Geodesic
The simplest transformation model of deformation of a rod-strip fixed on a double-sided support element through elastic interlayers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2024), pp. 98-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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An extremely simplified transformation model of dynamic deformation of a rod-strip consisting of two sections along its length is constructed. It is based on the classical geometrically nonlinear Kirchhoff-Love model on an unfixed section, and the fixed section of finite length is considered to be connected to a rigid and fixed support element through elastic layers. On the fixed section, the deflections of the rod and interlayers are considered zero, and for displacements in the axial direction within the thicknesses of the rod and interlayers, approximations are adopted according to the shear model of S.P. Timoshenko, subject to the conditions of continuity at the points of their connection with each other and immobility at the points of connection of the interlayers with the support element. The conditions for the kinematic coupling of the unfixed and fixed sections of the rod are formulated, and based on these, using the d'Alembert-Lagrange variational principle, the corresponding equations of motion and boundary conditions, as well as the force conditions for coupling of the sections, are derived for the sections introduced into consideration.
Keywords: rod-strip, unfixed and fixed sections, geometric nonlinearity, S.P. Timoshenko model, kinematic and force conditions for the coupling of sections.
Mots-clés : equations of motion 
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     title = {The simplest transformation model of deformation of a rod-strip fixed on a double-sided support element through elastic interlayers},
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V. N. Paimushin; V. M. Shishkin. The simplest transformation model of deformation of a rod-strip fixed on a double-sided support element through elastic interlayers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2024), pp. 98-106. http://geodesic.mathdoc.fr/item/IVM_2024_10_a9/

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