Static and dynamic analysis of homogeneous Micropolar-Cosserat panels

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.

Keywords:

• Couple-stress theory
• Micropolar-Cosserat panel
• size-dependent behavior
• eigenvalue problems

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.

Additional information

Funding

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.