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Nonlinear Equations for Beams and Degenerate Plates with Piers

  • Maurizio Garrione
  • Filippo Gazzola
Book

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the PoliMI SpringerBriefs book sub series (BRIEFSPOLIMI)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Maurizio Garrione, Filippo Gazzola
    Pages 1-8
  3. Maurizio Garrione, Filippo Gazzola
    Pages 9-17
  4. Maurizio Garrione, Filippo Gazzola
    Pages 19-67
  5. Maurizio Garrione, Filippo Gazzola
    Pages 69-98
  6. Maurizio Garrione, Filippo Gazzola
    Pages 99-103

About this book

Introduction

This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges.  New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.  

Keywords

Beams Degenerate plates Intermediate piers Optimal position Nonlinear initial-boundary value problems Floquet theory Stability Torsional instability

Authors and affiliations

  • Maurizio Garrione
    • 1
  • Filippo Gazzola
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-30218-4
  • Copyright Information The Author(s), under exclusive license to Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-30217-7
  • Online ISBN 978-3-030-30218-4
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site
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