Vibration Response Analysis Research Articles

Uncertainty Quantification and Sensitivity Analysis for the Self-Excited Vibration of a Spline-Shafting System

Abstract Self-excited vibrations can occur in the spline-shafting system due to internal friction of the tooth surface. However, due to manufacturing errors, design tolerances, and time-varying factors, the parameters that induce self-excited vibrations are always uncertain. This study provides new insights into the uncertainty quantification and sensitivity analysis of a spline-shaft system suffering from self-excited vibrations. The nonintrusive generalized polynomial chaos expansion (gPCE) with unknown deterministic coefficients is used to represent the propagation of uncertainties in the rotor dynamics, which allows rapid estimation of the statistics of the nonlinear responses. Furthermore, the global sensitivity analysis of the stochastic self-excited vibration response of the rotor system with probabilistic uncertain parameters is evaluated by Sobol indices. The relative influence of different random parameters on the vibration behavior and initial displacement conditions for the occurrence of self-excited vibration is investigated. The accuracy of the adopted method based on the gPCE metamodel is validated by conventional Monte Carlo simulation (MCS). Finally, the effects of parameter uncertainties considering random distribution characteristics on the stochastic vibration characteristics of the rotor system are discussed, which demonstrates the need to consider input uncertainties in analysis and design to ensure robust system performance.

Analysis of short-circuit electrodynamic vibration response of triangularly arranged iced transmission lines based on finite element method

The alternating reciprocating electrodynamic load with periodic variation of short-circuit current will be generated when the triangular arrangement of iced transmission lines is short-circuited, which may lead to the occurrence of adhesion accidents. In order to analyze the vibration law of triangularly arranged iced conductors under the action of short-circuit alternating electrodynamic force, this paper establishes a mathematical model of spatial magnetic field and electrodynamic load of triangularly arranged conductors according to the principle of field strength superposition. The transient solution domain of COMSOL finite element analysis software is used to establish the simulation model of transmission conductor. The variation law of alternating reciprocating load of transmission conductor under short-circuit state is clarified, and the mathematical model of adhesion judgment of triangularly arranged transmission conductor is established. The horizontal displacement and vertical displacement of transmission conductor under different conditions are solved. The results show that: 1) The electrodynamic force generated by short-circuit current changes periodically, and the amplitude will gradually decay. 2) The thicker the conductor icing is, the smaller the electrodynamic force is, and the smaller the displacement of the conductor is; 3) The horizontal displacement and vertical displacement amplitude of the triangular arrangement wire are similar, indicating that when the direction of the electric dynamic load is the same, considering the displacement of the two directions, it is found that the A and C two-phase wires first adhere.

Analysis of Vehicle-Induced Vibration Response and Comfort in Large-Scale High-Speed Rail Station Buildings with Integrated Bridges

Analysis of Vehicle-Induced Vibration Response and Comfort in Large-Scale High-Speed Rail Station Buildings with Integrated Bridges

Vibration response analysis of a two-stage vibration isolation system for large airborne equipment

PurposeThis paper aims to propose a two-stage vibration isolation system for large airborne equipment to isolate aircraft vibration load.Design/methodology/approachFirst, the vibration isolation law of the discrete model of large airborne equipment under different damping ratios, stiffness ratios and mass ratios is analyzed, which guides the establishment of a three-dimensional solid model of large airborne equipment. Subsequently, the vibration isolation transfer efficiency is analyzed based on the three-dimensional model of the airborne equipment, and the angular and linear vibration responses of the two-stage vibration isolation system under different frequencies are studied.FindingsFinally, studies have shown that the steady-state angular vibration at the non-resonant frequency changes little. In contrast, the maximum angular vibration at the resonance peak reaches 0.0033 rad, at least 20 times the response at the non-resonant frequency. The linear vibration at the resonant frequency is at least 2.14 times the response at the non-resonant frequency. Obviously, the amplification factor of linear vibration is less than that of angular vibration, and angular vibration has the most significant effect on the internal vibration of airborne equipment.Originality/valueThe two-stage vibration isolation equipment designed in this paper has a positive guiding significance for the vibration isolation design of large airborne equipment.

