Calculus Through Transfer-Matrix Method of Continuous Circular Plates for Applications to Chemical Reactors

Laurenţiu-Eusebiu Chifor, Mihai-Sorin Tripa, Ilie-Cristian Boldor, Cosmin-Sergiu Brisc, Nicolae Nedelcu, Andrei-Călin Szîrbe, Liviu Bolunduţ, Carmen-Gabriela Băcilă, Veronica Mîndrescu, Ioan-Aurel Cherecheş, Vlad Mureşan and Viorica-Mihaela Suciu ()
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Laurenţiu-Eusebiu Chifor: Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Mihai-Sorin Tripa: Department of Design Engineering and Robotics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Ilie-Cristian Boldor: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Cosmin-Sergiu Brisc: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Nicolae Nedelcu: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Andrei-Călin Szîrbe: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Liviu Bolunduţ: Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Carmen-Gabriela Băcilă: Department of Management and Economic Engineering, Technical University of Cluj-Napoca, 400012 Cluj-Napoca, Romania
Veronica Mîndrescu: Department of Motor Performance, Transylvania University of Braşov, 500036 Braşov, Romania
Ioan-Aurel Cherecheş: Department of Road Vehicles and Transport, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Vlad Mureşan: Department of Automation, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Viorica-Mihaela Suciu: Department of Mechanical Engineering, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: This paper presents an original approach through Transfer-Matrix Method applied for the calculus of the continuous circular plate embedded at the exterior circumference, charged with asymmetrical uniform load on the entire upper surface of the plate. Continuous circular plates are elements often found in practice, in the machine building, aeronautics, chemical industries (the bottoms of chemical reactors), and in petrochemical, mechanical, robotic, medical, military, nuclear, and aerospace industries. The calculus of continuous circular plates is a special problem both from the point of view of the theory of elasticity and from the point of view of the mathematical approach. The results obtained with Transfer-Matrix Method were compared and validated with those obtained from classical analytical calculation, the Theory of Elasticity. Transfer-Matrix Method is an elegant method and relatively easy to program. In future research, we want to validate our results with those given by the Finite Elements Method and those measured experimentally.

Keywords: continuous circular plate; circular embedded contour; axisymmetric uniform load; bending; Transfer-Matrix Method; state vector; transfer matrix; charge density (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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