Numerical and experimental analysis of the stiffness and band-gap properties of shell structures with periodically variable cross sections

Yukuan Dou; Jinguang Zhang; Yefa Hu; Xianglong Wen; Xu Xia; Meng Zang

doi:10.1016/j.heliyon.2023.e14191

Numerical and experimental analysis of the stiffness and band-gap properties of shell structures with periodically variable cross sections

Heliyon. 2023 Mar 1;9(3):e14191. doi: 10.1016/j.heliyon.2023.e14191. eCollection 2023 Mar.

Authors

Yukuan Dou^{1

2

3}, Jinguang Zhang^{2

4

3}, Yefa Hu^{2

4

3}, Xianglong Wen^{2

4

3}, Xu Xia^{2

3}, Meng Zang^{2

3}

Affiliations

¹ Sanya Science and Education Innovation Park, Wuhan University of Technology, Sanya 572000, China.
² School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China.
³ Institute of Advanced Material and Manufacturing Technology, Wuhan University of Technology, Wuhan 430070, China.
⁴ Hubei Provincial Engineering Technology Research Center for Magnetic Suspension, Wuhan 430070, China.

Abstract

This paper describes one-dimensional periodic shell structures that have variable cross sections, a new type of periodic shell structures made from photopolymer. This paper will discuss the stiffness of periodic sub-cells that have variable cross sections and the band gaps of Bragg scattering shell structures based on numerical analysis and a series of experiments. This paper uses the Bloch theorem and lumped-mass method to create a band gap model for periodic shell structures. In this paper, an equivalent stiffness model for sub-cells is also created based on the principle of superposition and validated by experiments. Numerical studies and experiments are conducted to examine the effects of geometrical parameters, number of sub-cells, and stiffness of sub-cells on band gaps of one-dimensional periodic shell structures and to test the effectiveness of the models. The findings in this paper prove that by varying the stiffness of sub-cells under a fixed lattice constant, band gaps of one-dimensional periodic shell structures can be decreased. The findings also confirmed that the initial band gap of one-dimensional periodic shell structures can be lowered by increasing the number of sub-cells in a period. Unlike other types of Bragg scattering periodic structures, one-dimensional periodic shell structures allow their longitudinal band gaps to be adjusted under a fixed lattice constant. Those findings serve as a theoretical foundation for the application of Bragg scattering periodic shell structures in low-frequency vibration.

Keywords: Band gaps; Periodic structures; Stiffness; Variable cross sections.