Dynamic Interaction Factor of Pipe Group Piles Considering the Scattering Effect of Passive Piles

Based on the plane–strain assumption, a calculation model of pile–soil–pile vertical coupling vibration response considering the scattering effect of passive piles is established in this paper. Using this model, the vertical displacement expressions of pile core soil and pile surrounding soil, soil displacement attenuation function, and longitudinal complex impedance are obtained. Then, based on the strict pile–soil coupling effect, the displacement of the active pile under vertical load and scattering effect, as well as the displacement of the passive pile under incident waves, are solved separately. A new type of dynamic interaction factor for pipe group piles is derived by introducing scattering effect factors. A numerical example shows that the degenerate solution in this paper is in good agreement with the existing solution, which verifies the rationality of the solution. Considering the scattering effect is helpful in improving the accuracy of vibration response analysis of pile groups. The variation in parameters such as slenderness ratio, pile spacing, and outer diameter has significant effects on the interaction factor, and compared with the solid pile, the influence of parameter change on the pipe pile is smaller.

An improved MITC3 element for vibration response analysis of piezoelectric functionally graded porous plates

The main goal of this paper is to improve the mixed interpolation of tensorial components triangular (MITC3) by using the edge-based smoothed finite element method (ES-FEM), so-called ES-MITC3, for analyzing the vibration of piezoelectric functionally graded porous (p-FGP) plates subjected to dynamic loading. The material properties of the FGP core vary through thickness with uneven porosity distribution. Besides, the linear relationship between the electric potential and the thickness of the piezoelectric sublayer is taken into account. A closed-loop control algorithm is employed to actively control the vibration of p-FGP plates, through feedback from displacement and velocity. The performance of the proposed method is verified through comparative examples. Finally, the authors hope that the present method can be effectively applied to many smart material models in a multiphysics environment and contribute to understanding texture control by piezoelectric materials through numerical results.

Vibration response analysis technique for elevator wire rope

Wire rope is an element often used in transportation infrastructure and systems such as bridges, elevators, ropeways, funiculars and so on. Generally, wire ropes require a high level of safety because they suspend heavy and important components such as roadways in bridges, cages and cabins in elevators, ropeways and funiculars. In addition to dead loads like roadways, wire ropes are subjected to dynamic loads caused by earthquakes, wind and moving cars, etc. Therefore, it is important to accurately simulate the dynamic response of wire ropes to dynamic loads to ensure safety of wire ropes. This paper deals with techniques for vibration response analyses of wire ropes. Techniques in this paper specially focused on a transverse vibration of wire ropes for elevators because their response is complicated by the moving cage and tension distribution. Vibration response analysis techniques using the difference method and a simplified mass point model will be introduced in this paper.

A modified IHB method for nonlinear dynamic and thermal coupling analysis of rotor-bearing systems

This paper presents a modified incremental harmonic balance (IHB) method to analyze the nonlinear dynamic and thermal coupling characteristics of rotor-bearing systems after thermal balance. The IHB method is modified by tensor contraction and fast Fourier transform (FFT) to efficiently calculate the residual vector and Jacobian matrix. Nonlinear dynamic and thermal full coupling is implemented through the nonlinear part of the Jacobian matrix. The presented method achieves the simultaneous and efficient calculation of the motion and heat balance equations in the frequency domain according to the improvement measures. The effectiveness of the presented method is tested using the vibration response and temperature variation analysis for the coupled thermo-mechanical model of a rotor-ball bearing system. Furthermore, the performance comparisons show the good consistency of results between the presented method and the step-by-step (S-S) method, which is a partitioned iterative solution method for dealing with fully coupled problems in the time domain. The presented method has greater computational efficiency, more accurate temperature prediction, and better recognition of nonlinear phenomena in the system rather than the S-S method. Consequently, the presented method has a broad application prospect in solving fully coupled thermo-mechanical problems of more complex and higher dimensional rotor-bearing systems.

Vibration response analysis of iced transmission line under short-circuit alternating electrodynamic force

When a short-circuit fault occurs in an AC transmission line, an alternating reciprocating load that changes periodically with the short-circuit current is generated, increasing the probability of adhesion accidents in the transmission line. To analyze the influence of alternating reciprocating load caused by short-circuit electrodynamic force on the spatial trajectory of iced transmission line vibration, the electrodynamic load is added to the vibration equation of transmission line, and the mathematical model of spatial magnetic field and an electrodynamic load of horizontal arrangement wire is established. The finite element software is used to establish the transmission line model under different short-circuit currents and working conditions. The state of electrodynamic load at each phase wire is clarified at each time. The electrodynamic load is matrixed, and the vibration equation of the transmission line is introduced. After obtaining the spatial displacement of the transmission line, the spatial displacement adhesion mechanism is used to determine whether the transmission line adheres. Clear the easiest adhesion conditions and critical adhesion current.

