A comprehensive investigation on nonlinear vibration and bending characteristics of bio-inspired helicoidal laminated composite structures

• Published in: Applied mathematics and mechanics Vol. 46; no. 1; pp. 81 - 100
• Main Authors: Saurabh, S., Kiran, R., Singh, D., Vaish, R., Chauhan, V. S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Boundary conditions; Classical Mechanics; Composite structures; Configurations; Finite element method; Fluid- and Aerodynamics; Free vibration; Laminar composites; Laminates; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Mechanical properties; Nonlinearity; Partial Differential Equations; Plates (structural members); Resonant frequencies; Shear deformation; Structural design; Thickness ratio; O322; bio-inspired composite plate; finite element method (FEM); Green-Lagrange; 74H60; nonlinear; inverse hyperbolic shear deformation theory (IHSDT); helicoidal
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3200-7

Bio-inspired helicoidal composite laminates, inspired by the intricate helical structures found in nature, present a promising frontier for enhancing the mechanical properties of structural designs. Hence, this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates. The inverse hyperbolic shear deformation theory (IHSDT) of plates is employed to characterize the displacement field, with the incorporation of Green-Lagrange nonlinearity. The problem is modeled using the C 0 finite element method (FEM), and an in-house code is developed in the MATLAB environment to solve it numerically. Various helicoidal layup configurations including helicoidal recursive (HR), helicoidal exponential (HE), helicoidal semi-circular (HS), linear helicoidal (LH), and Fibonacci helicoidal (FH) with different layup sequences and quasi-isotropic configurations are studied. The model is validated, and parametric studies are conducted. These studies investigate the effects of layup configurations, side-to-thickness ratio, modulus ratios, boundary conditions, and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates. The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors. Moreover, this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.