Dynamic analysis of rotating axially FG tapered beams based on a new rigid-flexible coupled dynamic model using the B-spline method

Dynamics of rotating axially functionally graded (FG) tapered beams are studied based on a new dynamic model by using the B-spline method (BSM). The slope angle and stretch strain of the centroid line of the beam are used to describe the deformation of the beam. By using the BSM and employing Lagrange's equations of the second kind, the second-order slope angle (SOSA) model by neglecting the third- and higher-order nonlinear terms from a quadratic Taylor expansion of the slope angle is derived. Simulation results from the SOSA model by using the BSM compare well with those from the previous model in literature by using the BSM, and have higher accuracy than those from the previous model by using the assumed modes method (AMM). Application of this new model provides good results for various of rotating axially FG tapered beams with different taper ratios and arbitrary variations of material properties along the beam axis. Natural frequencies of the system without and with the chordwise bending and stretching (B-S) coupling effect included are calculated and compared. Some new interesting phenomena of frequency veering and mode shift are observed in a rotating axially FG tapered beam when the B-S coupling effect is included.