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Table of contents
Chapter 1 Thin-walled beams, State of art. Motivation and Interest
1.1 Introduction
1.2 Thin-walled beams elements
1.3 Torsion and warping of thin-walled beams
1.3.1 Origin of the phenomenon
1.3.2 Uniform torsion (De Saint-Venant theory)
1.3.3 Non-uniform torsion (Vlasov’s theory)
1.4 Vibration analysis
1.4.1 Free vibration
1.4.2 Forced vibration
1.4.3 Time domain, frequency domain and Fourier Transform
1.4.4 Damping
1.4.5 Effect of elastic and viscous springs on the dynamic behavior of structures
1.5 Modeling linear vibrations of thin-walled beams
1.6 Assessment of subject positioning
1.7 Objectives of research topic
1.7.1 Free vibration of beams in flexural-torsional behavior
1.7.2. Forced vibration analysis of thin-walled beams
1.7.3. Effect of the elastic and viscous springs on vibration control
1.8 Conclusion
Chapter 2 Analytical method for the vibration behavior of thin-walled beams
2.1 Introduction
2.2 Free and forced vibration analyses
2.2.1 Kinematics of the model
2.2.2 Variational formulation of motion equations
2.2.3 Free vibration analysis
2.3 Validation and discussion
2.3.1 Simply supported beam with doubly-symmetric I cross-section
2.3.2 Simply supported beam with singly-symmetric C cross-section
2.3.3 Simply supported beam with mono-symmetric T cross-section
2.3.4 Cantilever beam with doubly-symmetric I cross-section
2.3.5 Cantilever beam with singly-symmetric C cross-section
2.3.6 Cantilever beam with mono-symmetric T cross-section
2.3.7 Doubly clamped beam with doubly-symmetric I cross-section
2.3.8 Doubly clamped beam with singly-symmetric C cross-section
2.3.9 Doubly clamped beam with mono-symmetric T cross-section
2.3.10 Free vibration of a singly-symmetric cross section cantilever beam
2.3.11 Flexural-torsional free vibration of a simply supported beam with arbitrary cross section
2.4 Conclusion
Chapter 3 Finite element method for vibrations of thin-walled beams
3.1 Introduction
3.2 Finite element discretization
3.3 Generic resolution of thin-walled structures
3.3.1 Finite element formulation of thin-walled structures free vibrations
3.3.2 Forced vibration of thin-walled structures in frequency domain (Steady-state dynamic analysis)
3.4 Numerical application and analysis
3.4.1 Free vibration of a singly-symmetric cross section cantilever beam
3.4.2 Flexural-torsional free vibration of a simply supported beam with arbitrary cross section
3.4.3 Hong Hu Chen benchmark numerical study
3.4.4 Double clamped cruciform cross-section beam
3.4.5 A simply supported beam under base motion load (Earth-quake, El Centro records, acc_NS)
3.4.6 Forced vibration analysis of thin-walled beams doubly-symmetrical section
3.4.7 Forced vibration analysis of thin-walled beams mono-symmetrical Tee section
3.4.8 Forced vibration analysis of thin-walled beams with mono-symmetrical channel section
3.5 Conclusion
Chapter 4 Experimental analysis on free and forced vibrations of thin-walled beams
4.1 Introduction
4.2 Experimental setup
4.2.1 Free vibration test procedure
4.2.2 Forced vibration test procedure
4.2.3 Acquisition device and Sensors characteristics
4.3 Specimens properties
4.4 Boundary conditions
4.5 Experimental tests results
4.5.1 Impact hammer tests results
4.5.2 Forced vibration test results for cantilever beam
4.6 Repeatability condition for the test results
4.7 Validation of the numerical model by comparison to experimental results
4.7.1 Free vibration
4.7.2 Forced vibration
4.8 Effect of intermediate bracings
4.9 Conclusion
Chapter 5 Vibration of braced beams
5.1 Introduction
5.2 Brace design
5.2.1 Vibration control by means of elastic bracings
5.2.2 Dynamic behavior of braced beams
5.2.3 Motion equations
5.3 Finite element formulation for braced thin-walled beams
5.4 Numerical applications
5.4.1 Torsion free vibration of braced thin-walled beams
5.4.2 Lateral free vibration of braced thin-walled beams
5.5 Conclusion
Conclusion and Perspectives
Résumé
References
