DYNAMIC MODELING AND SIMULATION OF ROTATING FGM TAPERED BEAMS WITH SHEAR EFFECT

In this paper, the rigid-flexible coupling dynamics of the rigid-flexible beam system under large overall rotating motion is studied. The flexible beam is a functionally graded material (FGM) tapered beam, and its material properties are assumed to vary along the beam axis with a power law relation. The geometrical displacement relationship of the flexible FGM beam is described by the arc coordinate. The transverse bending and longitudinal stretching of the flexible beam are considered by the variables of the slope angle and the stretching strain, respectively, and the shear effect is taken into account. The assumed modes method is used to describe the deformation field, and Lagrange’s equations of the second kind are used to derive the equations to obtain the rigid-flexible coupling dynamic model considering the shear effect. Based on the new rigid-flexible coupling dynamics modeling theory, dynamics of the FGM tapered beams with different axial gradients are studied. The influences of different rotating speeds, gradient distributions and variable cross-section parameters on the dynamic characteristics of the system are analyzed by numerical simulations. The results show that the effect of shear on the deformation of FGM tapered beam with depth-span ratio is obvious. The distribution of the material gradient and the selection of the cross-section parameters will have a great influence on the dynamic responses and frequencies of the rotating FGM tapered beam. The rigid-flexible coupling dynamic model considering the shear effect is a further improvement of the previous non-shear model, which can be applied to solve the dynamic problems of the Timoshenko beam structures.