共查询到19条相似文献,搜索用时 218 毫秒
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本文在理论分析基础上,将非线性问题有限元平衡方程中的各矩阵按随机变量Taylor级数展开,从而得到关于这些随机变量的非线性方程,并利用中心二阶摄动法,推导出非线性问题摄动随机限元的递归方程组,运用New-Raphson迭代法求解位移的二阶摄动量。 相似文献
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1引言
聚焦换能器可在焦点附近产生很强的非线性并且能有效地提高分辨率,从而被广泛应用于超声医学诊断及非线性超声显微镜中.章东、龚秀芬等基于近轴及准线性近似下的KZK非线性方程[1],利用高斯函数叠加法[2]来近似表示活塞聚焦声源的源分布函数,研究了生物组织样品插入后聚焦换能器的非线性声场,得到二次谐波分量的解析解[3].本文在此基础上进一步研究了在聚焦声场中用另一聚焦换能器接收到的二次谐波分量,并对生物组织样品(猪的肝组织、脂肪组织)插入到焦区后接收到的二次谐波分量与两换能器间距离的关系进行了数值模拟. 相似文献
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材料性能退化总是伴随着某种形式的材料非线性力学行为,从而引起超声波传播的非线性,即高频谐波的产生。研究了利用脉冲反转技术测量金属材料超声学非线性系数的实验方法和信号处理算法,发展了一套可靠的测试实验系统,在相同条件下测量了同一试样在不同输入电压下的二次谐波和基波幅度,二次谐波幅度和基波幅度的平方近似成线性关系,表明实验系统是可靠的。利用该系统进行了一组LY12铝合金疲劳试样非线性超声检测实验。实验结果表明,超声非线性系数可以表征镁合金的疲劳早期退化,脉冲反转技术能够有效提取二次谐波时域信号,增强二次谐波的幅度,抑制主要由实验系统所产生的奇次谐波分量,为材料和结构早期力学性能退化的无损检测和评价提供一种有效的方法。 相似文献
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提出一种用于求解确定性周期与非平稳随机激励联合作用下,单自由度非线性系统非平稳响应的统计线性化方法。将系统响应分解为确定性周期和零均值随机分量之和,则原非线性运动方程可等效地化为一组耦合的、分别以确定性和随机动力响应为未知量的非线性微分方程。利用统计线性化方法将非平稳随机激励作用下的非线性随机动力方程化为等效线性方程,得到关于线性随机响应二阶矩的李雅普诺夫方程。联立李雅普诺夫方程与谐波激励作用下的确定性微分方程,并利用数值算法对其进行求解。以蒙特卡洛模拟验证了此方法的适用性和精度。 相似文献
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圆弧拱平面内弯曲失稳一般理论 总被引:7,自引:2,他引:5
现有的拱的平面内稳定理论有很大分歧。本文采用平截面假定,未作任何近似地采用了有限变形理论中的应变位移关系,完整地考虑了横向应力和剪应力的二阶效应,用虚功原理推导了拱的平面内非线性分析的平衡方程。之所以引入横向应力的非线性效应,是因为保持平衡所需的各应力分量的二阶效应会部分相互抵消,忽略其中任何一个都可能导致不正确的结果。文中还给出了内力采用线性分析结果的近似非线性分析方程,可以用于绝大多数工程问题的求解。对拱的内力和位移的线性问题进行了精确求解,代入非线性方程后得到了圆弧拱屈曲分析的平衡微分方程。用Galerkin法求得了考虑/不考虑拱内弯矩和剪力影响、考虑/不考虑屈曲前变形影响的临界荷载,并讨论了拱轴不可伸长假定的影响。系统地与前人的研究进行了比较。 相似文献
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1引言
自从1997年T.Christopher提出使用超声波在传播过程中产生的谐波成分进行医学成像[1]以来,谐波成像方法和技术的研究得到重视,并逐步应用到医学诊断中.由于传声介质的非线性,声波在传播过程中发生畸变,并滋生谐波,谐波的阶次越高,谐波的能量越小,信号幅度越低.二次谐波的衰减较小,具有良好的指向性,因此作为医学谐波成像的首选信号.提高二次谐波信号是二次谐波医学成像的关键技术.传统的方法使用二次谐波带通滤波器,由于滤波器的带宽和品质因素的原因,实际效果不能令人满意.本文用反向脉冲技术消除基波,增强二次谐波,提高二次谐波成像的对比度,为二次谐波成像提供有效的方法. 相似文献
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借助色散导波的部分波分析方法、二阳微扰理论及同的声非线性反射处理技术,本文对声波导中广义兰姆波的积累二次谐波发生进行了理论研究。结果表明,在一定条件下,源于声波导介质的体非线性、由文义兰姆波的部分波非线性相互作用所发生的二次谐波具有随传播距离积累增长的性质,文中给出了广义兰姆波的积累二次谐波发生所要满足的条件,并求解出相应的积累二次谐波之解析式。 相似文献
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Gusev VE Lauriks W Thoen J 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》1998,45(1):170-178
The evolution equations for nonlinear Scholte waves (finite amplitude elastic waves propagating along liquid/solid interface), which account for the second order nonlinearity of a liquid, are derived for the first time. For mathematical simplicity the nonlinearity of the solid, which influence is expected to be weak in the case of weak localization of the Scholte wave, is not taken into consideration. The analysis of these equations demonstrates that the nonlinear processes contributing to the evolution of the Scholte wave can be divided into two groups. The first group includes nonlinear processes leading to wave spectrum broadening which are common to bulk pressure waves in liquids and gases. The second group includes the nonlinear processes which are active only in the frequency down-conversion (leading to wave spectrum conservation or narrowing), which are specific to the confined nature of the interface wave. It is demonstrated that the nonlinear parameters, which characterize the efficiency of various nonlinear processes in the interface wave, strongly depend on the relative properties of the contacting liquid and solid (or, in other words, on the deviation of the Scholte wave velocity from the velocities of sound in liquid and in solid). In particular, the sign of the nonlinear parameter responsible for the second harmonic generation can differ from the sign of the nonlinear acoustic parameter of the liquid. It is also verified that there are particular liquid/solid combinations where the nonlinear processes, which are inactive in the frequency up-conversion, dominate in the evolution of the Scholte wave. In this case distortionless propagation of the finite amplitude harmonic interface wave is possible. The proposed theory should find applications in nonlinear acoustics, geophysics, and nondestructive testing. 相似文献
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Jiang W Cao W 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》2004,51(2):153-162
Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6 mm and 3 m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO/sub 3/) crystal, and its third-order elastic constant c/sub 444/ is determined. 相似文献
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Krutyansky L Pernod P Brysev A Bunkin FV Preobrazhensky V 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》2002,49(4):409-414
Supercritical parametric wave phase conjugation (SWPC) is used for selection and phase conjugation of harmonic components of a nonlinear incident wave. The amplitude of the phase conjugate wave in a supercritical mode is high enough for acoustic nonlinearity of the propagation medium to appear. As a result, in particular, doubled and quadrupled frequencies of the incident wave become available for image formation at the same order of the medium nonlinearity. The improvement of the imaging system resolution because of harmonic analysis of the received acoustic signal and compensation of phase distortions caused by wave phase conjugation were observed simultaneously when the propagation medium was inhomogeneous. 相似文献
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Computer model for harmonic ultrasound imaging 总被引:2,自引:0,他引:2
Li Y Zagzebski JA 《IEEE transactions on ultrasonics, ferroelectrics, and frequency control》2000,47(5):1259-1272
Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging. 相似文献
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