Tuning Methodology of Nonlinear Vibration Absorbers Coupled to Nonlinear Mechanical Systems

2011 ◽  
Author(s):  
Re´gis Viguie´ ◽  
Gae¨tan Kerschen
Keyword(s):  
Nonlinear Dynamic ◽  
Large Body ◽  
Degree Of Freedom ◽  
Primary System ◽  
Vibration Absorbers ◽  
Strongly Nonlinear ◽  
Nonlinear Mechanical ◽  
Parametric Studies ◽  
Nonlinear Mechanical Systems ◽  
Nonlinear Regimes

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in engineering applications. Therefore, the present paper focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on extensive parametric studies, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this study proposes a tuning procedure which is computationally tractable and can treat strongly nonlinear regimes of motion. The proposed methodology relies on a frequency-energy based approach followed by bifurcation analysis. The results are illustrated using a one-degree-of-freedom primary system, which can, for instance, represent the vibrations of a specific mode of a multi-degree-of-freedom structure.

scholarly journals On-Line Modal Parameter Identification Applied to Linear and Nonlinear Vibration Absorbers

Actuators ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 119
Author(s):  
Luis Gerardo Trujillo-Franco ◽  
Gerardo Silva-Navarro ◽  
Francisco Beltran-Carbajal ◽  
Eduardo Campos-Mercado ◽  
Hugo Francisco Abundis-Fong
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Flexible Structure ◽  
Primary System ◽  
Vibration Absorbers ◽  
Modal Parameter ◽  
Vibration Absorption ◽  
Dynamic Vibration ◽  
On Line ◽  
Linear And Nonlinear

A solution of the vibration attention problem on a flexible structure from a dynamic vibration absorption perspective is experimentally and numerically studied in this article. Linear and nonlinear dynamic vibration absorbers are properly implemented on a primary structure of n degrees of freedom through a modal decomposition analysis and using the tuning condition when the primary system has one single degree of freedom. A time-domain algebraic identification scheme for on-line modal parameter estimation of flexible structures is presented. A fast frequency estimation of harmonic excitation force is also obtained. A Hilbert transform analysis of the frequency response function for the case of nonlinear dynamic vibration absorption is introduced. In this way, influence of this particular passive nonlinear control device on system dynamic response can be determined. The proposed approach is validated on an harmonically perturbed building-like structure, which is discretized in a finite number of degrees of freedom. The flexible structure is subjected to resonant operational conditions, and coupled to a pendulum vibration absorber configured as a tuned mass damper as well as an autoparametric system.

Passive Targeted Energy Transfers and Strong Modal Interactions in a Thin Plate With Strongly Nonlinear End Attachments of Different Configurations

2007 ◽  
Author(s):  
F. Georgiades ◽  
A. F. Vakakis
Keyword(s):  
Wavelet Transforms ◽  
Degree Of Freedom ◽  
Vibration Energy ◽  
Modal Interactions ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Single Degree ◽  
Energy Transfers ◽  
Parametric Studies ◽  
Underlying Mechanisms

In this paper we examine Targeted Energy Transfers (TETs) and nonlinear modal interactions occurring in a thin cantilever plate lying on an elastic foundation with strongly nonlinear lightweight attachments of different configurations. Under shock excitation of the plate we systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena between the plate and attachments of the following configurations: a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) NES; multiple SDOF attachments attached at different points of the plate; and a single multi-degree-of-freedom (MDOF) attachment with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and location of the attachments, in order to optimize TETs from the plate to the NES. We examine in detail the underlying mechanisms influencing TETs by means of Hilbert-Huang Transforms in combination with Wavelet Transforms. These transforms enable one to systematically study the strong modal interactions between the essentially nonlinear attachments and different plate modes. The efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed.

Impulsive Steering Between Coexisting Stable Periodic Solutions With an Application to Vibrating Plates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Daniël W. M. Veldman ◽  
Rob H. B. Fey ◽  
Hans Zwart
Keyword(s):  
Periodic Solutions ◽  
Degree Of Freedom ◽  
Limited Information ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonlinear Mechanical ◽  
Vibrating Plates ◽  
Stable Periodic ◽  
Nonlinear Mechanical Systems ◽  
Hardening Nonlinearity

Single-degree-of-freedom (single-DOF) nonlinear mechanical systems under periodic excitation may possess multiple coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. In energy-harvesting applications, the large-amplitude periodic solutions are preferred, and in vibration reduction problems, the small-amplitude periodic solutions are desired. We propose a method to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution, which requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity.

scholarly journals Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems

2013 ◽  
Vol 65 (2) ◽  
Author(s):  
Konstantin V. Avramov ◽  
Yuri V. Mikhlin
Keyword(s):  
Asymptotic Methods ◽  
Mechanical Systems ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Degree Of Freedom ◽  
Nonlinear Phenomena ◽  
Finite Degree ◽  
Nonlinear Mechanical ◽  
Nonlinear Normal ◽  
Nonlinear Mechanical Systems

This paper is an extension of the previous review, done by the same authors (Mikhlin, Y., and Avramov, K. V., 2010, “Nonlinear Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments,” ASME Appl. Mech. Rev., 63(6), p. 060802), and it is devoted to applications of nonlinear normal modes (NNMs) theory. NNMs are typical regimes of motions in wide classes of nonlinear mechanical systems. The significance of NNMs for mechanical engineering is determined by several important properties of these motions. Forced resonances motions of nonlinear systems occur close to NNMs. Nonlinear phenomena, such as nonlinear localization and transfer of energy, can be analyzed using NNMs. The NNMs analysis is an important step to study more complicated behavior of nonlinear mechanical systems.This review focuses on applications of Kauderer–Rosenberg and Shaw–Pierre concepts of nonlinear normal modes. The Kauderer–Rosenberg NNMs are applied for analysis of large amplitude dynamics of finite-degree-of-freedom nonlinear mechanical systems. Systems with cyclic symmetry, impact systems, mechanical systems with essentially nonlinear absorbers, and systems with nonlinear vibration isolation are studied using this concept. Applications of the Kauderer–Rosenberg NNMs for discretized structures are also discussed. The Shaw–Pierre NNMs are applied to analyze dynamics of finite-degree-of-freedom mechanical systems, such as floating offshore platforms, rotors, piece-wise linear systems. Studies of the Shaw–Pierre NNMs of beams, plates, and shallow shells are reviewed, too. Applications of Shaw–Pierre and King–Vakakis continuous nonlinear modes for beam structures are considered. Target energy transfer and localization of structures motions in light of NNMs theory are treated. Application of different asymptotic methods for NNMs analysis and NNMs based model reduction are reviewed.

scholarly journals Application of physical function model to state estimations of nonlinear mechanical systems

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Heisei Yonezawa ◽  
Itsuro Kajiwara ◽  
Shota Sato ◽  
Chiaki Nishidome ◽  
Takashi Hatano ◽  
...  
Keyword(s):  
Physical Function ◽  
Mechanical Systems ◽  
Function Model ◽  
Nonlinear Mechanical ◽  
State Estimations ◽  
Nonlinear Mechanical Systems

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

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