https://doi.org/10.1140/epjp/s13360-022-02357-8
Regular Article
Free vibration analysis of laminated elliptic cylindrical panel with varying thickness using a meshfree method
1
Department of Mechanical Science and Technology, Kim Chaek University of Technology, 950003, Pyongyang, Democratic People’s Republic of Korea
2
Department of Mechanical Engineering, Pyongyang University of Mechanical Engineering, 999093, Pyongyang, Democratic People’s Republic of Korea
3
Department of Organic Chemistry, Hamhung University of Chemical Engineering, Hamhung, Democratic People’s Republic of Korea
Received:
13
September
2021
Accepted:
6
January
2022
Published online:
27
January
2022
The aim of this paper is to study the free vibration behaviors of laminated elliptic cylindrical panel with varying thickness (LECPVT) based on the first-order shear deformation theory by means of a meshfree strong form method. The displacement functions are approximated by a meshfree Chebyshev-radial point interpolation method (Chebyshev-RPIM) shape function using the combined basis function of multi-quadrics radial function and Chebyshev polynomials. The governing equations and boundary conditions of LECPVT derived by Hamilton's principle are discretized by the meshfree Chebyshev-RPIM shape function, and the boundary conditions are generalized by introducing an artificial spring technique. In the stiffness matrices for the laminated panels with varying thickness are supplemented the partial derivatives of the stiffness coefficients. To verify the accuracy of the proposed method, comparison with published literature and finite element software ABAQUS is made, and very good agreement is observed. Effects of some geometries, boundary conditions, lamination schemes and thickness parameters on the natural frequencies of LECPVT are discussed. Through numerical examples, some new vibration analysis results of LECPVT with various geometries and boundary conditions are presented, which may serve as benchmark solutions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
