A mapping method of dynamic response and stiffness characteristics for realizing a customized nonlinear oscillator
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ORIGINAL PAPER
A mapping method of dynamic response and stiffness characteristics for realizing a customized nonlinear oscillator Zhongxin Yuan . Weiqun Liu
. Mengqi Ye
Received: 19 April 2020 / Accepted: 11 November 2020 Ó Springer Nature B.V. 2020
Abstract With nonlinear systems extensively studied for applications in vibration isolation, energy harvesting, etc., most of the studies focused on the response of the nonlinear oscillator defined by some explicit equations, namely the typical oscillator. Rare studies or approaches are devoted to the non-typical nonlinear oscillator for which the stiffness profile is possible defined by an arbitrary curve without an explicit function. This paper proposes a novel design method for both typical and non-typical monostable hardening oscillators, especially for the latter one in order to achieve some arbitrarily specified response. The key idea is to construct a series of linear equivalent oscillators to reproduce the response of the nonlinear oscillator. A trial stiffness characteristic expression of the linear equivalent oscillators has been given as a function of several particular variables. It has been verified that the linear equivalent oscillators can obtain the response for some typical nonlinear oscillators. Moreover, the method can be also used in a reversed way to identify the stiffness characteristics from a given response for either typical or non-typical systems. In particular, this parameter identification feature can be utilized to design a customized oscillator with arbitrarily specified hardening response. By constructing the linear equivalent Z. Yuan W. Liu (&) M. Ye School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China e-mail: [email protected]
oscillators to reproduce the desired response, the linear equivalent stiffness expression can be determined, while the customized nonlinear stiffness characteristics can be obtained accordingly. Experiments on an elaborated example have validated effectiveness of the proposed method. It shows that the mapping method can be used to determine the proper stiffness characteristics for customized hardening response beyond the scope of typical nonlinear oscillators. Keywords Nonlinear oscillators Equivalent linear oscillators Customized stiffness characteristics Arbitrary hardening response
1 Introduction In many cases, nonlinear behavior is often harmful and required to be controlled. However, many recent studies have shown that nonlinear systems perform well in some areas such as vibration isolation [1] and energy harvesting [2–7]. The special backbone response of nonlinear systems brings benefits in these applications. Take the monostable hardening oscillator as an example; the system has a much better response bending to the high-frequency side when excited by a forward-sweep excitation in comparison with the case of a much worse response when excited
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by a reverse-sweep excitation. Softeni
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