On the Analysis of the Timoshenko Beam Theory With and Without Internal Damping

The Timoshenko beam equation in terms of variable \u27wB\u27 is derived where \u27wB’ is the deflection due to the bending of a beam. The equation is used to analyze an infinite beam loaded with (i) a concentrated transverse load and (ii) an impulse. It is also shown that the rotatory damping in the equation eliminates the increasing amplitude in the propagation of the bending moment when an impulse is applied to an infinite beam. Also the general procedure for the anlysis of a non-homogeneous equation is explained