Analysis of an impact Duffing oscillator by means of a nonsmooth unfolding transformation

Аврамов, К. В.; Borysiuk, O.

doi:10.1016/j.jsv.2008.05.005

Cited by 8 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nonsmooth spatial unfolding transformation is used jointly the Van-der-Pol method to analyze single-DOF impact system in Ref. [154]. The Lie series is used to construct periodic solutions (in particular, NNMs) in the vibro-impact systems [155].…”

Section: Dynamics Of Piecewise Linear and Impact Systemsmentioning

confidence: 99%

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Mikhlin

Аврамов

2010

Applied Mechanics Reviews

View full text Add to dashboard Cite

Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer-Rosenberg and Shaw-Pierre concepts, are analyzed. Properties of the NNMs and methods of their analysis are presented. NNMs stability and bifurcations are discussed. Combined application of the NNMs and the Rauscher method to analyze forced and parametric vibrations is discussed. Generalization of the NNMs to continuous systems dynamics is also described.

show abstract

Section: Dynamics Of Piecewise Linear and Impact Systemsmentioning

confidence: 99%

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Mikhlin

Аврамов

2010

Applied Mechanics Reviews

View full text Add to dashboard Cite

show abstract

“…Other solutions methods for nonlinear systems with piecewise functions include Harmonic Balance Method [27][28][29], coordinate transformations [30][31][32], and path-following continuation methods [1,2,33]. For the last category, authors generally resort to Numerical Continuation toolboxes, like MatCont [34], COCO [35] and AUTO-07 [36].…”

Section: Introductionmentioning

confidence: 99%

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

2023

View full text Add to dashboard Cite

In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

show abstract

“…Previously, several investigations have been paid to the Duffing oscillator with impacts. For example, a theoretical study of Avramova and Borysiuk [3] employing a nonsmooth unfolding transformation to analyze the dynamics of a one-degree-of-freedom impact Duffing oscillator. The stochastic bifurcations and response of vibro-impact Duffing-Van der Pol oscillators, subjected to white noise were examined in several studies [4], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on the One Degree-of-Freedom Duffing Oscillator With Impact

Tuấn¹,

Dự²

2019

JST

View full text Add to dashboard Cite

Bài báo này trình bày kết quả nghiên cứu thực nghiệm về triển khai thiết bị và khảo sát vùng cộng hưởng của cơ cấu rung động Duffing một bậc tự do có va đập. Cơ cấu được phát triển dựa trên một máy phát rung động nhỏ, sử dụng tương tác điện từ nhằm biến dao động của tín hiệu nguồn thành dao động của ống dây bên trong. Vùng cộng hưởng được xác định dựa trên biểu đồ Bode, phản ánh tương quan giữa biên độ dao động, góc pha giữa tín hiệu nguồn và dao động với tần số kích thích. Vị trí vùng cộng hưởng, tương tác cơ-điện được khảo sát và phân tích từ kết quả thực nghiệm. Kết quả cho thấy, va đập làm thay đổi đáng kể tần số cộng hưởng của cơ cấu. Một phát hiện hữu ích khác là cường độ dòng điện kích thích giảm đáng kể khi xuất hiện cộng hưởng. Các kết quả thu được có thể là nguồn tham khảo cho các bài toán có va đập xuất hiện kèm rung động.

show abstract

Analysis of an impact Duffing oscillator by means of a nonsmooth unfolding transformation

Cited by 8 publications

References 13 publications

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

Experimental Study on the One Degree-of-Freedom Duffing Oscillator With Impact

Contact Info

Product

Resources

About