Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

Starosta, R.; Sypniewska–Kamińska, Grażyna; Awrejcewicz, Jan

doi:10.1016/j.ymssp.2016.07.022

Cited by 15 publications

(14 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of two time scales, the substitution of definitions (8)-(11) into Eqs. (5)- (6) and equating components at the same powers of e leads to the equations of the first and second-order approximation of the following form:…”

Section: Vibration Far From Resonancementioning

confidence: 99%

“…The solution obtained by the numerical integration of the governing Eqs. (5)- (6) are given in the same graphs to verify the accuracy of the approximate analytical solution. The relationship between initial conditions (7) and (27) has been determined using the analytical form of the solution (29) or (32) for the two and three time scales, respectively.…”

Section: Vibration Far From Resonancementioning

confidence: 99%

“…In that way, they produce a powerful procedure to study structural behavior. A one-dimensional mass-spring system of two degrees of freedom is studied in [6]. Its mathematical model consists of two strongly coupled differential equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear vibration of a lumped system with springs-in-series

2020

Self Cite

View full text Add to dashboard Cite

The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping are included into considerations. The mathematical model contains both differential and algebraic equations, so it belongs to the class of dynamical systems governed by the differential–algebraic system of equations (DAEs). An approximate analytical approach is used to solve the initial value problem for the DAEs. We adopt the multiple scales method (MSM) that allows one to obtain the sufficiently correct approximate solutions both far from the resonance and at the resonance conditions. The steady and non-steady resonant vibrations are analyzed by employing the modulation equations of the amplitudes and phases which are yielded by the MSM procedure.

show abstract

Section: Vibration Far From Resonancementioning

confidence: 99%

Section: Vibration Far From Resonancementioning

confidence: 99%

See 1 more Smart Citation

Nonlinear vibration of a lumped system with springs-in-series

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…When the analytical approach is applied, the harmonic balance method (HBM) is most often used 3 , 4 , 17 , 23 – 25 . Among other methods, the iteration method 25 – 27 , method of multiple scales 28 , perturbation method 29 , 30 or homotopy perturbation method 31 , 32 can be mentioned. Very often, during research, the methods are combined 23 .…”

Section: Introductionmentioning

confidence: 99%

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

Wawrzyński

2021

Sci Rep

View full text Add to dashboard Cite

For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.

show abstract

“…Hence, it is important to analyze the dynamic response of varying parameters in rotatable system. The dynamic response of a nonlinear system is investigated in [1,2]. The decomposition and study of the equations of motion proposed are beneficial in the analysis of vibration.…”

Section: Introductionmentioning

confidence: 99%

Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate

2017

Shock and Vibration

View full text Add to dashboard Cite

Nonlinear principal parametric resonance and stability are investigated for rotating circular plate subjected to parametric excitation resulting from the time-varying speed in the magnetic field. According to the conductive rotating thin circular plate in magnetic field, the magnetoelastic parametric vibration equations of a conductive rotating thin circular plate are deduced by the use of Hamilton principle with the expressions of kinetic energy and strain energy. The axisymmetric parameter vibration differential equation of the variable-velocity rotating circular plate is obtained through the application of Galerkin integral method. Then, the method of multiple scales is applied to derive the nonlinear principal parametric resonance amplitude-frequency equation. The stability and the critical condition of stability of the plate are discussed. The influences of detuning parameter, rotation rate, and magnetic induction intensity are investigated on the principal parametric resonance behavior. The result shows that stable and unstable solutions exist when detuning parameter is negative, and the resonance amplitude can be weakened by changing the magnetic induction intensity.

show abstract

Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach

Cited by 15 publications

References 9 publications

Nonlinear vibration of a lumped system with springs-in-series

Nonlinear vibration of a lumped system with springs-in-series

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate

Contact Info

Product

Resources

About