Reduced isogeometric model for vibration analysis of beams under damping based on a fifth-order generalized shear deformation theory

Abstract

This work aims to use the reduced isogeometric model for analyzing the vibration behavior of beams under damping based on a fifth-order generalized shear deformation theory (GSDT). This beam theory utilizes the fifth-order polynomial function to represent the displacements through the beam height. Whilst the isogeometric analysis (IGA) employs B-spline functions to approximate the displacements along the beam length. These basis functions can easily meet the requirement of high-order derivatives which come from the fifth-order shear deformation theory. In the reduced IGA, instead of establishing the finite element model with all degrees of freedom (DOFs), only a given number of DOFs are kept to derive the algebraic equation systems condensed in state space for damping vibration analysis. The vibration responses of beams with different boundary conditions, length-to-height ratios and damping intensities are studied. The reliability and the accuracy of the reduced-order IGA are verified by comparing the damping-free results with other existing publications. Meanwhile, the corresponding outcomes considering damping are reported and discussed in detail. Such solutions can be referred to by future research.