scholarly journals Wavelet Approach for Vibration Analysis of Fast Moving Load on a Viscoelastic Medium

2010 ◽  
Vol 17 (4-5) ◽  
pp. 461-472 ◽  
Author(s):  
Piotr Koziol ◽  
Cristinel Mares
Keyword(s):  
Boundary Conditions ◽  
Fast Moving ◽  
Moving Load ◽  
Finite Thickness ◽  
Constant Load ◽  
Order Of Accuracy ◽  
Wavelet Approximation ◽  
Complex Models ◽  
The Mathematical Model ◽  
Different Order

This paper analyses theoretically the response of a solid for fast moving trains using models related to real situations: a load moving in a tunnel and a load moving on a surface. The mathematical model is described by Navier's elastodynamic equation of motion for the soil and Euler-Bernoulli equation for the beam with appropriate boundary conditions. Two modelling approaches are investigated: the model with half space under the beam and the model with finite thickness of supporting medium. The problem of singularities for displacements calculation is discussed in relation with boundary conditions and types of considered loads: harmonic and constant, point and distributed moving loads. The analysis in frequency-time and frequency-velocity domains is presented and discussed with regard to critical velocities.A wavelet approximation method based on application of coiflet filters is used for the derivation of displacements in physical domain. A new, modified filter is used in numerical calculations allowing to alleviate numerical difficulties related to the form of approximating sequences based on classical filters, formulated in previous publications. The effectiveness of the coiflet approach is discussed for filter coefficients with different order of accuracy. This methodology is very efficient for the analysis in the range of relatively high and low load frequencies (treated as an approximation of a constant load) which are especially important for the analysis of vibrations generated by trains moving with velocities near critical values.Results of numerical simulations are presented, demonstrating their utility for modelling and preliminary analysis of complex models.

Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads

2020 ◽  
pp. 095440622097615
Author(s):  
Amit K Rai ◽  
Shakti S Gupta
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Circular Plate ◽  
Nonlinear Vibrations ◽  
Moving Load ◽  
Harmonic Balance Method ◽  
Angular Speed ◽  
Transverse Displacement ◽  
Governing Equations ◽  
Rotating Load

Here, we have studied the linear and nonlinear vibrations of a thin circular plate subjected to circularly, radially, and spirally moving transverse point loads. We follow Kirchoff’s theory and then incorporate von Kármán nonlinearity and employ Hamilton’s principle to obtain the governing equations and the associated boundary conditions. We solve the governing equations for the simply-supported and clamped boundary conditions using the mode summation method. Using the harmonic balance method for frequency response and Runge-Kutta method for time response, we solve the resulting coupled and cubic nonlinear ordinary differential equations. We show that the resonance instability due to a circularly moving load can be avoided by splitting it into multiple loads rotating at the same radius and angular speed. With the increasing magnitude of the rotating load, the frequency response of the transverse displacement shows jumps and modal interaction. The transverse response collected at the centre of the plate shows subharmonics of the axisymmetric frequencies only. The spectrum of the linear response due to spirally moving load contains axisymmetric frequencies, the angular speed of the load, their combination, and superharmonics of axisymmetric frequencies.

Study on the Dynamic Control Chart of Pumping Wells

2013 ◽  
Vol 734-737 ◽  
pp. 1276-1279
Author(s):  
Jing Guang Zhu
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Water Content ◽  
Control Chart ◽  
Dynamic Control ◽  
Scientific Basis ◽  
Leak Rate ◽  
Pump Efficiency ◽  
Pumping Wells ◽  
The Mathematical Model

In order to improve the pump efficiency of pumping wells, by means of the basic formula of pump efficiency, the mathematical model and boundary conditions of dynamic control chart is obtained, and the pump efficiency of pumping wells is drawn. Analysis shown that the pump efficiency is sensitive to the water content and pump leak rate. The higher the water content is, the higher pump efficiency is. The pump efficiency will be reduced with the increasing of pump leak rate. The dynamic control chart of class II block of A oilfield is given in the paper. After taking the measures, the pump efficiency of pumping wells is obviously improved. The dynamic control chart drawn by this method can provide a scientific basis for improving the pump efficiency of pumping wells in oilfield.

Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory

2019 ◽  
Vol 26 (11-12) ◽  
pp. 913-928 ◽  
Author(s):  
Seyed Amirhosein Hosseini ◽  
Farshad Khosravi ◽  
Majid Ghadiri
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Classical Theory ◽  
Moving Load ◽  
Nonlocal Parameter ◽  
Excitation Frequency ◽  
Single Walled Carbon Nanotubes ◽  
Axial Displacement ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes

The main objective of the present work is devoted to the study of both free and time-dependent forced axial vibration simultaneously in single-walled carbon nanotubes subjected to a moving load. The governing equation is derived via Hamilton’s principle. Classical theory, along with the Rayleigh and Bishop theories, is used to analyze the nonlocal vibrational behaviors of single-walled carbon nanotubes. A Galerkin method is established to solve the derived equations. The boundary conditions are assumed to be clamped-clamped and clamped-free. Firstly, the variation of nondimensional natural frequencies is calculated based on the classical theory, and the effect of the nonlocal parameter, the mode number and the length is illustrated and schematically compared for clamped-clamped and clamped-free boundary conditions. Besides, the obtained nondimensional responses are compared with the results of another study to validate the accuracy of the used method. Ultimately, the dynamic axial displacement due to the moving load in the time domain has been studied for the first time. Furthermore, the effects of the thickness, length, velocity of the moving load, excitation frequency, and the nonlocal parameter based on the classical, Rayleigh, and Bishop theories are investigated in this paper. Also, the influence of the nonlocal parameter on the variations of maximum axial displacement with respect to the velocity parameter for the aforementioned boundary conditions and theories is evaluated relative to each other.

scholarly journals Suppression of Ground Borne Vibration Induced by High-Speed Lines

2018 ◽  
Vol 152 ◽  
pp. 02001
Author(s):  
Ali Mohamed Rathiu ◽  
Mohammad Hosseini Fouladi ◽  
Satesh Narayana Namasivayam ◽  
Hasina Mamtaz
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
High Speed ◽  
Moving Load ◽  
Ground Vibration ◽  
Harmonic Excitation ◽  
Vibration Response ◽  
Vibration Velocity ◽  
Velocity Response ◽  
The Mathematical Model

Vibration of high-speed lines leads to annoyance of public and lowering real estate values near the railway lines. This hinders the development of railway infrastructures in urbanised areas. This paper investigates the vibration response of an isolated rail embankment system and modifies the component to better attenuate ground vibration. Mainly velocity response is used to compare the responses and the applied force is of 20 kN at excitation frequencies of 5.6 Hz and 8.3 Hz. Focus was made on ground-borne vibration and between the frequency range of 0 and 250 Hz. 3D Numerical model was made using SolidWork software and frequency response was produced using Harmonic Analysis module from ANSYS Workbench software. For analytical modelling MATLAB was used along with Simulink to verify the mathematical model. This paper also compares the vibration velocity decibels (VdB) of analytical two-degree of freedom model mathematical model with literature data. Harmonic excitation is used on the track to simulate the moving load of train. The results showed that modified analytical model gives the velocity response of 75 VdB at the maximum peak. Changes brought to the mass and spacing of the sleeper and to the thickness and the corresponding stiffness for the ballast does not result in significant vibration response. Limitations of two-degree analytical model is suspected to be the cause of this inactivity. But resonance vibration can be reduced with the aid of damping coefficient of rail pad. Statistical analysis methods t-test and ANOVA single factor test was used verify the values with 95% confidence.

scholarly journals Investigation of Thermostressed State of Coating Formation at Electric Contact Surfacing of “Shaft” Type Parts

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Olena V. Berezshnaya ◽  
Eduard P. Gribkov ◽  
Valeriy D. Kuznetsov
Keyword(s):  
Finite Thickness ◽  
Asymmetry Factor ◽  
Electric Contact ◽  
Technological Capabilities ◽  
Deformation Degree ◽  
Compact Material ◽  
Thermostressed State ◽  
Coating Formation ◽  
Difference Form ◽  
The Mathematical Model

