Content: 3.2.5. The [theta] Wilson method3.2.6. Modal analysis of the sandwich beam
4. Introduction to Nonlinear Dynamic Analysis
4.1. Introduction
4.2. Linear systems
4.2.1. Generalities
4.2.2. Simple examples of large displacements
4.2.3. Simple example of a variable
4.2.4. Simple example of dry friction
4.2.5. Material nonlinearties
4.3. The nonlinear 1 DOF system
4.3.1. Generalities
4.3.2. Movement without non-dampened excitation
4.3.3. Case of a stiffness in the form [kappa] (1 + [mu]x2)
4.3.4. Movement with non-dampened excitation
4.3.5. Movement with dampened excitation Cover
Half-Title Page
Title Page
Copyright Page
Contents
Preface
1. Introduction to Inverse Methods
1.1. Introduction
1.2. Identification methods
1.3. Identification of the strain hardening law
1.3.1. Example of an application
1.3.2. Validation test
1.3.3. Hydroforming a welded tube
2. Linear Differential Equation Systems of the First Order with Constant Coefficients: Application in Mechanical Engineering
2.1. Introduction
2.2. Modeling dissipative systems
2.2.1. Intrinsic solutions of autonomous systems
2.2.2. Intrinsic solutions 2.2.3. Intrinsic solutions of the adjoining system2.2.4. Relation between the intrinsic solutions of s and s
2.2.5. Relation between modal matrices X and X
2.3. Autonomous system general solution
2.3.1. Direct solution by using the exponential matrix
2.3.2. Indirect solution by modal transformation
2.4. General solution of the complete equation
2.4.1. Direct solution by the exponential matrix
2.4.2. Indirect solution by modal transformation
2.4.3. General solution in the particular case of harmonic excitation
2.5. Applications to mechanical structures 2.5.1. Discrete mechanical structure at n degrees of freedom, linear, regular and non-dissipative2.5.2. Discrete mechanical structure at n DOF, linear, regular and dissipative
2.5.3. Intrinsic vector norm
2.5.4. Particular solution of the system with a harmonic force
2.6. Inverse problems: expressions of the M, B, K matrices according to the intrinsic solutions
3. Introduction to Linear Structure Dynamics
3.1. Introduction
3.2. Problems in structure dynamics
3.2.1. Finite elements method
3.2.2. Modal superposition method
3.2.3. Direct integration
3.2.4. Newmark method 4.4. Nonlinear N DOF systems4.4.1. Generalities
4.4.2. Nonlinear connection with periodic movement
4.4.3. Direct integration of the equations
5. Condensation Methods Applied to Eigen Value Problems
5.1. Introduction
5.2. Mathematical generality: matrix transformation
5.3. Dynamic condensation methods
5.4. Guyan condensation
5.5. Rayleigh-Ritz method
5.6. Case of a temporary problem
5.6.1. Simplification with a full modal basis
6. Linear Substructure Approach for Dynamic Analysis
6.1. Generalities
6.2. Different types of Ritz vectors