He's frequency formulation for nonlinear vibration of a porous foundation with fractal derivative

被引：18

作者：

Feng, Guang-Qing ^{[1
]}

Niu, Jing-Yan ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China

[2] Jiaozuo Normal Coll, Coll Technol, Jiaozuo, Henan, Peoples R China

来源：

GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS | 2021年 / 12卷 / 01期

关键词：

Nonlinear vibration; Toda oscillator; Fractal derivative; He's frequency formula; The approximate analytical solution; VARIATIONAL ITERATION METHOD;

D O I：

10.1007/s13137-021-00181-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this article focuses on deriving a fractal modification of the nonlinear oscillator in a porous foundation vibration. The variational principle and frequency formula of the fractal nonlinear equation are found by simple methods that were proposed by Ji-Huan He. In order to make the error smaller, we modify the approximate analytical solution expression and prove its effectiveness through examples.

引用

页数：8

共 24 条

[1] ON TWO-SCALE DIMENSION AND ITS APPLICATIONS [J].

Aln, Qura Tul ;

He, Ji-Huan .

THERMAL SCIENCE, 2019, 23 (03) :1707-1712

[2] An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method [J].

Belendez, A. ;

Mendez, D. I. ;

Fernandez, E. ;

Marini, S. ;

Pascual, I. .

PHYSICS LETTERS A, 2009, 373 (32) :2805-2809

[3] Lasing optical cavities based on macroscopic scattering elements [J].

Consoli, Antonio ;

Lopez, Cefe .

SCIENTIFIC REPORTS, 2017, 7

[4]

Daniel OT., 2021, RES PHYS, V24

[5]

El- Dib Y. O., 2017, NONLINEAR SCI LETT A, V8, p352

[6] EQUIVALENT POWER-FORM REPRESENTATION OF THE FRACTAL TODA OSCILLATOR [J].

Elias-Zuniga, Alex ;

Manuel Palacios-Pineda, Luis ;

Jimenez-Cedeno, Isaac H. ;

Martinez-Romero, Oscar ;

Olvera Trejo, Daniel .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (02)

[7] He's frequency-amplitude formulation for nonlinear oscillators using Jacobi elliptic functions [J].

Elias-Zuniga, Alex ;

Manuel Palacios-Pineda, Luis ;

Jimenez-Cedeno, Isaac H. ;

Martinez-Romero, Oscar ;

Olvera Trejo, Daniel .

JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2020, 39 (04) :1216-1223

[8] Equivalent representation form in the sense of Lyapunov, of nonlinear forced, damped second-order differential equations [J].

Elias-Zuniga, Alex ;

Manuel Palacios-Pineda, Luis ;

Martinez-Romero, Oscar ;

Olvera-Trejo, Daniel .

NONLINEAR DYNAMICS, 2018, 92 (04) :2143-2158

[9] Quintication" method to obtain approximate analytical solutions of non-linear oscillators" [J].

Elías-Zúñiga, Alex .

Applied Mathematics and Computation, 2014, 243 :849-855

[10]

Feng GQ., 2021, J LOW FREQ NOISE V A, DOI [10.1177/1461348421992608, DOI 10.1177/1461348421992608]

← 1 2 3 →