Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory
This work analyzes the aero-elastic oscillations of cantilever beams reinforced by carbon nanotubes (CNTs). Four different distributions of single-walled CNTs are assumed as the reinforcing phase, in the thickness direction of the polymeric matrix. A modified third-order piston theory is used as an...
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2025-08-01
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| author | Mehdi Alimoradzadeh Francesco Tornabene Rossana Dimitri |
| author_facet | Mehdi Alimoradzadeh Francesco Tornabene Rossana Dimitri |
| author_sort | Mehdi Alimoradzadeh |
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| description | This work analyzes the aero-elastic oscillations of cantilever beams reinforced by carbon nanotubes (CNTs). Four different distributions of single-walled CNTs are assumed as the reinforcing phase, in the thickness direction of the polymeric matrix. A modified third-order piston theory is used as an accurate tool to model the supersonic air flow, rather than a first-order piston theory. The nonlinear dynamic equation governing the problem accounts for Von Kármán-type nonlinearities, and it is derived from Hamilton’s principle. Then, the Galerkin decomposition technique is adopted to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation. This is solved analytically according to a multiple time scale method. A comprehensive parametric analysis was conducted to assess the influence of CNT volume fraction, beam slenderness, Mach number, and thickness ratio on the fundamental frequency and lateral dynamic deflection. Results indicate that FG-X reinforcement yields the highest frequency response and lateral deflection, followed by UD and FG-A patterns, whereas FG-O consistently exhibits the lowest performance metrics. An increase in CNT volume fraction and a reduction in slenderness ratio enhance the system’s stiffness and frequency response up to a critical threshold, beyond which a damped beating phenomenon emerges. Moreover, higher Mach numbers and greater thickness ratios significantly amplify both frequency response and lateral deflections, although damping rates tend to decrease. These findings provide valuable insights into the optimization of CNTR composite structures for advanced aeroelastic applications under supersonic conditions, as useful for many engineering applications. |
| format | Article |
| id | doaj-art-e5b2a4555f2a4e2c8d2d30a6c277241d |
| institution | Kabale University |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-e5b2a4555f2a4e2c8d2d30a6c277241d2025-08-20T04:00:50ZengMDPI AGApplied Sciences2076-34172025-08-011515870010.3390/app15158700Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston TheoryMehdi Alimoradzadeh0Francesco Tornabene1Rossana Dimitri2Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, IranDepartment of Innovation Engineering, University of Salento, 73100 Lecce, ItalyDepartment of Innovation Engineering, University of Salento, 73100 Lecce, ItalyThis work analyzes the aero-elastic oscillations of cantilever beams reinforced by carbon nanotubes (CNTs). Four different distributions of single-walled CNTs are assumed as the reinforcing phase, in the thickness direction of the polymeric matrix. A modified third-order piston theory is used as an accurate tool to model the supersonic air flow, rather than a first-order piston theory. The nonlinear dynamic equation governing the problem accounts for Von Kármán-type nonlinearities, and it is derived from Hamilton’s principle. Then, the Galerkin decomposition technique is adopted to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation. This is solved analytically according to a multiple time scale method. A comprehensive parametric analysis was conducted to assess the influence of CNT volume fraction, beam slenderness, Mach number, and thickness ratio on the fundamental frequency and lateral dynamic deflection. Results indicate that FG-X reinforcement yields the highest frequency response and lateral deflection, followed by UD and FG-A patterns, whereas FG-O consistently exhibits the lowest performance metrics. An increase in CNT volume fraction and a reduction in slenderness ratio enhance the system’s stiffness and frequency response up to a critical threshold, beyond which a damped beating phenomenon emerges. Moreover, higher Mach numbers and greater thickness ratios significantly amplify both frequency response and lateral deflections, although damping rates tend to decrease. These findings provide valuable insights into the optimization of CNTR composite structures for advanced aeroelastic applications under supersonic conditions, as useful for many engineering applications.https://www.mdpi.com/2076-3417/15/15/8700carbon nanotubesEuler–Bernoulli beam theorymodified third-order piston theorymultiple time scale methodnonlinear vibrationsupersonic flow |
| spellingShingle | Mehdi Alimoradzadeh Francesco Tornabene Rossana Dimitri Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory Applied Sciences carbon nanotubes Euler–Bernoulli beam theory modified third-order piston theory multiple time scale method nonlinear vibration supersonic flow |
| title | Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory |
| title_full | Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory |
| title_fullStr | Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory |
| title_full_unstemmed | Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory |
| title_short | Aeroelastic Oscillations of Cantilever Beams Reinforced by Carbon Nanotubes Based on a Modified Third-Order Piston Theory |
| title_sort | aeroelastic oscillations of cantilever beams reinforced by carbon nanotubes based on a modified third order piston theory |
| topic | carbon nanotubes Euler–Bernoulli beam theory modified third-order piston theory multiple time scale method nonlinear vibration supersonic flow |
| url | https://www.mdpi.com/2076-3417/15/15/8700 |
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