<span lang="EN-US">The </span><span lang="EN-US">mathematical formulation</span><span lang="EN-US">of thick conical shells using third order shear deformation of thick shell theory are presented. The equations of motion are obtained using Hamilton’s principle. For present analysis, we consider shell's system transverse normal stress, rotary inertia and shear deformation.</span>
In this study, we apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells. The equations of motion are derived using Hamilton's principle of minimum energy and on the basis of the relationships between forces, moments, and stress displacements in the shell.We confirm the derived equations and analytical results through the finite element technique by using the well-known software packages MATLAB and ANSYS. We consider the fundamental natural frequencies and the mode shapes of simply supported spherical cross-ply (0, 90), (0, 90, 0), and (0, 90, 90, 0) laminated composite shells. Then, to increase accuracy and decrease calculation efforts, we compare the results obtained through classical theory and first-order shear deformation theory.
In this paper, we provide a mathematical model with a fractional-order to investigate the dynamics of oncolytic virotherapy. We focus on how the dynamics of oncolytic virotherapy models can rely on the burst size of the virus. The burst size of a virus is the number of new viruses released from the lysis of an infected cell. Different viruses have different burst sizes. The numerical simulations confirm that the fractional-order differential models have the ability can provide accurate descriptions of oncolytic virotherapy models and capture the memory of the dynamics.
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