TABLE OF CONTENTS The different assumptions and corresponding theories of transverse vibrations of beams are presented. The dispersive equation, its corresponding curve propagation constant frequency and its comparison with the exact dispersive curve are presented for each theory and discussed.
The exact dispersive curve corresponds to the first and second antisymmetrical Lamb's wave.
| c b | Velocity of longitudinal wave, | |
| c t | Velocity of shear wave, | |
| D 0 | Stiffness parameter, D 4 0 = EI z/(2 ? H) | |
| E, ?, ? | Young's modulus, Poisson's ratio and density of the beam material | |
| E 1, G | Longitudinal and shear modulus of elasticity, E 1 = E/(1 ? ? 2), G = E/2(1+ ?) | |
| F y | Shear force | |
| H | Height of the plate | |
| I z | Moment of inertia of a cross-section | |
| k | Propagation constant | |
| k b | Longitudinal propagation constant, k b = ?/ c b | |
| k t | Shear propagation constant, k t = ?/ c t | |
| k 0 | Bending wave number for Bernoulli Euler rod, k 4 0 = ? 2/ D 4 0 | |
| M | Bending moment | |
| p, q | Correct multipliers | |
| u x, u y | Longitudinal and transversal displacements | |
| w, ? | Average displacement and average slope | |
| x, y, z | Cartesian coordinates | |
| ? xx, ? xy | Longitudinal and shear stress | |
| ? t, ? | Dimensionless parameters, ? t |
