TABLE OF CONTENTS This chapter covers the fundamental aspects of transverse vibrations of beams. Among the aspects covered are mathematical models for different beam theories, boundary conditions, compatibility conditions, energetic expressions, and properties of the eigenfunctions. The assumptions for different beam theories were presented in Chapter 1.
| A | Cross-section area | |
| D | Rayleigh dissipation function | |
| DS | Deformable system | |
| E, G | Young's modulus and modulus of rigidity | |
| EI | Bending stiffness | |
| F, V | Shear force | |
| g | Gravitational acceleration | |
| G( x, ?, t, ?) | Green function | |
| H | Heaviside function | |
| I z | Moment of inertia of a cross-section | |
| j | Pure imaginary number, j 2 = ?1 | |
| k | Shear factor | |
| k tr, k rot | Stiffness coefficients of elastic supports | |
| k b | Flexural wave number | |
| l | Length of the beam | |
| MCD | Mechanical chain diagram (Mechanical network) | |
| m j, k j | Mass and stiffness coefficients | |
| M, J | Concentrated mass and moment inertia of the mass | |
| N, M | Axial force, bending moment | |
| P(t), P 0 | Force and amplitude of a force | |
| r | Dimensionless radius of gyration, r 2 Al 2 = I | |
| r tr, r rot | Transversal and rotational stiffness of foundation | |
| R x | Reaction of the foundation | |
| s | Dimensionless parameter, s 2 kAGl 2 = EI | |
| t | Time | |
| U, T | Potential and kinetic energy | |
| U, V | Real and imaginary parts... |
