scholarly journals On Integral Transforms and Matrix Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equation ◽  
Integral Transforms ◽  
General Linear ◽  
Viscous Damping ◽  
Matrix Functions ◽  
Vibration System ◽  
Elementary Matrix ◽  
Vibrating System ◽  
System A ◽  
Sumudu Transform

The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.

Study on Self-Excited Vibration Mechanism of Wheel-Rail Lateral Contact System

2013 ◽  
Vol 427-429 ◽  
pp. 257-261
Author(s):  
Li Xia Sun ◽  
Jian Wei Yao ◽  
Fu Guo Hou ◽  
Xin Zhao
Keyword(s):  
Feedback Mechanism ◽  
Point Of View ◽  
Contact System ◽  
Vibration System ◽  
Lateral Contact ◽  
System A ◽  
Vibration Model ◽  
Excited Vibration ◽  
Vibration Mechanism ◽  
The Stability

In order to investigate self-excited vibration mechanism of wheel-rail lateral contact system, a two DOF elasticity position wheelset lateral vibration model is established which considers the dry friction; the mechanism of the wheelset lateral self-excited vibration is investigated from the energy point of view. It shows that: the bifurcation diagram of this wheel-rail lateral contact system has a supercritical Hopf bifurcation. The energy of self-excited vibration derives from a part of traction energy; the creep rate in the wheel-rail system act as a feedback mechanism in the wheelset lateral self-excited vibration system. The stability of the wheelset self-excited vibration system depends mainly on the total energy removed from and imported into the system.

scholarly journals Mathematical modelling of the mass-spring-damper system - A fractional calculus approach

2012 ◽  
Vol 22 (5) ◽  
pp. 5-11 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Juan Rosales García ◽  
Jesus Bernal Alvarado ◽  
Manuel Guía
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Mathematical Modelling ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Time Derivative ◽  
System A ◽  
Fractional Differential ◽  
Mass Spring ◽  
Derivatives Of

In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter char­acterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed

scholarly journals Self-synchronization characteristics of a class of nonlinear vibration system with asymmetrical hysteresis

2019 ◽  
Vol 39 (1) ◽  
pp. 114-128
Author(s):  
Nan Zhang
Keyword(s):  
Nonlinear Vibration ◽  
Power Supply ◽  
The Self ◽  
Vibration System ◽  
Nonlinear Dynamic Model ◽  
Synchronous System ◽  
Vibrating System ◽  
Synchronous Operation ◽  
Hysteretic Characteristics ◽  
Nonlinear Vibration System

The self-synchronization characteristics of the two excited motors for the nonlinear vibration system with the asymmetrical hysteresis have been proposed in the exceptional circumstances of cutting off the power supply of one of the two excited motors. From the point of view of the hysteretic characteristics with the asymmetry, a class of nonlinear dynamic model of the self-synchronous vibrating system is presented for the analysis of the hysteretic characteristics of the soil, which is induced by the relation between the stress and the strain in the soil. The periodic solutions for the self-synchronous system with the asymmetrical hysteresis are investigated using nonlinear asymptotic method. The synchronization condition for the self-synchronous vibrating pile system with the asymmetrical hysteresis is theoretical analyzed using the rotor–rotation equations of the two excited motors. The synchronization stability condition also is theoretical analyzed using Jacobi matrix of the phase difference equation of the two excited motors. Using Matlab/Simlink, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous system with the asymmetrical hysteresis are analyzed through the selected parameters. Various synchronous phenomena are obtained through the difference rates of the two excited motors, including the different initial phase and the different initial angular velocity, and so on. Especially, when there is a certain difference in the two excited motors, the synchronous operation of the two excited motors and the synchronous stability operation of the self-synchronous vibrating system with the asymmetrical hysteresis can still be achieved after the power supply of one of the two excited motors has been disconnected. It has been shown that the research results can provide a theoretical basis for the research of the vibration synchronization theory.

On the Approximate Solutions of Heat-Conduction Problems

1963 ◽  
Vol 85 (3) ◽  
pp. 203-207 ◽  
Author(s):  
Fazil Erdogan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Approximate Solutions ◽  
Integral Transforms ◽  
Partial Differential ◽  
The Given

Integral transforms are used in the application of the weighted residual methods to the solution of problems in heat conduction. The procedure followed consists in reducing the given partial differential equation to an ordinary differential equation by successive applications of appropriate integral transforms, and finding its solution by using the weighted-residual methods. The undetermined coefficients contained in this solution are functions of transform variables. By inverting these functions the coefficients are obtained as functions of the actual variables.

Linear difference-differential equations

1948 ◽  
Vol 44 (2) ◽  
pp. 179-185 ◽  
Author(s):  
E. M. Wright
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Real Variable ◽  
General Linear ◽  
Image Position

The general linear difference-differential equation takes the formwhere x is a real variable, ν(x) and Aμν(x) are known functions and

scholarly journals Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems

2014 ◽  
Vol 22 (21) ◽  
pp. 26254 ◽  
Author(s):  
Jiayang Wu ◽  
Pan Cao ◽  
Xiaofeng Hu ◽  
Xinhong Jiang ◽  
Ting Pan ◽  
...  
Keyword(s):  
Differential Equation ◽  
Linear Time ◽  
General Linear ◽  
Linear Time Invariant ◽  
Silicon Photonic ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Dualities between Elzaki Transform and Some Useful Integral Transforms

2019 ◽  
Vol 8 (12) ◽  
pp. 4312-4318 ◽  
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Integral Transforms ◽  
Second Law ◽  
Electrical Networks ◽  
Carbon Dating ◽  
Motion Signal ◽  
Sumudu Transform ◽  
Basic Functions ◽  
Bending Of Beams

Integral transforms have wide applications in the various disciplines of engineering and science to solve the problems of heat transfer, springs, mixing problems, electrical networks, bending of beams, carbon dating problems, Newton’s second law of motion, signal processing, exponential growth and decay problems. In this paper, we will discuss the dualities between Elzaki transform and some useful integral transforms namely Laplace transform, Kamal transform, Aboodh transform, Sumudu transform, Mahgoub (Laplace-Carson) transform, Mohand transform and Sawi transform. To visualize the importance of dualities between Elzaki transform and mention integral transforms, we give tabular presentation of the integral transforms (Laplace transform, Kamal transform, Aboodh transform, Sumudu transform, Mahgoub transform, Mohand transform and Sawi transform) of mostly used basic functions by using mention dualities relations. Results show that the mention integral transforms are strongly related with Elzaki transform

scholarly journals Dualities between Mohand Transform and Some Useful Integral Transforms

2019 ◽  
Vol 8 (3) ◽  
pp. 843-847
Keyword(s):  
Signal Processing ◽  
Laplace Transform ◽  
Exponential Growth ◽  
Integral Transforms ◽  
Second Law ◽  
Electrical Networks ◽  
Carbon Dating ◽  
Sumudu Transform ◽  
Basic Functions ◽  
Bending Of Beams

Integral transforms have wide applications in the different areas of engineering and science to solve the problems of springs, Newton’s law of cooling, electrical networks, bending of beams, mixing problems, signal processing, carbon dating problems, Newton’s second law of motion, exponential growth and decay problems. In this paper, we will discuss the dualities of some useful integral transforms namely Laplace transform, Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub (Laplace- Carson) transform and Sawi transform with Mohand transform. To visualize the importance of dualities between Mohand transform and mention integral transforms, we give tabular presentation of the integral transforms (Laplace transform, Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub transform and Sawi transform) of mostly used basic functions by using mention dualities relations.

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