Dynamical Stability of Solitary Wave Propagation in Inhomogeneous Cylindrical Shells

doi:10.19596/j.cnki.1001-246x.7844

Abstract

Abstract: Dynamical stability of solitary wave propagation in inhomogeneous cylindrical shell was numerically studied in detail by using method of integrating factors. Stable propagation keeping structure of waveform and propagation speed of solitary wave for long time was examined, under three kinds of initial perturbations that is Gaussian wave perturbation, harmonic wave perturbation and stochastic perturbation. It shows that stable propagation of solitary wave is related to amplitude, width and wavelength of perturbations. Only with small enough amplitude, width and wavelength, solitary wave shows relatively strong anti-interference property, and has better dynamical stability.

Key words: inhomogeneous cylindrical shell, solitary wave, stability, method of integrating factors

CLC Number:

O411.1

Naranmandula, Chilimuge. Dynamical Stability of Solitary Wave Propagation in Inhomogeneous Cylindrical Shells[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 245-252.

References

[1] TIMOSHENKO S, WOINOWSKY-KRIEGER S. Theory of plates and shells[M]. 2nd ed. London:Mcgrawhill Book Company, 1959.
[2] NOVOZHILOV V V. The theory of thin shells[M]. Leningrad:Sudpromgiz, 1962.
[3] VENTSEL E, KRAUTHAMMER T. Thin plates and shells:Theory, analysis, and applications[M]. New York:Marcel Dekker Inc, 2001.
[4] VOL'MIR A S. Nonlinear dynamics of plates and shells[M]. Moscow:Nauka, 1972.
[5] EROFEEV V I, KLYUEVA N V. Solitons and nonlinear periodic strain waves in rods, plates, and shells (A review)[J]. Acoustical Physics, 2002, 48(6):643-655.
[6] ZEMLYANUKHIN A I,MOGILEVICH L I. Nonlinear waves in cylindrical shells[M]. Saratov:Saratov University Press, 1999.
[7] LOMBARD B, MERCIER J F. Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators[J]. Journal of Computational Physics, 2014, 259(2):421-443.
[8] 石玉仁, 张娟, 杨红娟, 等. 耦合KdV方程的双峰孤立子及其稳定性[J]. 物理学报, 2011, 60(2):020401-1-020401-8.
[9] 石玉仁, 周志刚, 张娟, 等. 修正cKdV方程组的孤立波结构及其稳定性[J]. 计算物理, 2012, 29(2):250-256.
[10] 王林雪, 宗谨, 王雪玲, 等. mBBM方程的双扭结孤立波及其动力学稳定性[J]. 计算物理, 2016, 33(2):212-220.
[11] ZEMLYANUKHIN A I, MOGILEVICH L I. Nonlinear waves in inhomogeneous cylindrical shells:A new evolution equation[J]. Acoustical Physics, 2001, 47(3):303-307.
[12] CHAN T F, KERKHOVEN T. Fourier methods with extended stability intervals for the Korteweg-De Vries equation[J]. SIAM Journal on Numerical Analysis,1985, 22(3):441-454.
[13] MILEWSKI P A, TABAK E G. A pseudo-spectral procedure for the solution of nonlinear wave equations with examples from free-surface flows[J]. SIAM Journal on Scientific Computing,1999, 21(3):1102-1114.

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