TABLE OF CONTENTS This chapter focuses on Bernoulli Euler uniform one-span beams with lumped and rotational masses. Beams with classic and non-classic boundary conditions, as well as elastic translational and torsional supports, are presented. Fundamental characteristics such as frequency equations, natural frequencies of vibration and mode shape vibrations are presented. For many cases, the frequency equation is presented in the different forms that occur in scientific problems. The chapter contains a vast amount of numerical results.
| A | Cross-sectional area | |
| A, B, C, D, E, S 1 | Hohenemser Prager functions | |
| E | Young's modulus | |
| EI | Bending stiffness | |
| g | Acceleration of gravity, g = 9.8 m/s 2 | |
| I z | Moment of inertia of a cross-section | |
| J | Moment inertia of the lumped mass | |
| J * | Moment inertia ratio | |
| k n | Frequency parameter, | |
| k tr, k rot | Translational and rotational stiffness coefficients | |
| k * tr, k * rot | Dimensionless translational and rotational stiffness coefficients | |
| l | Length of the beam | |
| M | Concentrated mass | |
| q | Uniformly distributed load | |
| S, T, U, V | Krylov Duncan functions | |
| x | Spatial coordinate | |
| X(x) | Mode shape | |
| x, y, z | Cartesian coordinates | |
| ? | Mass ratio | |
| ? | Frequency parameter, ? 4 EI = ml 4 ? 2 | |
| ? | Dimensionless coordinate, ? = x/l | |
| ?, m | Density of material and mass per unit length | |
| ? | Natural frequency, ? 2 = ? 4 EI / |
