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Structural Stability and Vibration

Part of the Springer Tracts in Mechanical Engineering Book Series

DOI: 10.1007/978-3-319-72721-9

ISBN: 978-3-319-72720-2

Publisher: Springer International Publishing - Springer Journals

Feb 17, 2018

1 - 10 of 16 Chapters

Available

Introduction

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 1 –4

[This small book covers the subjects of stability, of vibration, and of dynamic stability, in the first chapters restricted to 2D beam problems. The book is written for a course named stability and vibration, and the intention is to communicate the similarities and interactions of the three...
Available

Beam-Column Differential Equation

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 5 –11

[After classifying the modeling names of bar, column, beam, and beam-column, the important differential equations with boundary conditions (DE with BC) are derived. For this mathematical formulation of physical problems, the knowledge to set up static equilibrium is essential. It is important...
Available

Eigen Solutions for the Euler Cases

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 13 –22

[Specific cases with constant bending stiffness EI and non-elastic BC are named the Euler cases, and results for these are included in most textbooks on stability and vibration. Instability modes and eigenfrequency modes for bending of the Euler cases are presented in tables with corresponding...
Available

Beam-Columns and Applied Berry Functions

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 23 –31

[Beam-column theory is beam theory that includes bending moments from column forces. This problem is still linear in external bending loads but nonlinear in column loads for static equilibrium in displaced state.]
Available

Shear Beam Loads and Cantilever Beam-Columns

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 33 –39

[A basic problem with external beam shear Q load at a given position has close similarities to the case of external moments in this chapter, but the involved Berry functions (now with bar notation) are more complicated. In addition to rotational spring supports at the beam-column ends,...
Available

Beam-Column Eigenfrequencies

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 41 –46

[In Sect. 3.3, the DE for eigenfrequencies is derived and discussed in relation to simply supported BC. Now including rotational end springs to get further BC, the analytical solutions complicate and generalized basic Berry functions with an added tilde notation must be introduced. For each case...
Available

Buckling with Spring Supported BC

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 47 –57

[This chapter is initiated with a discussion of the concept of stability, because it is not well defined. The name stability covers broadly, and it is not limited to the subject of the present book. There is no unique definition but different subjective, problem-oriented definitions. The American...
Available

Eigenfrequencies of Beam-Columns with Spring Supported BC

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 59 –72

[The general eigenvalue problem with three supporting parameters (non-dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

Dynamic Stability Formulation

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 73 –84

[A cantilever loaded at its free end is used to introduce the subject of dynamic stability, including non-conservative axial external force such as the case presented at the end of Chap. 8. The essential difference between divergence instability with zero eigenfrequency and flutter instability,...
Available

Stability of 2D Frames

Wiggers, Sine Leergaard; Pedersen, Pauli

Pages: 85 –94

[Then a solution procedure for these rather simple frames is presented as a kind of “cookbook.” A case (Roorda–Koiter frame) of critical imperfection analysis is shown with solution obtained by applying Berry functions. The necessary statics to formulate this problem is a good exercise.]

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