Broadening the frequency bandwidth of a finite extensibility nonlinear vibration absorber by exploiting its internal res
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ORIGINAL PAPER
Broadening the frequency bandwidth of a finite extensibility nonlinear vibration absorber by exploiting its internal resonances Alex Elías-Zúñiga
· Luis Manuel Palacios-Pineda
· Daniel Olvera-Trejo
· Oscar Martínez-Romero
Received: 2 July 2019 / Accepted: 23 May 2020 © Springer Nature B.V. 2020
Abstract In this paper, the dynamics response of a finite extensibility nonlinear elastic (FENE) absorber attached to a nonlinear primary system is investigated by writing the modal form equations of motion as two decoupled, damped, and forced cubic–quintic expressions of the Duffing type. Then, numerical integration solutions of these decoupled expressions are used to find frequency–amplitude response plots, the largest Lyapunov exponents, suppression bandwidth, and force transmissibility that are used for investigating how the addition of the FENE absorber modifies the vibration conditions of the main system. The results suggest that the addition of the FENE absorber can lead to vibration mitigation of the primary system while enhancing its performance when the system operates in the vicinity of internal resonance conditions. A. Elías-Zúñiga (B)· L. M. Palacios-Pineda · D. Olvera-Trejo · O. Martínez-Romero Departamento de Ingeniería Mecánica y Materiales Avanzados, Tecnologico de Monterrey, Escuela de Ingenieria y Ciencias, Av. E. Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico e-mail: [email protected] D. Olvera-Trejo e-mail: [email protected] O. Martínez-Romero e-mail: [email protected] L. M. Palacios-Pineda Tecnológico Nacional de México, Instituto Tecnológico de Pachuca, Carr. México-Pachuca Km 87.5, 42080 Pachuca, Hidalgo, Mexico e-mail: [email protected]
Keywords Nonlinear absorber system · Nonlinear normal modes · Lyapunov stability · Chebyshev polynomials · Internal resonances
1 Introduction The dynamic vibration absorber (DVA) is a device used to control undesirable forced vibrational motion of a machine, a machine part, or various kinds of delicate equipment, especially at a frequency close to resonance. This decrease in vibration is accomplished by transferring the energy of the main system to the absorber. In an undamped linear system, the idea is to make the natural frequency of the absorber equal to the constant frequency of the disturbing force. When this is done, the small absorber system vibrates so that its spring force is then equal and opposite to the driving force at all times, and hence, the main system does no vibrate at all. Unfortunately, this concept cannot be used in such a straightforward manner for a damped system or when either the primary or the absorber system is nonlinear. Ormondroyd and Den Hartog [1] developed a theory to describe the dynamic behavior of a linear DVA and, in particular, how it must be tuned and damped, i.e., how the values for the absorber spring stiffness and the coefficient of viscosity of the damper must be chosen to provide optimum absorber performance. The design of DVA devices is usually based on one of two types of applicati
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