Dynamic study of a bounded cantilevered nonlinear spring for vibration reduction applications: a comparative study
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ORIGINAL PAPER
Dynamic study of a bounded cantilevered nonlinear spring for vibration reduction applications: a comparative study Christian E. Silva · James M. Gibert · Amin Maghareh · Shirley J. Dyke
Received: 6 December 2019 / Accepted: 28 July 2020 © Springer Nature B.V. 2020
Abstract The objective of this study is to develop, simulate and verify experimentally a model of a nonlinear spring, based on the principle of a cantilevered beam with a mass on its tip, and whose overall lateral vibration is constrained by a specially shaped rigid boundary. The focus here is the use of this spring for vibration reduction applications. The modeling approach uses concepts of plane kinematics of rigid bodies, combined with quasi-static analysis to develop suitable equations of motion for a base-excited spring with a ninth-order geometric nonlinearity. In addition, a parametric identification procedure is implemented for obtaining the required coefficients for computational simulations. An approximated analytical solution to the model is completed with the aid of the method of harmonic balance and its stability is assessed through Floquet theory. Finally, the model is experimentally verified, with the use of two specimens, fabricated specifically for this study. The model, simulations and experimental measurements show the hardening and broadband behavior of the nonlinear spring.
C. E. Silva (B)· J. M. Gibert · A. Maghareh · S. J. Dyke Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA e-mail: [email protected] C. E. Silva Facultad de Ingeniería Mecánica y Ciencias de la Producción, Escuela Superior Politécnica del Litoral, ESPOL, Km 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador
Keywords Nonlinear spring · Nonlinear cantilever beam · Nonlinear modeling
1 Introduction Nonlinear springs can be constructed from many types of physical systems that take advantage of geometric nonlinearities. Important applications of nonlinear springs that have received notable attention in recent years are nonlinear energy sinks (NESs) and energy harvesting systems. The former are basically nonlinear springs that can be attached to primary vibratory systems as nonlinear passive vibration dampers, to which the vibratory energy is pumped from the primary oscillator. However, the latter is implemented for an inverse purpose, i.e., the energy generated in the spring is stored by conveying it to an accumulation system. Several classes of physical realizations of NES devices based on nonlinear spring systems have been reported in the literature over the past twenty years. In a recent review paper, Lu provides a comprehensive overview of the contributions in the field of NES [10]. Amongst NES devices, a widely studied and physically implemented prototype is the wire NES, reported in the literature by several scholars [11,21,25,29]. However, other classes of nonlinear springs based on different physical phenomena have also been extensively reported [27,28,30]. More recent developments in nonlinear springs have been p
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