Shahrood University of Technology Journal of Solid and Fluid Mechanics 2251-9475 14 6 2025 01 20 Investigation of the internal resonances of a beam with a local bistable nonlinear energy sink Investigation of the internal resonances of a beam with a local bistable nonlinear energy sink 33 42 3436 10.22044/jsfm.2025.14638.3868 FA Seyed Sajjad Hoseini Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran Habib Ahmadi Faculty of Mechanical Engineering, Shahrood University of Technology Seyed Sajad Mirhashemi Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran Journal Article 2024 06 10 In this article, the nonlinear vibrations of a simply supported beam with a locally attached bistable nonlinear energy sink (NES) have been studied. This study focuses on the effects of internal resonance on the dynamic behavior of beams and how vibrations can be controlled by a nonlinear energy sink (NES). Bistable nonlinear energy sinks are increasingly utilized due to their higher efficiency compared to monostable nonlinear energy sinks. A key area of interest in such problems is the forced internal resonances, where the energy transferred from the beam to the nonlinear energy sink is substantial. To address this, the system's equations of motion were derived and made dimensionless, followed by discretization using Galerkin’s method. The method of multiple scales (MMS) was then applied to investigate the 3:1 primary internal resonance. The findings indicate that the frequency response curves are highly sensitive to slight changes in nonlinear energy sink parameters, particularly damping. However, the nonlinear energy sink's softening behavior in the frequency domain, as opposed to the beam's behavior, means that physical limitations due to nonlinear energy sink mass displacement can adversely impact its efficiency. Additionally, the use of NES in beams can significantly improve dynamic stability and extend the service life of structures. The findings of this study can contribute to more optimal design and effective utilization of NES in engineering applications. In this article, the nonlinear vibrations of a simply supported beam with a locally attached bistable nonlinear energy sink (NES) have been studied. This study focuses on the effects of internal resonance on the dynamic behavior of beams and how vibrations can be controlled by a nonlinear energy sink (NES). Bistable nonlinear energy sinks are increasingly utilized due to their higher efficiency compared to monostable nonlinear energy sinks. A key area of interest in such problems is the forced internal resonances, where the energy transferred from the beam to the nonlinear energy sink is substantial. To address this, the system's equations of motion were derived and made dimensionless, followed by discretization using Galerkin’s method. The method of multiple scales (MMS) was then applied to investigate the 3:1 primary internal resonance. The findings indicate that the frequency response curves are highly sensitive to slight changes in nonlinear energy sink parameters, particularly damping. However, the nonlinear energy sink's softening behavior in the frequency domain, as opposed to the beam's behavior, means that physical limitations due to nonlinear energy sink mass displacement can adversely impact its efficiency. Additionally, the use of NES in beams can significantly improve dynamic stability and extend the service life of structures. The findings of this study can contribute to more optimal design and effective utilization of NES in engineering applications. https://jsfm.shahroodut.ac.ir/article_3436_6d97afbb50ce0e60dd87b45c3b1af808.pdf