𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An asymptotic approach to the problem of the free oscillations of a beam

✍ Scribed by G.V. Kostin; V.V. Saurin

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
358 KB
Volume
71
Category
Article
ISSN
0021-8928

No coin nor oath required. For personal study only.

✦ Synopsis

Equations describing the free small longitudinal and transverse oscillations of a straight elastic beam of rectangular cross section are obtained using the plane linear theory of elasticity and the method of integrodifferential relations. The initial system of partial differential equations is reduced to a system of ordinary linear differential equations with constant coefficients. The effect of the geometrical and elastic characteristics of the beam on the frequency and form of the natural oscillations is investigated. For longitudinal motions it is shown that different types of natural displacements and internal stresses of the beam exist. For transverse oscillations, it is found that there are frequency zones corresponding to different forms of the solutions of the characteristic equation obtained using the proposed model.

πŸ“œ SIMILAR VOLUMES

An asymptotic-numerical approach to the
An asymptotic-numerical approach to the coronal loop problem
✍ F. Verhulst; P. A. Zegeling πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 331 KB

## Abstract The coronal loop problem is characterized by mixed boundary conditions and the loop length condition, which is global. Using singular perturbation methods one can identify and construct two boundary layers at the base of the loop. Extending this to a combined asymptotic‐numerical treat

An asymptotic solution to transverse fre
An asymptotic solution to transverse free vibrations of variable-section beams
✍ R.D. Firouz-Abadi; H. Haddadpour; A.B. Novinzadeh πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 239 KB

The transverse free vibration of a class of variable-cross-section beams is investigated using the Wentzel, Kramers, Brillouin (WKB) approximation. Here the governing equation of motion of the Euler–Bernoulli beam including axial force distribution is utilized to obtain a singular differential equat