Structural Stability and Vibration: An Integrated Introduction by Analytical and Numerical Methods

Description

This book offers an integrated introduction to the topic of stability and vibration. Strikingly, it describes stability as a function of boundary conditions and eigenfrequency as a function of both boundary conditions and column force. Based on a post graduate course held by the author at the University of Southern Denmark, it reports on fundamental formulas and makes uses of graphical representation to promote understanding. Thanks to the emphasis put on analytical methods and numerical results, the book is meant to make students and engineers familiar with all fundamental equations and their derivation, thus stimulating them to write interactive and dynamic programs to analyze instability and vibrational modes. Front Matter ....Pages i-xvi Introduction (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 1-4 Beam-Column Differential Equation (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 5-11 Eigen Solutions for the Euler Cases (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 13-22 Beam-Columns and Applied Berry Functions (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 23-31 Shear Beam Loads and Cantilever Beam-Columns (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 33-39 Beam-Column Eigenfrequencies (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 41-46 Buckling with Spring Supported BC (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 47-57 Eigenfrequencies of Beam-Columns with Spring Supported BC (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 59-72 Dynamic Stability Formulation (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 73-84 Stability of 2D Frames (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 85-94 Buckling Stresses, Material Nonlinearity, and Beam Modeling (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 95-104 Large Displacements, Pre-buckling Strains, and Snap-Through (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 105-114 Dynamics of Discretized Linear Systems (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 115-122 Discretized Stability Analysis (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 123-132 Routh–Hurwitz-Liénard–Chipart Criteria (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 133-140 Numerical Tools (Sine Leergaard Wiggers, Pauli Pedersen)....Pages 141-152 Back Matter ....Pages 153-158