TABLE OF CONTENTS This chapter focuses on prismatic Bernoulli Euler beams under compressive and tensile loading. Analytic results for frequency equations and mode shape functions for beams with classical boundary conditions are presented. Galef's formula is discussed in detail. Upper and lower values for the frequency of vibrations are evaluated.
| A | Cross-sectional area of the beam | |
| E, v | Modulus of elasticity and Poisson ratio of the beam material | |
| EI | Bending stiffness | |
| G | Gauge factor | |
| i | Bending stiffness per unit length, i = El/l | |
| I | Moment of inertia of a cross-sectional area of the beam | |
| k | Frequency parameter, | |
| l | Length of the beam | |
| M, N | Dimensionless frequency parameters | |
| t | Time | |
| T | Axial load | |
| T E | First Euler critical load | |
| T mi | Critical buckling load corresponding to mode i. | |
| U, U mi | Dimensionless parameter, | |
| x | Spatial coordinate | |
| x, y, z | Cartesian coordinates | |
| X(x) | Mode shape | |
| y(x, t), w | Lateral displacement of the beam | |
| ?, m | Density of material and mass per unit length of beam, m = ?A | |
| ? | Frequency parameter, ? 2 = k 2l 2 | |
| ? | Circular natural frequency of the transverse vibration of a compressed beam (relative natural frequency) | |
| ? 0 i | Circular natural frequency of transverse vibration of a beam with no axial force in the ith mode of vibration | |
| ? | Dimensionless natural frequency parameter of a compressed beam (relative natural... |
