Theory of micropolar gyroelastic continua

Abstract

This paper is devoted to the dynamic modeling of micropolar gyroelastic continua and explores some of the modeling and analysis issues related to them. It can be considered as an extension of the previous studies on equivalent continuum modeling of truss structures with or without angular momentum devices. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing the micropolar theory of elasticity, the energy expressions and equations of motion for undamped micropolar gyroelastic continua are derived. Whereas the micropolar gyroelastic continuum model with extra coefficients and degrees of freedom is primarily developed to account for the asymmetric stress–strain analysis in the gyroelastic continua, it also proves to be beneficial for a more comprehensive representation of the actual gyroelastic structure. The dynamic equations of the general gyroelastic continua are reduced to the case of one-dimensional gyroelastic beams. Simplified micropolar beam torsion and bending theories are used to derive the governing dynamic equations of micropolar gyroelastic beams from Hamilton’s principle. A finite element model corresponding to the micropolar gyrobeams is built in MATLAB\({^{\circledR}}\) and is used in numerical examples to study the spectral and modal behavior of simply supported micropolar gyroelastic beams.