Application of the Mode-Acceleration Technique to the Solution of the Moving Oscillator Problem

1999 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lawrence A. Bergman
Keyword(s):  
Shear Force ◽  
Series Representation ◽  
Bending Moment ◽  
Static Solution ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
One Dimensional ◽  
Acceleration Technique ◽  
Moving Oscillator

Abstract The problem of calculating the dynamic response of a one-dimensional distributed parameter system excited by an oscillator traversing the system with an arbitrarily varying speed is investigated. An improved series representation for the solution is derived that takes into account the jump in the shear force at the point of the attachment of the oscillator, which makes it possible to efficiently calculate the distributed shear force and, where applicable, bending moment. The improvement is achieved through the introduction of the “quasi-static” solution, an approximation to the desired one, which makes it possible to apply to the moving oscillator problem the “mode-acceleration” technique conventionally used for acceleration of series in problems related to the steady-state vibration of distributed systems. Numerical results illustrating the efficiency of the method are presented.

An Improved Series Expansion of the Solution to the Moving Oscillator Problem

1999 ◽  
Vol 122 (1) ◽  
pp. 54-61 ◽  
Author(s):  
A. V. Pesterev ◽  
L. A. Bergman
Keyword(s):  
Shear Force ◽  
Series Representation ◽  
Bending Moment ◽  
Static Solution ◽  
Distributed Parameter ◽  
One Dimensional ◽  
Moving Force ◽  
Coupling Force ◽  
Force Problem ◽  
Moving Oscillator

The problem of calculating the dynamic response of a one-dimensional distributed parameter system excited by an oscillator traversing the system with an arbitrarily varying speed is investigated. An improved series representation for the solution is derived that takes into account the jump in the shear force at the point of the attachment of the oscillator, which makes it possible to efficiently calculate the distributed shear force and, where applicable, bending moment. The improvement is achieved through the introduction of the “quasi-static” solution, which is an approximation to the desired solution, and is also based on the explicit representation of the solution of the moving oscillator problem as the sum of the solution of the corresponding moving force problem and that of the problem of vibration of the distributed system subject to the elastic coupling force. Numerical results illustrating the efficiency of the method are presented. [S0739-3717(00)01001-1]

A New Method for Calculating Bending Moment and Shear Force in Moving Load Problems

2000 ◽  
Vol 68 (2) ◽  
pp. 252-259 ◽  
Author(s):  
A. V. Pesterev ◽  
C. A. Tan ◽  
L. A. Bergman
Keyword(s):  
Series Expansion ◽  
Shear Force ◽  
Moving Load ◽  
A Priori ◽  
Series Representation ◽  
Bending Moment ◽  
Continuous System ◽  
Distributed Parameter ◽  
Moving Loads ◽  
Moving Oscillator

In this paper, a new series expansion for calculating the bending moment and the shear force in a proportionally damped, one-dimensional distributed parameter system due to moving loads is suggested. The number of moving forces, which may be functions of time and spatial coordinate, and their velocities are arbitrary. The derivation of the series expansion is not limited to moving forces that are a priori known, making this method also applicable to problems in which the moving forces depend on the interactions between the continuous system and the subsystems it carries, e.g., the moving oscillator problem. A main advantage of the proposed method is in the accurate and efficient evaluation of the bending moment and shear force, and in particular, the shear jumps at the locations where the moving forces are applied. Numerical results are presented to demonstrate the rapid convergence of the new series representation.

The Response of a Nonconservative Distributed System to a Moving Oscillator

1997 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lawrence A. Bergman
Keyword(s):  
Distributed System ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Concentrated Load ◽  
Moving Vehicle ◽  
Conservative Oscillator ◽  
Method Of Solution ◽  
Moving Oscillator ◽  
The Continuum

Abstract The problem of calculating the response of a nonconservative distributed parameter system of a general type excited by a moving concentrated load is investigated. A method of solution based on the expansion of the response in a series in terms of complex eigenfunctions of the distributed system is proposed. A set of ordinary differential equations in the time-dependent coefficients of the expansion is established first, in terms of the unknown force acting on the continuum from a moving vehicle, which allows one to investigate different models of concentrated loads. Then, for the case of a conservative oscillator moving with an arbitrarily varying speed, the coefficients of the equations are obtained in explicit terms.

Equivalent One-Dimensional System for Analysis of Taper Leaf Springs

1976 ◽  
Vol 98 (1) ◽  
pp. 39-42 ◽  
Author(s):  
N. J. Nigro ◽  
S. P. Bhatia
Keyword(s):  
Vehicle Suspension ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Equivalent System ◽  
Distributed Parameter System ◽  
Parameter System ◽  
One Dimensional ◽  
Suspension Systems ◽  
Leaf Springs ◽  
Good Agreement

In this paper an equivalent one-dimensional system for taper leaf springs (similar to those used in vehicle suspension systems) is developed so that results obtained from it are in good agreement with those obtained from the distributed parameter system. Curves which simplify the calculation of the parameters of the equivalent system are also provided.

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