Marynowski Dynamics of the Axially Moving Orthotropic Web

1. Auflage 2010
ISBN: 978-3-540-78989-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 154 Seiten

A material continuum moving axially at high speed can be met in numerous different technical applications. These comprise band saws, web papers during manufacturing, processing and printing processes, textile bands during manufacturing and processing, pipes transporting fluids, transmission belts as well as flat objects moving at high speeds in space. In all these so varied technical applications, the maximum transport speed or the transportation speed is aimed at in order to increase efficiency and optimize investment and performance costs of sometimes very expensive and complex machines and installations. The dynamic behavior of axially moving systems very often hinders from reaching these aims. The book is devoted to dynamics of axially moving material objects of low flexural stiffness that are referred to as webs. Webs are moving at high speed, for example, in paper production the paper webs are transported with longitudinal speeds of up to 3000 m/min. Above the critical speed one can expect various dynamical instabilities mainly of divergent and flutter type. The up-to-date state of investigations conducted in the field of the axially moving system dynamics is presented in the beginning of the book. Special attention is paid on nonlinear dynamic investigations of translating systems. In the next chapters various mathematical models that can be employed in dynamic investigations of such objects and the results of analysis of the dynamic behavior of the axially moving orthotropic material web are presented. To make tracing the dynamic considerations easier, a paper web is the main object of investigations in the book.

Autoren/Hrsg.

Marynowski, Krzysztof

Inhaltsverzeichnis

1;Contents;6
2;Fundamental Notations;8
3;Introduction;10
3.1;1.1 Identification of Rheological Parameters of the Paper Web;11
3.1.1;1.1.1 Identification Method;12
3.1.2;1.1.2 Results of the Experimental Identification;14
3.2;1.2 Identification of the Corrugated Board as a Composite;15
3.2.1;1.2.1 Homogenization Method;16
3.2.2;1.2.2 Identification Results;18
3.3;References;19
4;State of Knowledge on Dynamics of Axially Moving Systems;20
4.1;2.1 String Systems;20
4.1.1;2.1.1 Linear Models;20
4.1.2;2.1.2 Nonlinear String Systems;22
4.2;2.2 Beam Systems;26
4.2.1;2.2.1 Linear Models;26
4.2.2;2.2.2 Nonlinear Beam Systems;28
4.3;2.3 Plate Systems;34
4.3.1;2.3.1 Numerical Investigations;34
4.3.2;2.3.2 Experimental Investigations of Axially Moving Plate Systems;40
4.4;2.4 Final Remarks;47
4.5;References;48
5;Dynamical Analysis of the Undamped Axially Moving Web System;51
5.1;3.1 One-Layered Orthotropic Web;51
5.1.1;3.1.1 Formulation of Nonlinear Equations of the Web Motion;51
5.1.2;3.1.2 Solution to the Mathematical Model;55
5.1.3;3.1.3 Results of Comparative Studies;62
5.1.4;3.1.4 Results of Dynamic Investigations of the Moving Paper Web;64
5.2;3.2 Multi-Layered Composite Web;73
5.2.1;3.2.1 Mathematical Model of the Axially Moving Multi-Layered Web;73
5.2.2;3.2.2 Solution of the Mathematical Model;78
5.2.3;3.2.3 Results of the Comparative Studies;81
5.2.4;3.2.4 Results of the Dynamic Investigations of the Axially Moving Corrugated Board Web;83
5.3;3.3 Final Remarks;90
5.4;References;91
6;Displacements of the Web in Equilibrium States of the Linearized System;92
6.1;4.1 Mathematical Models of the Axially Moving Orthotropic Web;92
6.2;4.2 Solution to the Mathematical Model of the Web Loaded with Constant Longitudinal Force;94
6.3;4.3 Displacements of the Web Loaded with Constant Longitudinal Force;97
6.4;4.4 Web Loaded with a Non-Uniform Longitudinal Force;101
6.5;4.5 Wrinkling of the Web Loaded with a Non-Uniformly Distributed Longitudinal Force;105
6.6;4.6 Final Remarks;108
6.7;References;109
7;Dynamics of the Axially Moving Viscoelastic Web;110
7.1;5.1 Two-Dimensional Rheological Model for Viscoelastic Materials;111
7.2;5.2 Mathematical Model of the Moving Viscoelastic Web;113
7.3;5.3 Solution to the Problem;116
7.4;5.4 Results of the Numerical Investigations;117
7.5;5.5 Final Remarks;121
7.6;References;122
8;Beam Model of the Moving Viscoelastic Web;123
8.1;6.1 Nonlinear Beam Model of the Viscoelastic Web;124
8.1.1;6.1.1 Kelvin-Voigt Model of Material;125
8.1.2;6.1.2 Poynting-Thompson Model of Material;126
8.1.3;6.1.3 Solution to the Problems;128
8.2;6.2 Investigations Results of the Model with the K-V Element;129
8.2.1;6.2.1 Linearized System;129
8.2.2;6.2.2 Non-Linear System;130
8.3;6.3 Investigations Results of the Model with a P-T Element;135
8.3.1;6.3.1 Linearized System;135
8.3.2;6.3.2 Nonlinear System;136
8.4;6.4 Final Remarks;141
8.5;References;142
9;Concluding Remarks;143
10;Appendix A;146
11;Appendix B;148
12;Appendix C;151
13;Index;154