Forced vibration of a novel beam model considering the shear deformation induced rotary inertia

Since the Timoshenko beam was introduced to engineering fields, many efforts have been devoted and many problems are yet to handle. Based on the classical Timoshenko beam theory, the rotary inertia caused by the shear deformation is further considered and the dynamic response under forced vibration is derived in this paper. Numerical analysis on beams with different lengths and different boundary conditions are conducted by four different beam theories including the Euler beam theory, shear beam theory, Timoshenko beam theory, and novel modified Timoshenko beam theory. It is found that the effect of the shear deformation induced rotary inertia is small for thin and slender beams; however, it is evident for short and deep beams with high stiffness. Meanwhile, the modification of the shear rotary inertia is obvious when the external load frequency is close to the first natural frequency of the beam. This study shows that the proposed modified Timoshenko beam theory is a more reasonable and accurate model to calculate the responses of the beam under forced vibration.