Experimental implementation of an optimum viscoelastic vibration absorber for cubic nonlinear systems

• Published in: Engineering structures 2018-05, Vol.163, p.323-331
• Main Authors: Bronkhorst, Klaas B., Febbo, Mariano, Lopes, Eduardo M.O., Bavastri, Carlos A.
• Format: Article
• Language: English
• Subjects: Absorbers; Computer simulation; Cubic nonlinear systems; Equations of motion; Harmonic balance method; Least squares method; Mathematical models; Nonlinear equations; Nonlinear systems; Optimization; Parameter identification; Physical properties; Stiffness; Vibration; Vibration analysis; Vibration control; Vibrations; Viscoelastic dynamic vibration absorber; Viscoelasticity
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2018.02.074

[Display omitted] •An identification process using transmissibility for a cubic nonlinear system is proposed.•An optimum design of a VDVA is carried out based on a simple mathematical model.•An experimental implementation of the optimum VDVA validates theoretical predictions.•A large reduction of the vibration amplitude of the cubic nonlinear system is obtained. The design of vibration control devices requires an accurate knowledge of the dynamic behavior of the system to be controlled. The present work aims to propose a methodology to identify a single degree-of-freedom nonlinear system with cubic stiffness and a methodology for the optimum design of a viscoelastic dynamic absorber with linear behavior, intending to reduce the vibrations of the cubic system to as low a level as possible. The identification is performed through an inverse process. The nonlinear model with cubic stiffness used in this work produces a transmissibility curve which is fitted using the least squares method to the experimentally obtained transmissibility curve. With the identified physical parameters of the nonlinear system, a viscoelastic dynamic vibration absorber is optimally designed. To achieve these goals, the following tools are employed: the concept of generalized equivalent parameters, to couple the viscoelastic dynamic absorber to the nonlinear system; the four-parameter fractional derivative model, to represent the viscoelastic material; and nonlinear optimization techniques and the harmonic balance method to solve the nonlinear equation of motion. Numerical simulations and the corresponding physical implementation of the system are carried out and their results are compared.