Spectral element formulation for damped transversely isotropic Micropolar-Cosserat layered composite panels

The present paper aims to develop governing equation of motion for in-plane dynamics of Micropolar-Cosserat composite models with damping. Constitutive model of linear elastic damping system is formulated for an anisotropic domain fiber-reinforced composite panels (FRCP); undergoing large macro as well as micro geometric deformations. The air damping and Kelvin–Voigt strain linear rate damping have been considered into the governing equations of model, while mathematical modelling and simulation of composite panel is restricted to the free-vibration and in-plane static response. The composite panel has been modeled as a Micropolar-Cosserat continuum assuming second-order micro-length of the fiber deformation; by embedding an additional equation of kinematics through the micro-rotation degree of freedom in the classical continuum model. This account for the in-plane curvature bending effects of composite panels during the loss of ellipticity of the governing equations. A transformation matrix based on Rodrigues’ rotational formula for transversely isotropic Micropolar-Cosserat lamina has been introduced; which reduces it to the well-known non-classical (classical and couple-stress) elastic formulation. The equivalent single layer (ESL) resultant stresses of FRCP in global coordinates is introduced to calculate in-plane damped and undamped response. The geometric and material linear elastic model for FRCP is derived using the spectral element method within state–space approach, and the corresponding plane-stress finite element model is validated with the undamped responses. Analytical response of damped composite panel is proposed based on available undamped simulation results.