“…Further, the fractal modification of Yao-Cheng oscillator also reflects the closed phase portrait. 1 In conclusion, we revisited the work on the non-linear oscillator with damping term of Yao and Cheng oscillator by employing analytical as well as numerical approaches. In both the approaches, the solutions of the non-linear oscillator show oscillatory nature without showing any signature of damping.…”
Section: Consideringmentioning
confidence: 99%
“…Further, the fractal modification of Yao-Cheng oscillator also reflects the closed phase portrait. 1 Figure 4.Time evolution of the analytical solution of equation (1) for k=1,c=2 and b=1.Figure 5.Analytically obtained phase portrait of equation (1) for k=1,c=2,A=5and10 and b=1.…”
Section: Consideringmentioning
confidence: 99%
“…In recent years, the study on Yao-Cheng non-linear oscillator has attracted the research attention due to its usefulness for understanding the oscillation behaviour associated with many physical systems. 1 The equation of motion of the Yao-Cheng non-linear oscillator is of the form 1 where…”
We revisited the characteristic features of Yao-Cheng non-linear oscillator by employing both analytical as well as numerical approaches. Our study indicates that the solution of the non-linear oscillator shows oscillatory behaviour. Further, the phase portrait for this oscillator system reflects the closed loop signifying the stability of the system. Our results suggest the absence of damping in this physical system.
“…Further, the fractal modification of Yao-Cheng oscillator also reflects the closed phase portrait. 1 In conclusion, we revisited the work on the non-linear oscillator with damping term of Yao and Cheng oscillator by employing analytical as well as numerical approaches. In both the approaches, the solutions of the non-linear oscillator show oscillatory nature without showing any signature of damping.…”
Section: Consideringmentioning
confidence: 99%
“…Further, the fractal modification of Yao-Cheng oscillator also reflects the closed phase portrait. 1 Figure 4.Time evolution of the analytical solution of equation (1) for k=1,c=2 and b=1.Figure 5.Analytically obtained phase portrait of equation (1) for k=1,c=2,A=5and10 and b=1.…”
Section: Consideringmentioning
confidence: 99%
“…In recent years, the study on Yao-Cheng non-linear oscillator has attracted the research attention due to its usefulness for understanding the oscillation behaviour associated with many physical systems. 1 The equation of motion of the Yao-Cheng non-linear oscillator is of the form 1 where…”
We revisited the characteristic features of Yao-Cheng non-linear oscillator by employing both analytical as well as numerical approaches. Our study indicates that the solution of the non-linear oscillator shows oscillatory behaviour. Further, the phase portrait for this oscillator system reflects the closed loop signifying the stability of the system. Our results suggest the absence of damping in this physical system.
“…8 Recently, there are lots of work on the fractal modifications of the nonlinear oscillators that can be found in the literatures. [10][11][12][13][14] This topic focused on fractal N/MEMS system, fractal Zhiber-Shabat oscillator, fractal Duffing-Van der Pol oscillator, fractal Toda oscillator and fractal Yao-Cheng oscillator and others. Some numerical or analytical techniques were suggested for solving these fractal oscillators, including variational principle, 15,16 He's frequency formulation, 17 homotopy perturbation method 18,19 and so on.…”
Section: Introductionmentioning
confidence: 99%
“…This approach was first proposed by Lu and Chen for the numerical analysis of the fractal Yao-Cheng oscillator in a fractal space. 14 TST-GRHBM consists of two steps, the fractal nonlinear oscillator is first represented as a classical nonlinear oscillator by the two-scale transformation (TST) proposed by He [20][21][22][23][24][25][26] and the approximations for the transformed oscillator can be obtained by the global residue harmonic balance method (GRHBM). 14,[27][28][29][30] For illustrating the procedure of TST-GRHBM for (2), we first transform the fractal capillary oscillator as the classical capillary oscillator by using the two-scale fractal transformation.…”
This paper focuses on the numerical investigation of a fractal modification of capillary oscillator by using a coupling technique based on the two-scale transformation and the global residue harmonic balance method. This fractal oscillator can be transformed as the classical capillary oscillator with the help of the two-scale transformation. We further obtain an approximated oscillator by using Taylor approximation. The approximations or frequencies are given by applying the global residue harmonic balance method without discretization. Numerical sensitive analysis of the approximations about different parameters is considered in detail. Compared results with Runge–Kutta method and homotopy perturbation method are given to illustrate the efficiency and stability of the present technology.
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