Abstract
This paper communicates an analytical study on computing the natural frequencies and in-plane deflections caused by static forces in the panel walls using Euler-Bernoulli, Timoshenko, Timoshenko and Goodier, Couple-stress, and Micropolar-Cosserat theory. The study highlights the formulation of the transfer matrix via the state-space method in the spatial domain; from coupled governing equations of motion that arises from the Micropolar-Cosserat theory. This theory captures the novel curvature of edges and moments of the panels at energy density level due to its unique feature of asymmetric shear stresses; that emphasizes the loss of ellipticity of governing equations. The analytical solution of the Micropolar-Cosserat theory yield appropriate results compared to plane-stress simulation of the panels using finite element analysis.
Acknowledgement
AB acknowledges Inspire Faculty award, Department of Science and Technology, India, grant number DST/INSPIRE/04/2018/000052 and SKS, AB, RV and SD acknowledge Indo-Canada (IC-Impact grant): DST/INT/CAN/P-03/2019 for partial financial support.
Data availability statement
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.