The forming of coating at electric contact surfacing is considered. The mathematical model of the coating formation is developed. The method of numerical recurrent solution of the finite-difference form of static equilibrium conditions of the selected elementary volume of coating is used. This model considers distribution of thermal properties and geometric parameters along the thermal deformation zone during the process of electric contact surfacing by compact material. It is found that the change of value of speed asymmetry factor leads to increasing of the friction coefficient in zone of surfacing. This provides the forming of the coating of higher quality. The limitation of the technological capabilities of equipment for electric contact surfacing is related to the size of recoverable parts and application of high electromechanical powers. The regulation of the speed asymmetry factor allows for expanding the technological capabilities of equipment for electric contact surfacing. The nomograms for determination of the stress on the roller electrode and the finite thickness of the coating as the function of the initial thickness of the compact material and the deformation degree are shown.

scholarly journals Numerical study of the effect of droplet coagulation intensity on polydisperse aerosol fraction distribution

2021 ◽  
Vol 1 (1) ◽  
pp. 73-80
Author(s):  
D.A. Tukmakov ◽  
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Volume Content ◽  
Fine Particles ◽  
Stokes Equations ◽  
Numerical Study ◽  
Dispersed Phase ◽  
Mass Force ◽  
Carrier Medium ◽  
The Mathematical Model

The paper is devoted to the study of the effect of the intensity of aerosol fluctuations on the dis-tribution of fractions of the dispersed component of the coagulating aerosol. Oscillations of aerosol in closed channel are numerically modeled in operation. To describe the dynamics of the carrier medium, a two-dimensional non-stationary system of Navier-Stokes equations for compressed gas is used. They are written taking into account interfacial power interaction and interfacial heat ex-change. To describe the dynamics of the dispersed phase, a system of equations is solved for each of its fractions. It includes an equation of continuity for the “average density” of the fraction, equa-tions of preservation of spatial components of the pulse and an equation of preservation of thermal energy of the fraction of the dispersed phase of the gas suspension. Phase-to-phase power interac-tion included Archimedes force, attached mass force, and aerodynamic drag force. Heat exchange between the carrier medium-gas and each of the fractions of the dispersed phase was also taken into account. The mathematical model of dynamics of polydisperse aerosol was supplemented by the mathematical model of collision coagulation of aerosol. For the velocity components of the mixture, uniform Dirichlet boundary conditions were set. For the remaining functions of the dynamics of the multiphase mixture, uniform Neumann boundary conditions were set. The equations were solved by the explicit McCormack method with a nonlinear correction scheme that allows to obtain a mono-tone solution. As a result of numerical calculations, it was determined that in the vicinity of the os-cillating piston, an area with an increased content of coarse particles is formed. The coagulation process results in a monotonous increase in volume content of the coarse particle fraction and a mo-notonous decrease in volume content of fine particles. Increasing the intensity of gas fluctuations leads to intensification of the process of coagulation of aerosol droplets.

scholarly journals Spatial behaviour of thermoelasticity with microtemperatures and microconcentrations

2020 ◽  
Vol 34 ◽  
pp. 02001
Author(s):  
Adina Chirilă ◽  
Marin Marin
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Integrated Circuits ◽  
Boundary Conditions ◽  
Chemical Potential ◽  
Lateral Boundary ◽  
Spatial Behaviour ◽  
Cross Sectional ◽  
Lateral Boundary Conditions ◽  
The Mathematical Model

We consider a thermoelastic material with microtemperatures and microconcentrations. The mathematical model is represented by a system of partial differential equations with the coupling of the displacement, temperature, chemical potential, microconcentrations and microtemperatures fields. The processes of heat and mass diffusion play an important role in many engineering applications, such as satellite problems, manufacturing of integrated circuits or oil extractions. We study the spatial behaviour in a prismatic cylinder occupied by an anisotropic and inhomogeneous material. We impose final prescribed data that are proportional, but not identical, to their initial values. Moreover, we have zero body forces and zero lateral boundary conditions. The spatial behaviour is analysed in terms of some cross-sectional integrals of the solution that depend on the axial variable.

scholarly journals On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions

2019 ◽  
Vol 9 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Ozgur Yildirim
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Order Difference

In this paper, third and fourth order of accuracy stable difference schemes for approximately solving multipoint nonlocal boundary value problems for hyperbolic equations with the Neumann boundary conditions are considered. Stability estimates for the solutions of these difference schemes are presented. Finite difference method is used to obtain numerical solutions. Numerical results of errors and CPU times are presented and are analyzed.

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