Exact and approximate analytical solutions of oscillator with piecewise linear asymmetrical damping

Silveira, Marcos; Wahi, Pankaj; Fernandes, Janainny Magalhães

doi:10.1016/j.ijnonlinmec.2018.12.007

Cited by 12 publications

(9 citation statements)

References 22 publications

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“…8. Taking (15) as the fitting model to fit the experimental data shown in Fig. 8, the values of k 2 and c 2 are identified as k 2 = 3747.44 N/m and c 2 = 0.560 N • s/m by the least square method.…”

Section: B Experimental Resultsmentioning

confidence: 99%

“…(c) k 2 -k 1 and c 2 -c 1 are used to denote the deformation and energy loss during the collision, respectively. Taking (15) as the fitting model, the value of k 2 and c 2 can be determined to fit the experimental data by the least square method [31].…”

Section: A Experimental Setupmentioning

confidence: 99%

“…Zou and Nagarajaiah [14] were the first to study a piecewise linear system with negative and positive stiffness by a modified Lindstedt-Poincaré method. For the forced vibration of an oscillator with piecewise linear asymmetrical damping, Silveira et al [15] obtained the exact analytical solutions by joining the solutions for the compression and expansion phases and the approximate solutions by the HIB method. Wang et al [16] studied the effect of the system parameters on the dynamical behaviours of a piecewise linear SDOF oscillator with fractional-order derivative by the averaging method.…”

mentioning

confidence: 99%

“…FIGURE 2. Frequency-amplitude response for the primary resonance (The black solid line represents the stable state for l = ∞; the red solid and dashed lines represent the stable and unstable states derived from(15) for l = 0.2, respectively; the green dots represent the stable state by numerically solving (3). ).…”

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confidence: 99%

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Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

Sun

2021

IEEE Access

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The amplitude-frequency response of a nonlinear vibration system with the coexistence of stiffness and viscous damping piecewise linearities are analysed by means of analytical, numerical and experimental investigations. First, a mechanical model of the piecewise linear system under simple harmonic base excitation is established, and the amplitude-frequency response equation is obtained by the averaging method. Second, an experimental device is built to realize the piecewise linear system. The stiffness and damping coefficients are identified by the least square method. Third, case studies are conducted to illustrate the effect of the clearance and base excitation amplitude on the amplitude-frequency response. The experimental results show that the introduction of the piecewise linear stiffness and damping significantly decreases the response amplitude at the primary resonance. The piecewise linear stiffness, damping coefficients, primary resonance frequency and frequency range of the bi-stable state depend on the clearance and excitation amplitude. The experimental results are consistent with the theoretical predictions and numerical simulation results of the method of backward differentiation formulas. This research provides instructive ideas to the design of the nonlinear isolator in practical engineering.

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Section: B Experimental Resultsmentioning

confidence: 99%

Section: A Experimental Setupmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

Sun

2021

IEEE Access

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“…C. Rajalingham [ 18 ] solved the exact solution of a quarter vehicle system by the Laplace transform method, it was found that the asymmetric damping of the damper leads to a change in the compression volume of the suspension spring, resulting in a shift in the mean position of the vehicle body, but this asymmetric damping does not cause a change in the mean position of the unsprung mass. M. Silveira [ 19 ] established a single-degree-of-freedom oscillator with damping asymmetric characteristic and solved the accurate analytical solutions of all possible combinations of the system under underdamped, critically damped, overdamped, and undamped conditions, arguing that the asymmetric damping caused the difference in the time spent by the isolated body in the compression and extension travels, resulting in the change in the mean position of the vibration of the isolated body. Fernandes [ 20 ] presented a vehicle model with asymmetric damping, it was found that the asymmetric damping causes a change in the mean position of the vehicle body, however, it does not induce significant changes in the displacement amplitude of the vehicle body.…”

Section: Introductionmentioning

confidence: 99%

Research and application of a new method for adjusting the vehicle body height

Yao

2022

PLoS ONE

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The use of active suspension for vehicle height adjustment has problems of high cost, high energy consumption, slow response, and complex structure. This paper proposes a new method for adjusting the vehicle body using the damping asymmetric characteristic of semi-active suspensions, which is based on the idea that the dampers with damping asymmetric characteristics will cause a change in the mean position of the vehicle body vibration. To verify the feasibility of this method, a single-wheel vehicle model containing asymmetric damping is established. The system’s responses under the sinusoidal and random roads excitation are obtained by the fourth-order Runge-Kutta method, the influences of key parameters on the vehicle body’s shifting height are analyzed, and the mechanism of vehicle body’s shift is explained from the perspective of energy conservation. Then a vehicle body height controller based on third-order linear active disturbance rejection control (LADRC) is designed. Simulation results show that the proposed method for controlling the vehicle height with asymmetric damping can quickly adjust the vehicle to the expected height whether under the sinusoidal road or random road. In addition, no additional hardware and energy consumption are required, providing a new idea for vehicle height control.

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Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort

2019

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Exact and approximate analytical solutions of oscillator with piecewise linear asymmetrical damping

Cited by 12 publications

References 22 publications

Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

Research and application of a new method for adjusting the vehicle body height

Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort

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