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.

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SynopsisThe relation between the maximum term and the maximum modulus of an entire function is exhibited by means of general theorems and specific examples. Functions of zero order and of infinite order are mainly considered.

Abstract. In this article, the necessary conditions for the hyponormality of Toeplitz operator T φ with harmonic polynomial symbols φ on the Fock space are explored.

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