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.
Author(s): Krzysztof Marynowski
Series: Lecture Notes in Applied and Computational Mechanics
Edition: 1
Publisher: Springer
Year: 2008
Language: English
Pages: 159
Cover......Page 1
Lecture Notes in Applied and Computational Mechanics......Page 2
Dynamics of the Axially Moving Orthotropic Web......Page 4
Copyright......Page 5
Contents......Page 6
Fundamental Notations......Page 8
Introduction......Page 10
1.1 Identification of Rheological Parameters of the Paper Web......Page 11
1.1.1 Identification Method......Page 12
1.1.2 Results of the Experimental Identification......Page 14
1.2 Identification of the Corrugated Board as a Composite......Page 15
1.2.1 Homogenization Method......Page 16
1.2.2 Identification Results......Page 18
References......Page 19
2.1.1 Linear Models......Page 20
2.1.2 Nonlinear String Systems......Page 22
2.2.1 Linear Models......Page 26
2.2.2 Nonlinear Beam Systems......Page 28
2.3.1 Numerical Investigations......Page 34
2.3.2 Experimental Investigations of Axially Moving Plate Systems......Page 40
2.4 Final Remarks......Page 47
References......Page 48
3.1.1 Formulation of Nonlinear Equations of the Web Motion......Page 51
3.1.2 Solution to the Mathematical Model......Page 55
3.1.3 Results of Comparative Studies......Page 62
3.1.4 Results of Dynamic Investigations of the Moving Paper Web......Page 64
3.2.1 Mathematical Model of the Axially Moving Multi-Layered Web......Page 73
3.2.2 Solution of the Mathematical Model......Page 78
3.2.3 Results of the Comparative Studies......Page 81
3.2.4 Results of the Dynamic Investigations of the Axially Moving Corrugated Board Web......Page 83
3.3 Final Remarks......Page 90
References......Page 91
4.1 Mathematical Models of the Axially Moving Orthotropic Web......Page 92
4.2 Solution to the Mathematical Model of the Web Loaded with Constant Longitudinal Force......Page 94
4.3 Displacements of the Web Loaded with Constant Longitudinal Force......Page 97
4.4 Web Loaded with a Non-Uniform Longitudinal Force......Page 101
4.5 Wrinkling of the Web Loaded with a Non-Uniformly Distributed Longitudinal Force......Page 105
4.6 Final Remarks......Page 108
References......Page 109
Dynamics of the Axially Moving Viscoelastic Web......Page 110
5.1 Two-Dimensional Rheological Model for Viscoelastic Materials......Page 111
5.2 Mathematical Model of the Moving Viscoelastic Web......Page 113
5.3 Solution to the Problem......Page 116
5.4 Results of the Numerical Investigations......Page 117
5.5 Final Remarks......Page 121
References......Page 122
Beam Model of the Moving Viscoelastic Web......Page 123
6.1 Nonlinear Beam Model of the Viscoelastic Web......Page 124
6.1.1 Kelvin-Voigt Model of Material......Page 125
6.1.2 Poynting-Thompson Model of Material......Page 126
6.1.3 Solution to the Problems......Page 128
6.2.1 Linearized System......Page 129
6.2.2 Non-Linear System......Page 130
6.3.1 Linearized System......Page 135
6.3.2 Nonlinear System......Page 136
6.4 Final Remarks......Page 141
References......Page 142
Concluding Remarks......Page 143
Appendix A......Page 146
Appendix B......Page 148
Appendix C......Page 152
Index......Page 156
