. The focus is imposed on the impacts of different reaction conditions (water-to-solid ratios and pressures of CO2). Based on the FT-IR, XRD and ESEM-EDS analysis, CO2 is transformed into carbonates of five vibrational models after mineralization and largely sequestered as calcite by portlandite, which forms a passivated layer on the FA surface. The particle size of carbonated FA particles gets smaller and less uniform, and the variation laws of the particle size at full scale are analyzed by particle size intervals. The variation process of the pore can be divided into the dissolution of FA for pore expansion, the low degree of CO2 mineralization reaction for further expanding the pore and the high reaction degree for pore shrinkage. This paper provides theoretical bases for improving the direct CO2 sequestration capacity and research directions for the subsequent application properties of carbon sequestration products.