Modelling, analyzing and simulating the complex dynamics of mass sensors based on a functionally graded nanobeam model

• Published in: Applied mathematical modelling Vol. 109; pp. 21 - 35
• Main Authors: Li, Mingyuan, Zhang, Wei, Wu, Qiliang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2022
• Subjects: Functionally graded nanobeam; Infinite-dimensional homoclinic chaos; Size-dependent effect; Viscoelastic effect; Functionally graded nanobeam; Size-dependent effect; Viscoelastic effect; Infinite-dimensional homoclinic chaos
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.04.002

•Size-dependent, FG and viscoelastic effects are incorporated to model the mass sensor.•Dirac delta function is used to describe the attached particles.•An analytic expression determining chaotic threshold is derived by infinite-dimensional global perturbation method.•Size-dependent, FG and viscoelastic effects on chaotic dynamics and vibration characteristics of FG nanobeam are highlighted. This paper proposes a theoretical, miniature, structural model, a functionally graded nanobeam (FGNB), to investigate the complex dynamic mechanism and the responses of particle mass sensors to an electric load in practical applications. The Kelvin-Voigt model and the nonlocal strain gradient theory (NSGT) describe the viscoelastic and size-dependent effects. A generalized Hamilton's principle is used to obtain a mathematical model of FGNB with attached particles. The multiple-scale method and global perturbation method of an infinite-dimensional system are applied to derive the threshold of the homoclinic chaos phenomenon. Then, the differential quadrature method (DQM) is employed to numerically test the validity of the proposed model and the theoretical predication. Numerical results highlight the FG index, size-dependent parameters, and viscoelastic coefficient to determine the influencing vibration characteristics of the FGNB. The results are useful for studying the vibration responses of sensitive and high-efficiency sensors.