Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: In this paper, a nonlinear vibration system composed of a linear spring-mass-damper structure system of any order and a hysteresis damper is derived and it is shown that the function remains upper half plane in the complex plane.
Abstract: Hysteresis elements such as elasto-plastic dampers are important for mechanical structures. They have nonlinearities and thus the vibration characteristics of mechanical structures with hysteresis elements are not clarified yet and need further studies. In this paper, the investigation of the dynamical stability of mechanical structures with a hysteresis element is performed by means of describing function method, which is on the basis of linear approximation of the hysteresis element. The nonlinear vibration system is composed of a linear spring-mass-damper structure system of any order and a hysteresis damper. The describing function of a hysteresis damper is derived and it is shown that the function remains upper half plane in the complex plane. According to the passivity of the linear structure system, this fact leads to the vibration system that is stable for any harmonic excitation. Next, the responses for seismic excitation are examined in simulation by using two typical models of the hysteresis element, a bilinear model and a Ramberg-Osgood model. The effects of the second stiffness of the dampers and the amplitude of the excitation motion are investigated using an actually recorded earthquake motion. The simulation results imply that the determination of the second stiffness requires the trade-off between an oscillation and a drift for designing earthquake-proof mechanical structures with the hysteresis damper.
4 citations
TL;DR: In this article, the internal nonlinear forces are expressed using describing functions and the complex equations governing the responses of multiple frequency components are established and are iteratively solved using the Inverse Matrix Update Method.
Abstract: Considering the operating point drift in the dynamic responses of locally nonlinear structures, a new iterative method based on describing functions is introduced to solve for the steady-state frequency response. Drift in the operating point arises in the presence of asymmetric nonlinearity, pre-deformation or static loads. In this study, the internal nonlinear forces are expressed using describing functions. The complex equations governing the responses of multiple frequency components are established and are iteratively solved using the Inverse Matrix Update Method. The nonlinear frequency responses can thus be rapidly obtained, and the validity of the method is verified by simulations. The presented method can be applied to large-scale structures with multiple nonlinear elements.
4 citations
TL;DR: It is shown in this paper that the dithered designs which contain a saturating nonlinear element may have sensor noise properties worse than the LTI design for the same uncertainty or disturbance problem, despite the considerably smaller bandwidth of the nonlinear d ithered design.
4 citations
TL;DR: A tuning method that optimizes the PID control gain for tracking control is introduced herein and the results demonstrate the effectiveness of the proposed method.
4 citations
25 May 1993
TL;DR: In this paper, the stability analysis of a nonlinear system using simplicial algorithms is presented, where the system analyzed is a unstable first-order plant driven by a Bang-Bang actuator.
Abstract: This paper covers a new method for the stability analysis of a nonlinear system using simplicial algorithms. The system analyzed is a unstable first order plant, driven by a Bang-Bang actuator. A describing function model of the actuator is used in this analysis. This system is implemented on a digital computer, and in analog circuit form, to demonstrate the practicality of the method.
4 citations