Dynamic Deflection of a Cantilever Beam Carrying Moving Mass

2014 ◽  
Vol 592-594 ◽  
pp. 1040-1044
Author(s):  
Shakti P. Jena ◽  
D.R. Parhi
Keyword(s):  
Differential Equation ◽  
Numerical Analysis ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Continuum Mechanics ◽  
Fourth Order ◽  
Moving Mass ◽  
Kutta Method ◽  
Beam Structure ◽  
Runge Kutta Method

In the present work, the dynamic deflection of a cantilever beam subjected to moving mass has been investigated theoretically and numerically. The mass is moved by an external force. The effects of mass magnitude and the speed of the moving mass on the response of the beam structure have been investigated. Using continuum mechanics the differential equation for the systems have been developed and solved by fourth order Runge-Kutta method with different boundary conditions. Numerical analysis has been carried out with different examples to describe the response of the beam structure.

Simplified Dynamics Modeling of Seat-Passenger in Vehicle Frontal Crash

2014 ◽  
Vol 597 ◽  
pp. 544-550
Author(s):  
Yao Yuan Wang ◽  
Zhuo Yang Lyu ◽  
Liang Liang Wang ◽  
Zhen Hua Yan
Keyword(s):  
Differential Equation ◽  
Dynamic Model ◽  
Fourth Order ◽  
Dynamics Analysis ◽  
Kutta Method ◽  
Analysis Method ◽  
Dynamics Modeling ◽  
Frontal Crash ◽  
Runge Kutta Method ◽  
Initial Stage

To quickly predict the performance of the seat in frontal crash during the initial stage of the seat development, in this paper a simplified coupled dynamic model of seat-passenger interaction is established according to the dynamics analysis method of Lagrange, and the fourth order Runge-Kutta method is used to resolve differential equation. Moreover, the simulation of Madymo testifies the simplified coupled dynamic model of seat-passenger interaction in frontal crash. Therefore, this model will be effective and feasible in predicting the performance of the seat in frontal crash during the initial stage of the seat development, for example, the performance of anti-submarining protection.

DYNAMIC DEFLECTION OF A CRACKED SHAFT SUBJECTED TO MOVING MASS

1997 ◽  
Vol 21 (3) ◽  
pp. 295-316 ◽  
Author(s):  
D.R. Parhi ◽  
A.K. Behera
Keyword(s):  
Differential Equation ◽  
Dynamic Behaviour ◽  
Normal Modes ◽  
Moving Mass ◽  
Kutta Method ◽  
Mass System ◽  
Simply Supported ◽  
Runge Kutta Method ◽  
Local Flexibility ◽  
Cracked Shaft

The dynamic behaviour of a cracked shaft is greatly affected by the mass moving on it. Magnitude and the travelling velocity of the mass along with the position of the crack on the shaft are the major parameters, considered in this investigation. The local flexibility due to the crack is evaluated from the theory of fracture mechanics. Then the normal modes for the cracked shaft are found and are used for formulating the equation of the moving mass system. Runge-Kutta method is used to solve the differential equation for the dynamic deflection of a simply supported cracked shaft, subjected to a moving mass of varying magnitudes and velocities. Significant change in the dynamic behaviour of the shaft is observed from the above analysis.

Dynamic deflection of a cracked beam with moving mass

1997 ◽  
Vol 211 (1) ◽  
pp. 77-87 ◽  
Author(s):  
D R Parhi ◽  
A K Behera
Keyword(s):  
Differential Equations ◽  
Cantilever Beam ◽  
Experimental Verification ◽  
Analytical Method ◽  
Stiffness Matrix ◽  
Moving Mass ◽  
Kutta Method ◽  
Cracked Beam ◽  
Runge Kutta Method ◽  
Local Stiffness

An analytical method along with the experimental verification have been utilized to investigate the vibrational behaviour of a cracked beam with a moving mass. The local stiffness matrix is taken into account when analysing the cracked beam. The Runge—Kutta method has been used to solve the differential equations involved in analysing the dynamic deflection of a cantilever beam.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

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