Free Vibration Behavior of Three-skin Conical Shells with Composite Lattice Core Based on Semi-analytical and Finite Element Methods

Document Type : Dynamics, Vibrations, and Control

Authors

1 Ph.D. Student, Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

2 Corresponding author: Associate Professor, Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

3 Associate Professor, Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

Abstract

In this paper, free vibration behavior of three-skin conical shells with arbitrary boundary conditions is studied based on semi-analytical and numerical methods. The three-layer shell consists of identical outer-inner composite face sheets and a lattice core with regular hexagonal cells made of composite helical and circumferential ribs. For this purpose, t, the dynamic equations along with the boundary conditions of such sandwich shells are derived using the equivalent stiffness method, Donnell’s classic shell theory, and Hamilton’s principle. The frequency equation is presented by solving the integral form of these governing equations based on the Galerkin method. The vibration mode shapes in the form of forward or backward waves in the circumferential direction and standing waves in the direction of the cone length (Euler-Bernoulli beam modal functions) are used in order to obtain natural frequencies. Also, ABAQUS FE simulations are carried out to verify the vibration behavior predicted by the Galerkin solution method. Finally, parametric studies are performed to investigate the effects of geometric dimensions and boundary conditions on the response quantities. Numerical results show that there is a very good agreement between the natural frequencies obtained by Galerkin and ABAQUS FE methods (i.e., the maximum difference in the results is less than 10%). Also, the effects of face sheet thickness and the rib width on the natural frequencies of three-layer composite lattice conical shell with different supports are significant.

Highlights

  • Free vibration analysis of sandwich conical shells is presented based on the semi-analytical and numerical methods.
  • The closed-form solution of natural frequencies is developed for various boundary conditions.
  • A comparison between the results of closed-form solution and ABAQUS FEM simulations is presented. 

Keywords

Main Subjects

References

[1] Vasiliev VV, Morozov EV. Advanced mechanics of composite materials and structures. Elsevier; 2018.
[2] Davies JM, editor. Lightweight sandwich construction. John Wiley & Sons; 2008.
[3] Vinson J. The behavior of sandwich structures of isotropic and composite materials. Routledge; 2018. DOI 10.1201/9780203737101.
[4] Shatov AV, Burov AE, Lopatin AV. Buckling of composite sandwich cylindrical shell with lattice anisogrid core under hydrostatic pressure. InJournal of Physics: Conference Series 2020 (Vol. 1546, No. 1, p. 012139). IOP Publishing. DOI 10.1088/1742-6596/1546/1/012139.
[5] Zarei M, Rahimi GH, Hemmatnezhad M. Global buckling analysis of laminated sandwich conical shells with reinforced lattice cores based on the first-order shear deformation theory. International Journal of Mechanical Sciences. 2020;187:105872. DOI 10.1016/j.ijmecsci.2020.105872.
[6] Yang JS, Liu ZD, Schmidt R, Schröder KU, Ma L, Wu LZ. Vibration-based damage diagnosis of composite sandwich panels with bi-directional corrugated lattice cores. Composites Part A: Applied Science and Manufacturing. 2020;131:105781. DOI 10.1016/j.compositesa.2020.105781.
[7] Shahgholian-Ghahfarokhi D, Rahimi G, Zarei M, Salehipour H. Free vibration analyses of composite sandwich cylindrical shells with grid cores: Experimental study and numerical simulation. Mechanics Based Design of Structures and Machines. 2022;50(2):687-706. DOI 10.1080/15397734.2020.1725565.
[8] Fallah F, Taati E, Asghari M. Decoupled stability equation for buckling analysis of FG and multilayered cylindrical shells based on the first-order shear deformation theory. Composites Part B: Engineering. 2018 Dec 1;154:225-41.  DOI 10.1016/j.compositesb.2018.07.051.
[9] Fallah F, Taati E. On the nonlinear bending and post-buckling behavior of laminated sandwich cylindrical shells with FG or isogrid lattice cores. Acta Mechanica. 2019;230:2145-69. DOI 10.1007/s00707-019-02385-z.
[10] Chai Y, Li F, Song Z. Nonlinear flutter suppression and thermal buckling elimination for composite lattice sandwich panels. AIAA Journal. 2019 Nov;57(11):4863-72.  DOI 10.2514/1.J058307.
[11] Nazari A, Naderi AA, Malekzadefard K, Hatami A. Experimental and numerical analysis of vibration of FML-stiffened circular cylindrical shell under clamp-free boundary condition. DOI 10.22068/jstc.2018.80212.1415.
[12] Shahgholian-Ghahfarokhi D, Rahimi G. New analytical approach for buckling of composite sandwich pipes with iso-grid core under uniform external lateral pressure. Journal of Sandwich Structures & Materials. 2021;23(1):65-93.  DOI 10.1177/1099636218821397.
[13] Karttunen AT, Reddy JN, Romanoff J. Two-scale constitutive modeling of a lattice core sandwich beam. Composites Part B: Engineering. 2019 Mar 1;160:66-75. DOI 10.1016/j.compositesb.2018.09.098.
[14] Li C, Shen HS, Yang J. Low-velocity impact response of cylindrical sandwich shells with auxetic 3D double-V meta-lattice core and FG GRC facesheets. Ocean Engineering. 2022 Oct 15;262:112299. DOI 10.1016/j.oceaneng.2022.112299.
[15] Zarei M, Rahimi GH. Buckling resistance of joined composite sandwich conical–cylindrical​ shells with lattice core under lateral pressure. Thin-Walled Structures. 2022 May 1;174:109027.  DOI 10.1016/j.tws.2022.109027.
[16] Reddy JN. Mechanics of laminated composite plates and shells: theory and analysis. CRC press; 2003.
[17] Totaro G. Flexural, torsional, and axial global stiffness properties of anisogrid lattice conical shells in composite material. Composite Structures. 2016;153:738-45.  DOI 10.1016/j.compstruct.2016.06.072.
[18] Taati E, Fallah F, Ahmadian MT. Closed-form solution for free vibration of variable-thickness cylindrical shells rotating with a constant angular velocity. Thin-Walled Structures. 2021;166:108062.. Thin-Walled Structures, 2021: 166, 108062.  DOI 10.1016/j.tws.2021.108062.
[19] Sharma CB, Johns DJ. Vibration characteristics of a clamped-free and clamped-ring-stiffened circular cylindrical shell. Journal of Sound and Vibration. 1971;14(4):459-74.  DOI 10.1016/0263-8231(84)90011-9.
[20] Rao SS. Vibration of continuous systems. John Wiley & Sons; 2019.
[21] Barbero EJ. Finite element analysis of composite materials using Abaqus®. CRC press; 2023.  DOI 10.1201/9781003108153.
[22] Gibson, R. F. Principles of composite material mechanics. CRC press, 2016.  DOI 10.1201/b19626
[23] Halpin, J. C., & Tsai, S. W. Environmental factors in composite materials design. US Air Force Technical Report AFML TR, 1967: 67423, 749-767.
[24] Rahnama M, Hamzeloo SR, Morad Sheikhi M. Vibration analysis of anisogrid composite lattice sandwich truncated conical shells: Theoretical and experimental approaches. Journal of Composite Materials. 2024;58(22):2429-42. DOI 10.1177/00219983241264364.
Aerospace Mechanics
Volume 20, Issue 3 - Serial Number 77
Serial No. 77, Summer
November 2024
Pages 75-86

Files

History

  • Receive Date: 01 March 2024
  • Revise Date: 20 April 2024
  • Accept Date: 25 April 2024
  • Publish Date: 21 November 2024

Share

How to cite

Statistics