Self-shrouded torsional blade model equivalence and blade vibration response analysis

In steam turbines, the operation of turbine blades can lead to vibrations, which may result in turbine accidents. Traditional calculation methods are difficult to use due to the complex structure of the torsional blade, and simulation analysis can be time-consuming. Therefore, it is necessary to use the equivalent model instead. Most of the previous studies have simplified the straight blade to a cantilever beam model without considering the shear effect, and used harmonic response analysis to study the vibration of the blade for simulation. The blade body of the torsional blade can be regarded as a torsional variable section beam, and the Timoshenko beam model is the same as the variable section beam. Therefore, the Timoshenko beam model can be regarded as the equivalent of the sheathed torsional blade. Considering the complexity of the calculation of the self-shrouded torsional blade model. According to the theory of Timoshenko beam, the model of the shrouded blade of Timoshenko beam with different torsion angles was established. The first sixth-order modes of the blade model and the vibration response of the adjacent blades under forced vibration are compared, respectively. The results show that the results obtained from the Timoshenko beam blade model considering the torsion angle are closer to the torsional blade model. In addition, the blade vibration response of the same model under different excitation force amplitudes was further compared, and the results showed that the vibration amplitude, acceleration and velocity of the shrouded blade increased with the increase of the excitation force amplitude. However, the magnitude of the inter-shroud collision force and the number of collisions between adjacent blade shrouds are non-linearly related to the amplitude of the excitation force.

Influence of Fiber Angle on the Steady State Periodic Response of Annular Sectorial Plates

Structural elements in the form of annular sectorial plates are widely used in aeronautical, biomedical, and marine engineering. When these components are exposed to dynamic load, large-amplitude vibrations occur. The vibration response analysis based on the linear strain-displacement relation typically yields a conservative estimate and can be used as a first approximation to the actual solution for thin structural elements. As a result, geometric nonlinearity must be incorporated for the efficient and fail-proof design of such elements. This paper shows non-linear and linear steady-state forced vibration responses of the annular sectorial plates. The governing equations of motion have been solved in the time domain by using a modified shooting method and an arc-length/pseudo-arc length continuation technique at the bifurcation point to obtain the complete response curve comprised of stable and unstable branches. This work investigates the effect of fibre angle on the non-linear steady-state forced vibration response of annular sectorial plates. The strain/stress fluctuation throughout the thickness of the laminated annular sectorial plate is determined to explain why hardening nonlinearity has increased. The cyclic fluctuation of the non-linear steady-state normal stress during a time period at the centre of the top and bottom surface is also provided in relation to the forcing frequency ratio of peak amplitude in the non-linear response. Due to the change in restoring forces, the frequency spectra reveal much increased harmonic involvement along with the fundamental harmonic for all fibre angles.

Numerical analysis of random vibration fatigue for a typical airborne equipment

In this paper, the fuel pump impeller was selected as a typical airborne equipment for the investigation of random vibration fatigue. First, based on the platform of ANSYS WORKBENCH, the reasonable calculation of FSI for the impeller was carried out. Then, the stress was transferred to modal analysis, and the prestress-structure modal was extracted. Through random vibration response analysis, the stress of the impeller was obtained. The Palmgren and Miner rule and Dirlik fatigue calculation method was used to calculate fatigue life, and the result was consistent with practice. The work in this paper provided a method about how to obtain random vibration fatigue life with prestress-structure, which was critical references for aviation technologists.

Temporal-spatial analysis on multi-mode interaction of a flexible pipe subject to external current and internal flow

The vortex-induced vibration (VIV) in relation to a flexible pipe is numerically studied in order to examine the coupled effects occurring between the external shear current and the varying density internal flow. The analysis is performed using numerical methods and interpreted with position-frequency-energy (PFE) and time-frequency-energy (TFE) illustrations. The results indicate that the external shear current and varying density internal flow play different roles in affecting the VIV response. Due to temporal-spatial multi-mode competition, the phenomenon of mode switching is captured, showing alternating amplitude trough and peak in the TFE spectrum. The vibration response at the amplitude trough is commonly characterized by a wide range of frequencies, but the vibration response at the amplitude peak is usually dominated by a single frequency or a narrow range of frequencies. Based on the analysis related to spanwise waveforms, it is found that the standing wave commonly corresponds to a relatively stable equilibrium state of energy transfer between fluid-structure and mode-mode at local segments, and that the traveling waveform corresponds to an unsteady status of energy transfer between fluid-structure along the pipe span. Finally, through the contrast analysis of lift force and vibration response, one can find that the lift force along the pipe span is highly periodic and is in phase with the vibration displacement.

