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Three‐dimensional vibration analysis of simply supported laminated cylindrical shells and panels by a strong SaS formulation
Author(s) -
Kulikov G. M.,
Plotnikova S. V.,
Kulikov M. G.
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800100
Subject(s) - lagrange polynomial , statics , shell (structure) , chebyshev polynomials , vibration , interpolation (computer graphics) , surface (topology) , mathematics , chebyshev filter , polynomial , structural engineering , mathematical analysis , geometry , computer science , motion (physics) , engineering , physics , classical mechanics , mechanical engineering , acoustics , artificial intelligence
In this paper, the strong sampling surfaces (SaS) formulation developed earlier by the authors to solve the statics problems for plates and shells is extended to the three‐dimensional (3D) vibration analysis of laminated composite shells. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange polynomials in approximations of displacements and strains through the layer thicknesses leads to a robust laminated shell formulation. The feature of the proposed strong SaS formulation is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D vibration analysis of laminated cylindrical shells and panels.