TABLE OF CONTENTS This chapter contains analytical and numerical results for Bernoulli Euler multispan beams on rigid and/or the elastic supports.
| A | Cross-sectional area of the beam | |
| E | Modulus of elasticity of the beam material | |
| EI | Bending stiffness | |
| i | Bending stiffness per unit length, i = EI/ l | |
| I | Moment of inertia of a cross-sectional area of the beam | |
| k | Frequency parameter, | |
| l | Length of the beam | |
| M | Bending moment, amplitude of harmonic moment | |
| r ik | Unit reaction of the slope-deflection method | |
| S, T, U, V | Krylov Duncan functions | |
| t | Time | |
| x | Spatial coordinate | |
| x, y, z | Cartesian coordinates | |
| X(x) | Mode shape | |
| y(x, t), w | Lateral displacement of the beam | |
| Z | Unknown of the slope-deflection method | |
| ? | Frequency parameter, ? 2 = k 2 l 2 | |
| ?, m | Density of material and mass per unit length of beam, m = ? A | |
| ?(?), ? (?) | Zal'tsberg functions | |
| ? | Natural frequency of free transverse vibration |
The eigenvalue problem for uniform multispan beams with a distributed mass and with/without lumped masses may be studied by using different classical methods. The most effective among these methods are the slope-deflection method, which uses specific functions (see Chapter 4), and the force method in the form of three moment equations. These methods lead to a governing equation for eigenvalues in exact analytical form.
Natural frequencies...
