Dynamic Response of Doubly-Curved Shallow Shells to Periodic External Action

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Abstract

Shallow shells of double curvature are often used as elements of building structures and are subjected to various external effects, including dynamic periodic loads. The paper proposes to extend the previously proposed approach to modeling the process of deformation of thin shells to a class of problems with periodic effects. A mathematical model is used based on the Timoshenko - Reissner hypotheses, taking into account transverse shears, geometric nonlinearity and rotational inertia. The calculation algorithm is based on the method of L.V. Kantorovich and the Rosenbrock method for solving rigid ODE systems. The calculations are performed in Maple. Dynamic responses are obtained for an isotropic shallow shell of double curvature at different frequency values, and vertical displacement fields are shown at peak values of the oscillation amplitude.

About the authors

Alexey A. Semenov

Saint Petersburg State University of Architecture and Civil Engineering

Author for correspondence.
Email: sw.semenov@gmail.com
ORCID iD: 0000-0001-9490-7364
SPIN-code: 9057-9882

Doctor of Technical Sciences, Professor of the Department of Information Systems and Technologies

Saint Petersburg, Russia

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