Numerical analysis method of ship-ice collision-induced vibration of the polar transport vessel based on the full coupling of ship-ice-water-air

As the Arctic Channel continues to be developed, collisions between polar navigation vessels and sea ice are inevitable, which will directly affect structural safety and vibration comfort. However, the numerical analysis method of ship–ice collision-induced vibration is not perfect, and the effect of fluid coupling is not typically considered. In this paper, a simplified numerical analysis method for ship–ice collision-induced vibration is proposed, in which a reliable ice load is obtained by first performing ship–ice–water–air coupled collision calculations, followed by ship–ice–water coupled vibration calculations to obtain the vibration response of the structure. In addition, this paper investigates the full coupling method and the modeling ranges and meshing sizes involved in the analysis ship–ice collision-induced vibration, and the computational efficiencies of the traditional ALE algorithm and S-ALE algorithm are compared. The results indicate that the simplified simulation analysis method and gradient meshing model improve the calculation accuracy and efficiency in ship-ice collision and vibration response analysis. Moreover, the modeling range of the water and air models cannot be less than 6 times the ship width, 2 times the ship length, and 1 times the ship depth, and the S-ALE algorithm saves 47.86% time compared to the ALE algorithm. The research results in this paper can provide a reference for the numerical simulation of ship–ice collision-induced vibration.

Sensitivity analysis of vibration response of timoshenko beam to mass ratio and velocity of moving mass and boundary conditions: Semi-analytical approach

In real-world physics phenomena, the boundary conditions of structural members in the structural beam systems affect the system response. Also, moving load or mass problems are used widely in many engineering fields, such as structural, transportation, mechanical engineering, etc. Therefore, it is necessary to study the effect of boundary conditions on beam vibrations. Hence, a semi-analytical approach for the Timoshenko beam with various boundary conditions under moving mass is presented in this paper. Dynamic Green Function is introduced for modeling the beam under moving mass. An accurate formulation is illustrated for modeling a Timoshenko beam under moving mass with different boundary conditions. Finally, some examples demonstrate to assess of the effect of different boundary conditions, the mass ratio of moving mass, and the speed of moving mass. The numerical results are shown the efficiency and simplicity of the present approach. Based on the results, it is found that the mass ratio affects the dynamic response shape. For moving mass, the delay of the maximum dynamic deflection with respect to the mass position, increases with the speed at the higher speeds. But for smaller values of the speed, the same results of the maximum dynamic deflection for the moving load model along with the moving mass model are obtained. On the other hand, the maximum dynamic deflection points of the curves move slightly towards the right end of the beam with an increasing mass ratio. Also, the location of the constraint in the asymmetric beams is more significant in dynamic response. It is found that the dynamic behavior of the beam under moving mass changes dramatically based on the type of boundary conditions. Furthermore, the displacement obtained for each boundary condition decreases with increasing mass speed.

Dynamic characteristic analysis of beam structures with nonlinear elastic foundations and boundaries

The research of structures with elastic foundations has attracted extensive attention and many dynamic modeling and analysis methods for beam structures with elastic foundations have been proposed in current mainstream research. However, the low-dimension and high-accuracy models are more in line with the requirements of engineering practice. Hence, this paper aims to establish a novel nonlinear dynamic model of beam structures with nonlinear elastic foundations and boundaries. The global modes are first obtained by using the global mode method, and the forced vibration response analysis of the beam structures is subsequently carried out by developing a corresponding solving procedure. Thereafter, case studies are conducted on a cantilever beam with nonlinear elastic foundations and boundaries to validate the established nonlinear dynamic model. The consistency of the results obtained by the established model and finite element analysis demonstrates the accuracy of the established model. Finally, the effects of elastic foundations, boundaries, external excitation amplitude and nonlinear coupling terms on the dynamic characteristics of the cantilever beam structure are analyzed through the comparative case studies.

Numerical analysis of vibration response of elastic tube bundle of heat exchanger based on fluid structure coupling analysis

