Analytical approximate solutions for the generalized nonlinear oscillator

Younesian, Davood; Argani, Hassan; Saadatnia, Zia; Kalami-Yazdi, M.

doi:10.1080/00036811.2011.559464

Cited by 27 publications

(22 citation statements)

References 32 publications

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“…It should be emphasized that the generalized forms of the Duffing equation (in Example 1) and the oscillator (in Example 3) have been solved by Energy Balance Method [12,16], and the generalized form of the nonlinear oscillator with fractional elastic force (in Example 5) has been solved by Energy Balance Method and Variational Approach [14]; these solutions are achieved by Younesian et al [12,14,16]. The frequency-amplitude relationship is analytically obtained by using this proposed method.…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

“…For = 0.1, = 0.5, = 0.75, and = 0.95, comparison of the approximate periods in (56), the approximate Variational Iteration Method (VIM) periods VIM [5] in (57), and the Energy Balance Method (EBM) periods EBM [16] in (58) with exact periods ex in (59) is tabulated in Table 4. From Table 4, the accuracy of this proposed method can be observed.…”

Section: Examplementioning

confidence: 99%

“…As -periodic functions ( ) can be expanded into Fourier series; hence we can easily calculate (15) by using (16).…”

Section: Thementioning

confidence: 99%

“…The approximate period obtained by Variational Iteration Method is as follows [5]: The approximate period obtained by Energy Balance Method is as follows [16]:…”

Section: Examplementioning

confidence: 99%

“…Due to the limitation of existing exact solutions, many analytical approaches have been investigated. Many researchers have been working on various analytical methods for solving nonlinear oscillation systems in the last decades, such as Homotopy Perturbation Method (HPM) [1][2][3][4][5], Max-Min Approach (MMA) [5][6][7][8][9][10], Variational Iteration Method (VIM) [2,5], Energy Balance Method (EBM) [5,[11][12][13][14][15][16], Amplitude-Frequency Formulation (AFF) [5-7, 15, 17, 18], Improved Amplitude-Frequency Formulation (IAFF) [5], Parameter Expansion Method (PEM) [5,7,[18][19][20], Homotopy Analysis Method (HAM) [5,21], Modified Homotopy Perturbation Method (MHPM) [5,6], Modified LindstedtPoincare Method [22], Harmonic Balance Method [23,24], and combined Newton's Method with the Harmonic Balance Method [25].…”

Section: Introductionmentioning

confidence: 99%

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The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

Hieu

Hai

Hung

2018

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Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

“…As -periodic functions ( ) can be expanded into Fourier series; hence we can easily calculate (15) by using (16).…”

Section: Thementioning

confidence: 99%

“…The approximate period obtained by Variational Iteration Method is as follows [5]: The approximate period obtained by Energy Balance Method is as follows [16]:…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

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Tire Condition Monitoring and Intelligent Tires Using Nanogenerators Based on Piezoelectric, Electromagnetic, and Triboelectric Effects

Argani

Hashemi

Khajepour

et al. 2018

Adv Materials Technologies

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With the prospect of autonomous driving on roads in near future, it is paramount to make the vehicles safe on any driving and road condition. This is only possible by additional sensors to make up for the driver's cognitive and sensory system. Measuring road condition and tire forces especially in autonomous vehicles are vital in their safety, reliability, and public confidence in automated driving. Real time measurement of road condition and tire forces in buses and trucks can significantly improve the safety of road transportation system, and in miming/construction and off-road vehicles can improve performance, tire life, and reduce operational costs.There are three particular branches of research in the area of tire condition monitoring systems (TCMS) including estimation, sensing, and power harvesting. The main focus of this review article would be on progress in estimation techniques, energy harvesting, and also sensing approaches for TCMS based on piezoelectric, electromagnetic, and triboelectric nanogenerators (TENGs). Indeed, the fusion of these three areas in a singular package leads to designing future intelligent tires. The implementation of intelligent tires is highly advantageous for reduction of disastrous accidents,CO 2 , and noise emissions, and also fuel consumption. Figure 1 depicts an intelligent tire with its basic parts, its crucial applications, and advantages. In Figure 1, NGs, PEGs, and EMGs refer to nanogenerators, piezoelectric nanogenerators, and electromagnetic generators, respectively.Advances in applications of sensor technologies, sensor fusion, and cooperative estimation in intelligent transportation systems facilitate having reliable tire forces. Consequently, developing a flexible estimation structure to operate the available sensor data in production vehicles is a preeminent objective of the car manufacturers. In this direction, reliable estimation of tire forces at a reasonable cost is necessary for proper functioning of active safety systems in current vehicles. Longitudinal, lateral, and vertical tire forces make major contributions to velocity estimation, [3] traction and stability control, [4,5] and obstacle avoidance systems. [6,7] This article provides a comprehensive review on intelligent tire and TCMS. The first part of the article describes tire models, techniques for tire force, and tire-road friction The quest to utilize intelligent tires has prompted substantial multidisciplinary research including vehicle dynamics, control, estimation, energy harvesting, and even nanotechnology. This review article presents the progress in the area of tire condition monitoring systems (TCMS) and intelligent tires using devices fabricated based on piezoelectric, electromagnetic, and triboelectric effects. Three main branches of the research in this area are presented, including estimation techniques, sensing, and energy harvesting approaches. The authors delineate the importance of TCMS for vehicle active safety systems, its importance for transportation safety, and also its remarka...

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Vibration Analysis of Oscillators with Generalized Inertial and Geometrical Nonlinearities

Younesian

Esmailzadeh

Argani

2018

Nonlinear Approaches in Engineering Applications

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Analytical approximate solutions for the generalized nonlinear oscillator

Cited by 27 publications

References 32 publications

The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

Tire Condition Monitoring and Intelligent Tires Using Nanogenerators Based on Piezoelectric, Electromagnetic, and Triboelectric Effects

Vibration Analysis of Oscillators with Generalized Inertial and Geometrical Nonlinearities

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