【摘要】：由于在工業(yè)方面的重要應(yīng)用,關(guān)于薄殼中波傳播問題的研究已有很長的歷史。隨著科學(xué)技術(shù)的飛速發(fā)展,各科學(xué)研究領(lǐng)域的相互滲透,多種新型材料的出現(xiàn),人們對這一類問題的研究也越來越重視,所取得的研究成果對解決很多實際問題提供了重要的理論依據(jù)。首先,本文采用偽譜方法,對立方非線性應(yīng)力—應(yīng)變關(guān)系下所建立的非均勻圓柱殼中非線性波傳播模型進(jìn)行了數(shù)值研究。主要以簡諧波擾動,高斯波包擾動和隨機(jī)擾動作為初始擾動,考察了在這些擾動的影響下孤立波能否穩(wěn)定傳播的問題。研究結(jié)果表明,在這三種小擾動下非均勻圓柱殼中的孤立波都具有較強(qiáng)的抗干擾性,表現(xiàn)出很好的動力學(xué)穩(wěn)定性,能夠在圓柱殼中穩(wěn)定傳播。另外,對非均勻圓柱殼中傳播的兩種孤立波的相互作用也進(jìn)行了數(shù)值研究。研究發(fā)現(xiàn)相互作用之后兩個孤立波除了相位有較大的變化外,波幅和速度基本恢復(fù)了相互作用之前的狀態(tài),表現(xiàn)出較好的動力學(xué)穩(wěn)定性。最后對正弦波在非均勻圓柱殼中傳播時的波形畸變進(jìn)行了數(shù)值研究。其次,對平方非線性應(yīng)力—應(yīng)變關(guān)系下,建立了非均勻圓柱殼中非線性波傳播模型也進(jìn)行了研究。同樣以簡諧波擾動,高斯波包擾動和隨機(jī)擾動作為初始擾動,采用偽譜方法詳細(xì)研究了受擾孤立波能否穩(wěn)定傳播問題。結(jié)果表明,在三種小擾動下非均勻圓柱殼中的孤立波都具有較強(qiáng)的抗干擾性,表現(xiàn)出很好的動力學(xué)穩(wěn)定性。另外,對非均勻圓柱殼中傳播的兩種孤立波的相互作用也進(jìn)行了數(shù)值研究研究。研究發(fā)現(xiàn),波幅和速度都很好地恢復(fù)了相互作用以前的狀態(tài),但相位上還是有明顯的變化。最后也研究了正弦波在非均勻圓柱殼中傳播時的波形畸變現(xiàn)象。通過對兩種模型中受擾孤立波的穩(wěn)定傳播特性進(jìn)行比較可發(fā)現(xiàn),低次非線性波模型描述的孤立波表現(xiàn)出更好的動力學(xué)穩(wěn)定性。兩種孤立波相互作用時,同樣低次非線性波模型描述的孤立波表現(xiàn)出更好的穩(wěn)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.
【學(xué)位授予單位】：內(nèi)蒙古民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.29

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本文編號：2507807