TABLE OF CONTENTS Chapter 11 focuses on uniform Bress Timoshenko beams. Eigenvalues and eigenfunctions for beams with a classical boundary conditions are presented.
| A | Cross-sectional area of the beam | |
| E, G | Modulus of elasticity and modulus of rigidity of the beam material | |
| EI | Bending stiffness | |
| r 0 | Radius of gyration of a cross-sectional area of the beam | |
| I | Moment of inertia of a cross-sectional area of the beam | |
| k | Shear coefficient | |
| l | Length of the beam | |
| R | Correction factor | |
| s | Notation of stiffness coefficients | |
| s( M ?) | Flexural stiffness coefficient of moment due to rotational deformation | |
| s( MX) | Flexural stiffness coefficient of moment due to transverse deformation | |
| s( V ?) | Flexural stiffness coefficient of shear due to rotational deformation | |
| s( VX) | Flexural stiffness coefficient of shear due to transverse deformation | |
| t | Time | |
| v 1 v 2 | Velocities of propagation of the waves | |
| Q, M | Shear force and bending moment | |
| x | Spatial coordinate | |
| x, y, z | Cartesian coordinates | |
| X(x) ?( x) | Mode shape | |
| y(x, t), ?( x, t) | Lateral displacement of the beam | |
| v | Poisson coefficient | |
| ?, m | Density of material and mass per unit length of beam, m = ? A | |
| ? | Circular natural frequency of the transverse vibration of the beam |
The Bress-Timoshenko theory is used for describing the...
