CLOSED-FORM SOLUTION FOR THE TIMOSHENKO BEAM THEORY USING A COMPUTER-BASED MATHEMATICAL PACKAGE

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.