Abstract A tube bundle heat exchanger is a typical heat exchange equipment that exchanges heat between two fluids with different temperatures. Through this equipment, one fluid can be cooled down and another fluid can be heated up to meet their respective needs. The equipment is widely used in chemical, petroleum, pharmaceutical, energy, and other industrial sectors, and is one of the indispensable and important equipments in chemical production. To improve the heat transfer performance and service life of the heat exchanger, a numerical analysis of the vibration response of the elastic tube bundle in the heat exchanger based on fluid–structure coupling analysis is proposed. Using the weak coupling method of fluid–structure coupling, the vibration response of multiple rows of elastic tube bundles induced by shell side fluid in a heat exchanger with different tube row spacing and different tube row numbers is studied numerically, and the effects of shell side fluid and tube side fluid on the vibration response of elastic tube bundles are compared and analyzed. The results show that the maximum relative error of monitoring point amplitude is 43.36% when H = 40 mm and 10.17% when H = 70 mm. For connection IV, the maximum relative error of monitoring point amplitude is 31.71% when H = 40 mm and 24.08% when H = 70 mm. This is because when H is small, the interaction between rows of tube bundles is strong, so the amplitude changes violently with the number of the tube bundle. The step-by-step calculation strategy of rough calculation and actuarial calculation proposed in this article can greatly reduce the calculation time and improve the calculation efficiency.

Vibration response analysis of footbridge based on pedestrian perception

This article aims to study the influence of random crowd loading on the perceived vibration response of pedestrians. Firstly, a vertical vibration response analysis method considering pedestrian perception was established based on the random crowd walking model. Secondly, change rules of maximum vibration response of pedestrians, occurrence time and position interval under different random walk models were compared and analyzed. Finally, the vibration response reduction factor was defined by studying the correlation between the maximum vibration response of pedestrians and the peak acceleration of the structure, and the approximate calculation method of the maximum vibration response of pedestrians was proposed. The results show that the maximum acceleration perceived by pedestrians obeys the normal distribution under the four crowd walking models, the response distribution of ordered arrangement model (OAM) is larger than that of the other three models; The location and occurrence time of the maximum response depend on the distribution of pedestrian locations on the footbridge, and there is no significant change with the increase of population density. In addition, the distribution of OAM and stochastic arrival model (SAM) are consistent, which is concentrated in the middle of the total time-history. In contrast, the distribution of stochastic distribution model (SDM) and dynamic equilibrium model (DEM) are relatively uniform. The maximum error between the calculated acceleration maximum value and the actual acceleration value felt by the pedestrian is less than 5%. These results can provide reference for quantitative evaluation of pedestrian-induced vibration comfort.

Theoretical Analysis of Free Vibration and Transient Response of Rectangular Plate–Cavity System Under Impact Loading

AbstractThis paper presents a theoretical method to solve the free vibration and transient responses of a rectangular plate–cavity system. The spectral collocation method was used to solve the resonant frequencies and corresponding mode shapes of rectangular plates based on Kirchhoff thin plate and Mindlin–Reissner thick plate theories. A linear velocity potential function was employed to model the fluid pressure applied to the plate surface. Unlike in previous studies, it was not assumed that the wet-mode shapes were the same as the dry-mode ones. Rather, the wet modes were assumed to be the superposition of the dry modes; then, the resonant frequencies and corresponding mode shapes of the wet modes could be obtained by solving the equations of the coupled system by exploiting the orthogonality of dry modes. Using dry modes’ orthogonality and superposition of the wet modes, the transient responses of the rectangular plate–cavity system under impact loading can be solved. A method for estimating the resonant frequencies of the coupled system is proposed based on parametric studies to determine the influence of the fluid properties and plate materials on resonant frequencies. As a result, the resonant frequencies and transient responses obtained from the proposed theoretical methods are in excellent agreement with those obtained from finite element analysis.

Random Fatigue Analysis of Cryogenic Liquid Tanker Under Road Spectrum Load and a Simplified Algorithm

AbstractThe lightweight of liquefied natural gas (LNG) tanker can reduce transportation cost and improve transportation efficiency. However, in lightweight design, the random vibration analysis based on fluid–structure interaction (FSI) is difficult, which demands to be effectively solved by simplifying the finite element model and load. The vibration test and fluid–structure interaction modal numerical analysis of a tanker model were carried out, respectively, and the results are in good agreement. Taking the DC18 LNG tanker as an example, the random vibration response analysis was carried out based on the fluid–structure interaction modal numerical analysis, and the random fatigue damage coefficient of the support region of the inner container was obtained, which was used as the benchmark for the model and load simplification. The finite element model of the LNG tanker was simplified by applying the equivalent liquid mass to the walls of the inner container in the form of density. It is found that when the equivalent liquid mass ratio is 40%, the random vibration response characteristics of the DC18 LNG tanker are close to the actual structure. In the static calculation of the simplified model, the stress response of the container support area is close to the actual structural when the equivalent road spectrum load is 0.95 g vertical acceleration. In this case, the stress result and the overall damage coefficient equivalent to the actual structure can be obtained just by static calculation, which greatly simplifies the solution process.