Am. Horr et Lc. Schmidt, CLOSED-FORM SOLUTION FOR THE TIMOSHENKO BEAM THEORY USING A COMPUTER-BASED MATHEMATICAL PACKAGE, Computers & structures, 55(3), 1995, pp. 405-412
There has been considerable research interest in applying Timoshenko b
eam theory to the transient response of beams as well as for free and
forced vibration. Conventional finite elements treat the dynamic load
induced by the mass and rotary inertia of the beam as concentrated loa
ds and moments applied at the ends of the element. In many structures
the structural joints may be far apart, and therefore many elements mu
st be used if the inertia distributions are to be modelled accurately.
The purpose of this study is to determine the influence of distribute
d rotary inertia and shear deformation on the motion of a mass-loaded
clamped-free Timoshenko beam by means of an exact solution. The govern
ing differential equations are solved, and the frequency results are p
resented graphically and are compared with those derived for a Euler-B
ernoulli beam. Mathematica, which is a computer-based mathematical pac
kage, has been used to solve the frequency equation.