The Dynamics of a Vibromachine With Parametric Excitation

Belovodsky, V. N.; Tsyfansky, S.L.; Beresnevich, Vitaly

doi:10.1006/jsvi.2001.4134

Cited by 13 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to evaluate the next point ð2i þ 2Þðt 2iþ2 ; _ x 2iþ2 Þ on R r , the differential Eq. 15with initial conditions (16) gives a solution expressed with the function x s , (read s as system), defined as follows,…”

Section: Scheme Of the Iterative Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Andreaus¹,

Placidi²,

Rega³

2010

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Systems constituted by moving components that make intermittent contacts with each other can be modelled by a system of ordinary differential equations containing piecewise linear terms. We consider a soft impact bilinear oscillator for which we obtain bifurcation diagrams, Lyapunov coefficients, return maps and phase portraits of the response. Besides Lyapunov coefficients diagrams, bifurcation diagrams are represented in terms of both non-dimensional time instants of contact (when the mass impacts the obstacle) and of portions of contact duration (the percentage-time interval when the material point is inside the obstacle) vs. non-dimensional external force frequency (or amplitude). The second kind of diagrams is needed because the contact duration (or the complementary flight time duration) are quantities that can easily be measured in an experiment aiming at confirming the validity of the present model. Lyapunov coefficients are evaluated converting the piecewise linear system of ordinary differential equations into a map, the so-called impact map, where time and velocity corresponding to a given impact are evaluated as functions of time and velocity corresponding to the previous impact. Thus, the usual methods related to this last map are used. The trajectories are represented in terms of return maps (all points in the time-velocity plane involved in the impact events) and phase portraits (the trajectory-itself in the displacement-velocity plane). In the bifurcation diagrams, transition between different responses is evidenced and a perfect correlation between chaotic (periodic) attractors and positive (negative) values of the maximum Lyapunov coefficient is found. (C) 2009 Elsevier B.V. All rights reserved

show abstract

Section: Scheme Of the Iterative Solutionmentioning

confidence: 99%

“…The simplest continuous PSS is the piecewise (or bilinear) oscillator, that is the object of an important work by Shaw and Holmes [15] and is also recently analyzed in many papers, see e.g. [16,17].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Andreaus¹,

Placidi²,

Rega³

2010

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

show abstract

“…Presently, some methods have been used to achieve the parametric stiffness excitation in the laboratory, such as beams and plates subjected to a periodic axial or in-plane loading (Bolotin 1964;lvan-Ewanowski 1976;Deolasi and Datta 1997), axial moving systems (belt (Pellicano et al 2004;Michon et al 2008) and plate (Kartik and Wickert 2008)), a pendulum under two-frequency parametric motion (Yatawara et al 2006), base excited cantilever beam (Rhoads et al 2008) or wire (Mullin et al 2003). In addition, Belovodsky et al (2002) described several designs of elastic elements with periodically time-varying elasticity. Echer (2008) and Dohnal et al (2006) respectively gave two ideas for creating a mechanical element with time-dependent stiffness.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of stiffness characteristics of an electromagnetic device

Han

Wang

2011

Journal of Vibration and Control

View full text Add to dashboard Cite

An electromagnetic device, consisting of a pair of permanent magnets and a non-magnetic coil, has shown its linear advantages for inducing parametric stiffness excitation in the laboratory. The electromagnetic device powered by a DC coil current acts like a mechanical spring with constant stiffness. The effects of design parameters upon the electromagnetic stiffness and its linear operating range (referred as the stiffness characteristics) are important and crucial for the design and usage of the device. Thus, a numerical method, based upon the commercial finite element method (FEM) package ANSYS/Emag, was presented for analyzing the stiffness characteristics of the device with DC coil current. The theory foundation for computing the electromagnetic force using FEM was derived and the program realization in ANSYS was introduced briefly. Two typical examples were chosen to verify the accuracy of the numerical analysis method. Based upon these, the restoring force characteristics of the electromagnetic device with various DC coil currents were obtained utilizing the numerical method. Two important indicators (proportional coefficient between linear stiffness and coil current and linear range of the stiffness) were defined for measuring the stiffness characteristics of the electromagnetic device. Then, the effects of the design parameters (both the electromagnetic and structural parameters) on the two indicators were investigated, respectively. The research results provide useful references for the stiffness design of the electromagnetic device in actual practice.

show abstract

Oscillators with Time Variable Parameters

Cvetićanin

2014

Strongly Nonlinear Oscillators

View full text Add to dashboard Cite

The Dynamics of a Vibromachine With Parametric Excitation

Cited by 13 publications

References 8 publications

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator

Finite element analysis of stiffness characteristics of an electromagnetic device

Oscillators with Time Variable Parameters

Contact Info

Product

Resources

About