Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects

Abstract

An improved mathematical model of pre-twisted tapered rotating micro beams made of bidirectional functionally graded material (BFGM) is presented to study its free vibration behavior. The effects of spin-softening and Coriolis acceleration are incorporated, and modified couple stress theory is employed to address the size effect. The mathematical formulation is based on first-order shear deformation theory and is developed in a global non-inertial frame incorporating appropriate transformations between the global inertial frame and the local non-inertial frame. Two different but interrelated steps are employed, where the first step determines the centrifugally deformed configuration using minimum potential energy principle, and the second step determines the free vibration behavior through tangent stiffness of the deformed rotating beam using Hamilton's principle. The direct use of tangent stiffness considers the centrifugal stiffening effect through von Kármán non-linearity and bypasses the need of strain energy functional for the vibrating beam. The governing equations are transformed to an eigenvalue problem through state-space approach and solved following Ritz method. The effects of spin-softening, Coriolis acceleration, and pre-twist angle are shown and discussed. The effects of different parameters such as size-dependent parameter, aspect ratio, material gradation indices, operating temperature, FGM constituent, taperness parameters, and slender parameter are discussed.