Modified harmonic balance method for the solution of nonlinear jerk equations

Rahman, Mohammad Shaifur; Hasan, Abu

doi:10.1016/j.rinp.2018.01.030

Cited by 24 publications

(13 citation statements)

References 26 publications

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“…In recent years, the discussion of jerk equations has attracted much attention because it arises in a variety of different scientific fields, such as the theory of chaos, secure communication, electrical engineering, and economic systems. For recent results, we refer the readers to [12][13][14][15][16][17][18][19][20] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

Han

Zhang

2021

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By coincidence degree theory due to Mawhin, some sufficient conditions for the existence of solution for a class of coupled jerk equations with multi-point conditions are established. The new existence results have not yet been reported before. Novel coupled fractional jerk equations with resonant boundary value conditions are discussed in detail for the first time. Our work is interesting and complements known results.

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Section: Introductionmentioning

confidence: 99%

“…As far as nonlinear jerk equations are concerned, most of the efforts on this topic are related to the initial value problem. For example, see [15,16] and the references therein. Among the existing results, no one result can be applied to our problem.…”

Section: Introductionmentioning

confidence: 99%

On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

Han

Zhang

2021

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“…The ideal starting process of the belt conveyor should ensure a smooth continuous acceleration and its maximum value is small to reduce the jolting impact of the motor on the belt conveyor. That is, the maximum jerk must be kept within a reasonable range to ensure a soft impact of motor on the belt conveyor [1][2][3][4][5][6]. Hence the speed curve should be S-shaped and the output smooth [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Cosine‐Trapezoidal Soft‐Starting Control Strategy for a Belt Conveyor

Ji¹,

Miao²,

Li³

2019

Mathematical Problems in Engineering

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To improve the soft-starting performance of a belt conveyor, a cosine-trapezoidal soft-starting control strategy is proposed. With this strategy, the speed curve for soft-starting is S-shaped, continuous, and smooth. The acceleration and jerk are also continuous and smooth without discontinuities. The time-interval ratio of the horizontal and cosine curves can be changed via a single parameter setting, so that the strategy can be modified to meet different practical needs. In this paper, the soft-starting control strategy of cosine trapezoid is analyzed and simulated based on current international and domestic standards. The results show that compared with the classical soft-starting control strategy, the cosine-trapezoidal soft-starting control strategy enables the belt conveyor to start at its highest efficiency. Moreover, the energy savings are obvious, the safety performance is good, and the controllable performance is excellent.

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“…New algorithm for the numerical solutions of nonlinear third-order differential equations was used jacobi-gauss collocation method in [5], He's variational iteration method was used in [6] for nonlinear Jerk equations. Modified harmonic balance method was used for nonlinear Jerk equations in [7]. In this paper, we consider a Jerk equation of the form ( ) .…”

Section: Introductionmentioning

confidence: 99%