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Nonlinear Vibration Analysis of Laminated Composite Cylindrical Shell Under External Loading Utilizing Meta-Heuristic Optimization Algorithms

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This paper investigates nonlinear vibration analysis of laminated composite cylindrical shells under external loading considering three, four, and five layers. The objective of this study is to optimize fiber angles through the utilization of various meta-heuristic optimization algorithms. The basic equations are derived by the classical shell theory combined with von-Kármán’s nonlinearity. These equations are subsequently solved using the Galerkin method. In the optimization problem, two objective functions are considered including the minimization of vibration amplitude and the maximization of natural frequency. Moreover, in the final optimization process, both objective functions are simultaneously considered. To tackle these optimization problems, two swarm-based metaheuristic algorithms, namely particle swarm optimization (PSO) and whale optimization algorithm (WOA), are employed. The WOA algorithm yields more suitable results for cases with three and four layers, while the PSO algorithm performs better in the five layers case. Thus, considering the antiquity and power of the PSO algorithm, the most famous and powerful swarm-based optimization algorithm, the WOA algorithm's capabilities can also be confirmed for this optimization problem.

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Abbreviations

\(a\) :

Convergence factor

\(b\) :

A constant in the WOA algorithm

\({c}_{1}\) :

Individual learning coefficient

\({c}_{2}\) :

Social learning coefficient

\({E}_{1}\), \({E}_{2}\), \({\nu }_{12}\), \({G}_{12}\) :

Four independent material constants

\({F}_{1}\) :

The objective function of Case1

\({F}_{2}\) :

The objective function of Case2

\({F}_{3}\) :

The objective function of Case2

\({G}_{\mathrm{best}}\) :

Whole swarm's best location

\({J}_{ij}\) :

Bending, extensional, and coupling component’s stiffness

\(k\) :

Number of layers

\(h\) :

Thickness of shell

\({h}_{i}\left(i=\mathrm{1,2},\dots ,k\right)\) :

Thickness of layers

\(Iter\) :

Current iteration number

\({J}_{ij}\) :

Bending, extensional, and coupling components stiffness

\(Q\) :

Excitation amplitude

\({Q}_{ij}\) :

Plane stress-reduced stiffness

\({\overline{Q} }_{ij}\) :

Transformed plane stress-reduced Stiffness

\(R\) :

The radius of the shell

\(r\) :

Random number in the range of 0 and 1

\(t\) :

Time

\({u}_{1}\) :

Random number in the range of 0 and 1

\({u}_{2}\) :

Random number in the range of 0 and 1

\(u, v\) :

Displacements along \(x, y\) axes, respectively

\({V}_{j}\) :

The velocity of the jth particle

\(W\left(t\right)\) :

Deflection amplitude

\(X\) :

Vector of the design variables

\({X}_{j}\) :

Position of the jth particle

\({\overrightarrow{X}}_{\mathrm{rand}}\) :

A random position vector

\(x, y, z\) :

The axial, circumferential, and radial direction of the cylindrical shell

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Acknowledgements

This research is funded by the Project number CN.22.11 of VNU Hanoi – University of Engineering and Technology. The authors are grateful for this support.

Funding

Trường Đại học Công nghệ, Đại học Quốc Gia Hà Nội, CN22.11, Nguyen Dinh Duc.

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Authors and Affiliations

  1. Faculty of Civil Engineering, VNU Hanoi–University of Engineering and Technology, 144 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam

    Nguyen Dinh Duc

  2. Faculty of Mechanical Engineering, Shahrood University of Technology, P. O. Box 316, Shahrood, Iran

    Kamran Foroutan, Seyyed Mojtaba Varedi-Koulaei & Habib Ahmadi

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  1. Nguyen Dinh Duc
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  2. Kamran Foroutan
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Correspondence to Nguyen Dinh Duc.

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Duc, N.D., Foroutan, K., Varedi-Koulaei, S.M. et al. Nonlinear Vibration Analysis of Laminated Composite Cylindrical Shell Under External Loading Utilizing Meta-Heuristic Optimization Algorithms. Iran J Sci Technol Trans Mech Eng (2023). https://doi.org/10.1007/s40997-023-00685-3

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