Research on dynamics of a rotating internal tapered FGM microbeam

Based on the modified couple stress theory, the dynamic characteristics of an internal flexible tapered microbeam made from functionally graded material (FGM) were studied. The mechanical properties of Euler–Bernoulli beam made of two-component FGM varied with power law along the thickness direction. The transverse bending deformation and axial tensile deformation of the flexible beam were considered, and the longitudinal shortening caused by the transverse bending deformation was taken into account namely the nonlinear coupling deformation. The deformation field of the flexible beam was discretized by the hypothetical mode method, and the geometric nonlinear strain of von Kármán was taken into account. The first-order approximate rigid-flexible coupling dynamic equation of the system was derived by using the second kind of Lagrange equation, and the dynamic simulation software is developed based on C++. Then, the dynamic characteristics and critical speed of the system were studied through simulation examples. The results show that the hub radius ratio, taper ratio, section shape, functional gradient index, and material length size parameters of the internal functionally graded microbeam have a great influence on the dynamic characteristics of the system. The damping effect of only changing the width of the beam is better, and adopting the tapered beam design and selecting a reasonable taper ratio will effectively increase the critical speed of the system.