Flutter of high-dimension nonlinear system for a FGM truncated conical shell

• Published in: Mechanics of advanced materials and structures Vol. 25; no. 1; pp. 47 - 61
• Main Authors: Hao, Y. X., Yang, S. W., Zhang, W., Yao, M. H., Wang, A. W.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02-01-2018; Taylor & Francis Ltd
• Subjects: Aerodynamic heating; Aerodynamics; Concentration (composition); Conical shells; Curvature; Differential equations; Dynamic characteristics; Eigenvalues; Equilibrium equations; Flutter; Flutter boundary; functionally graded materials; Functionally gradient materials; Galerkin method; Hamilton's principle; high dimension; nonlinear dynamics; Nonlinear systems; Piston theory; Runge-Kutta method; Supersonic aircraft; Temperature distribution; truncated conical shell; Vibration
• ISSN: 1537-6494; 1537-6532
• DOI: 10.1080/15376494.2016.1255815

The nonlinear flutters of a truncated conical shell, which is subjected to aerodynamic pressure and aerodynamic heating, are researched. Material properties with gradient features along the radial direction depend on the temperature. The supersonic aerodynamic force is obtained by applying the first-order piston theory, including the correction factor for curvature. The temperature in the external surface of the functionally graded material truncated conical shell rises as a result of viscous aerodynamic heating, and the temperature distribution along the thickness can be described by polynomial series. Hamilton's principle is utilized to obtain the nonlinear partial differential equilibrium equation of the system. Using Galerkin's method, a high-dimensional nonlinear system can be derived. Without considering the parts of nonlinear terms and the external forcing excitation, the flutter boundaries are obtained by solving the eigenvalues problem. The influences of ratios of top radius to thickness, semi-vertex angle, and volume fraction index on nonlinear dynamic characteristics of functionally graded material truncated conical shell are studied in detail by the fourth-order Runge-Kutta algorithm.