Numerical solution of the impact problem for a rigid mass and a viscoelastic rod of finite length

1973 ◽  
Vol 7 (3) ◽  
pp. 400-405 ◽  
Author(s):  
S. M. Kokoshvili ◽  
V. P. Muzychenko ◽  
V. P. Tamuzh
Keyword(s):  
Numerical Solution ◽  
Finite Length ◽  
Rigid Mass ◽  
The Impact ◽  
Rod Of Finite Length ◽  
Impact Problem ◽  
Viscoelastic Rod

Free Vibration Analysis for Thin Wire of Modern Wiresaw Between Sliced Wafers in Wafer Manufacturing Processes

2000 ◽  
Author(s):  
Songbin Wei ◽  
Imin Kao
Keyword(s):  
High Speed ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Manufacturing Processes ◽  
Thin Wire ◽  
Wire Vibration ◽  
The Wire ◽  
The Impact ◽  
Wafer Manufacturing ◽  
Impact Problem

Abstract In wiresaw manufacturing process where thin wire moving at high speed is pushed onto ingot to produce slices of wafer, the wire is constrained by two wafer walls as it slices into the ingot. In this paper, we investigate the vibration of such wire under the constraints of wafer walls. To address this problem, the model for wire vibration with impact to wafer walls is developed. The equation of motion is discretized using the Galerkin’s method. The principle of impulse and momentum is utilized to solve the impact problem. The results of analysis and simulation indicate that the response under a pointwise sinusoidal excitation is neither periodical nor symmetric with respect to the horizontal axis, due to the excitation from the impact. The wire vibration behavior is affected dramatically by the wafer wall constraints.

Transient Heat Conduction in a Rod of Finite Length With Variable Thermal Properties

1960 ◽  
Vol 27 (4) ◽  
pp. 617-622 ◽  
Author(s):  
W. H. Chu ◽  
H. N. Abramson
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Finite Length ◽  
Thermophysical Properties ◽  
Numerical Procedure ◽  
Transient Heat Conduction ◽  
Theoretical Solution ◽  
Rod Of Finite Length

This paper presents a theoretical solution for transient heat conduction in a rod of finite length with variable thermal properties. A numerical procedure is developed and the results of one example are presented and compared with the corresponding solution for the case of constant properties. Application to the problem of determination of thermophysical properties is discussed briefly.

Kinematics and Dynamics of a Sliding/Bouncing Two Mass System

2011 ◽  
Author(s):  
Mohamed Gharib ◽  
Ali Tavakoli ◽  
Yildirim Hurmuzlu
Keyword(s):  
Slope Angle ◽  
Surface Friction ◽  
Correlation Ratio ◽  
Constrained Motion ◽  
Mass System ◽  
Inclined Planes ◽  
Ground Impact ◽  
The Impact ◽  
Wall Slope ◽  
Impact Problem

This paper presents the solution of the impact problem for a sliding/bouncing baton on flat and inclined planes subject to surface friction. The baton is assumed to have unilaterally constrained motion, which means one end slides on the ground while the other end collides with the ground. We use the impulse momentum approach and incorporate the impulse correlation ratio (ICR) hypothesis to solve the ground impact problem when the system has unilaterally constrained dynamics. Parametric investigations were carried out to examine the effect of the baton’s length and the inclined wall slope angle on the impulse correlation ratio. Numerical simulation and experiments were carried out to validate the model.

Derivation of Effective Ratio of Acoustic Impedance for Impacting Viscoelastic Slug (Standard Linear Solid Model) and Elastic Rod

2014 ◽  
Vol 554 ◽  
pp. 701-711
Author(s):  
Abu Bakar Musa
Keyword(s):  
Acoustic Impedance ◽  
Multiple Scales ◽  
Numerical Results ◽  
Viscoelastic Materials ◽  
Elastic Rod ◽  
Time Constants ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Impact ◽  
Viscoelastic Rod

The study is about impact of a short viscoelastic slug on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when a viscoelastic slug moving at a speed impacts a semi-infinite stationary viscoelastic rod. In order to validate the numerical results, we derive the effective ratio of acoustic impedance for impacting rods which will be used in the viscoelastic discontinuity analysis. The objective of this study is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of viscoelastic discontinuity analysis is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

Collision of Two Mass Baton With Massive External Surfaces

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Ali Tavakoli ◽  
Mohamed Gharib ◽  
Yildirim Hurmuzlu
Keyword(s):  
Slope Angle ◽  
Surface Friction ◽  
Correlation Ratio ◽  
Constrained Motion ◽  
Surface Slope ◽  
Inclined Planes ◽  
Ground Impact ◽  
The Impact ◽  
Inclined Surface ◽  
Impact Problem

This paper presents the solution of the impact problem for a sliding/bouncing baton on flat and inclined planes subject to surface friction. The baton is assumed to have unilaterally constrained motion, which means one end slides on the ground while the other end collides with the ground. We use the impulse momentum approach and incorporate the impulse correlation ratio (ICR) hypothesis to solve the ground impact problem when the system has unilaterally constrained dynamics. Parametric investigations were carried out to examine the effect of the baton’s length and the inclined surface slope angle on the impulse correlation ratio. Numerical simulation and experiments were carried out to validate the model.

Effect of oil starvation on the isothermal impact problem

2017 ◽  
Vol 232 (10) ◽  
pp. 1332-1339
Author(s):  
Duohuan Wu ◽  
Jing Wang ◽  
Peiran Yang ◽  
Ton Lubrecht
Keyword(s):  
Film Thickness ◽  
Pressure Gradient ◽  
Thickness Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Maximum Pressure ◽  
Numerical Techniques ◽  
Minimum Film Thickness ◽  
The Impact ◽  
Impact Motion ◽  
Impact Problem

In this study, the effect of oil starvation on isothermal elastohydrodynamic lubrication of an impact motion is explored with the aid of numerical techniques. During the impact process, on comparison with the fully lubricated results, the pressure and film thickness are much lower and the entrapped film shape does not happen. The rebound is delayed by the oil starvation assumption. During the rebound process, a periphery entrapment is seen in the starved film thickness distribution. Under the starved condition, the maximum pressure gradient is higher. The central film thickness and minimum film thickness exhibit different variations compared with the results by fully flooded assumption.

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