非均匀圆柱壳中孤立波稳定传播的数值研究

发布时间：2019-06-29 12:14

【摘要】：由于在工业方面的重要应用,关于薄壳中波传播问题的研究已有很长的历史。随着科学技术的飞速发展,各科学研究领域的相互渗透,多种新型材料的出现,人们对这一类问题的研究也越来越重视,所取得的研究成果对解决很多实际问题提供了重要的理论依据。首先,本文采用伪谱方法,对立方非线性应力—应变关系下所建立的非均匀圆柱壳中非线性波传播模型进行了数值研究。主要以简谐波扰动,高斯波包扰动和随机扰动作为初始扰动,考察了在这些扰动的影响下孤立波能否稳定传播的问题。研究结果表明,在这三种小扰动下非均匀圆柱壳中的孤立波都具有较强的抗干扰性,表现出很好的动力学稳定性,能够在圆柱壳中稳定传播。另外,对非均匀圆柱壳中传播的两种孤立波的相互作用也进行了数值研究。研究发现相互作用之后两个孤立波除了相位有较大的变化外,波幅和速度基本恢复了相互作用之前的状态,表现出较好的动力学稳定性。最后对正弦波在非均匀圆柱壳中传播时的波形畸变进行了数值研究。其次,对平方非线性应力—应变关系下,建立了非均匀圆柱壳中非线性波传播模型也进行了研究。同样以简谐波扰动,高斯波包扰动和随机扰动作为初始扰动,采用伪谱方法详细研究了受扰孤立波能否稳定传播问题。结果表明,在三种小扰动下非均匀圆柱壳中的孤立波都具有较强的抗干扰性,表现出很好的动力学稳定性。另外,对非均匀圆柱壳中传播的两种孤立波的相互作用也进行了数值研究研究。研究发现,波幅和速度都很好地恢复了相互作用以前的状态,但相位上还是有明显的变化。最后也研究了正弦波在非均匀圆柱壳中传播时的波形畸变现象。通过对两种模型中受扰孤立波的稳定传播特性进行比较可发现,低次非线性波模型描述的孤立波表现出更好的动力学稳定性。两种孤立波相互作用时,同样低次非线性波模型描述的孤立波表现出更好的稳定性。
[Abstract]:Due to its important application in industry, the study of wave propagation in thin shells has been studied for a long time. With the rapid development of science and technology, the mutual penetration of various scientific research fields and the emergence of a variety of new materials, people pay more and more attention to this kind of problems, and the research results provide an important theoretical basis for solving many practical problems. In this paper, the pseudo-spectral method is used to study the nonlinear wave propagation model in inhomogeneous cylindrical shells under cubic nonlinear stress-strain relationship. Taking simple harmonic disturbance, Gaussian wave packet disturbance and random disturbance as initial disturbances, the problem of stable propagation of solitary waves under the influence of these disturbances is investigated. The results show that the solitary waves in inhomogeneous cylindrical shells have strong anti-interference, show good dynamic stability, and can propagate stably in cylindrical shells under these three kinds of small disturbances. In addition, the interaction between two kinds of solitary waves propagated in inhomogeneous cylindrical shells is also studied. It is found that after the interaction, the amplitude and velocity of the two solitary waves basically return to the state before the interaction, showing good dynamic stability, except that the phase of the two solitary waves changes greatly. Finally, the waveform distortion of sine wave propagating in inhomogeneous cylindrical shell is studied. Secondly, under the square nonlinear stress-strain relationship, the nonlinear wave propagation model in inhomogeneous cylindrical shells is also studied. In the same way, using simple harmonic disturbance, Gaussian wave packet disturbance and random disturbance as initial disturbances, the pseudo-spectral method is used to study the stable propagation of disturbed solitary waves in detail. The results show that the solitary waves in inhomogeneous cylindrical shells have strong anti-interference and good dynamic stability under three kinds of small disturbances. In addition, the interaction between two kinds of solitary waves propagated in inhomogeneous cylindrical shells is also studied. It is found that the amplitude and velocity return to the state before the interaction, but the phase still changes obviously. Finally, the waveform distortion of sinusoidal wave propagation in inhomogeneous cylindrical shell is also studied. By comparing the stable propagation characteristics of disturbed solitary waves in the two models, it can be found that the solitary waves described by the low-order nonlinear wave model show better dynamic stability. When two kinds of solitary waves interact, the solitary waves described by the same low-order nonlinear wave model show better stability.
【学位授予单位】：内蒙古民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.29

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