非线性摄动随机有限元元递归方程组分析及求解

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。     

一种由横波激发的特殊非线性声现象

目前对非线性超声的研究多集中在纵波激发的谐波性质以及对材料微观结构变化的实验检测上,横波激发的非线性声波性质少有研究。对横波激发的一维非线性声波方程入手,利用摄动法求解该方程,并改写为一阶偏微分方程,然后利用交错网格的有限差分形式进行数值求解。结果表明:采用横波激发,能产生线性横波和非线性纵波,且纵波的高次谐波内有两个信号,分别以纵波和横波两种速度传播。若采用较长的激发信号,纵波谐波能形成"拍"现象,成为一种奇特的声传播现象。     

共聚焦非线性声场的研究

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.     

脉冲反转技术在金属疲劳损伤非线性超声检测中的应用

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。     

声源强度对超谐波特性的影响

1引言 有限振幅声波在媒质中传播时将产生非线性效应.当声源的强度较大或者使用的频率较高时,由媒质引起的声波非线性特性如波形畸变、谐波滋生、非线性附加衰减等无法忽略.二次谐波成像有效地提高了超声图像的质量.但是二次谐波的强度相比基波很小,要求接收端有很好的灵敏度和动态范围,以保证接收信号的信噪比,这给实际应用带来了诸多不便.超谐波为这些谐波信号中某些分量的叠加而得[1],在一定的条件下其幅度和径向指向性等特性会优于二次谐波,有助于提高信噪比.     

确定性周期与随机激励联合作用下非线性系统非平稳响应的统计线性化方法

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。     

圆弧拱平面内弯曲失稳一般理论

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。     

非线性方程的2阶正交解法

对于非线性动力学方程的数值求解,一般的处理方法是,通过坐标变化将其转化为1阶形式,然后借助计算机进行求解,获取系统的一些非线性特征,如滑移、分叉等。本文中的2阶正交法是在原有的微分方程的基础上对非线性方程的弱非线性特性进行直接分解,获取非线性项对频响函数与动力学方程响应的贡献分量,可快速获取非线性动力学方程的频响函数表达通式以及动力学方程的响应,并通过对Duffing方程进行算例说明。     

反向脉冲二次谐波增强研究

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.     

考虑几何非线性的旋转薄壁圆柱壳进动响应分析

选取悬臂旋转薄壁圆柱壳作为研究对象,利用能量法推导了其振型进动因子,并考虑了阻尼以及几何非线性的影响.应用Donnell's简化壳理论建立考虑几何非线性以及振型进动的非线性波动方程,使用Galerkin法对非线性波动方程进行离散化,获得模态坐标上的非线性微分方程组,分别应用Runge-Kutta法和谐波平衡法对其进行数值求解和近似解析求解,并分析了近似解析解的稳定性.结果表明,几何非线性不影响振型进动因子,但使系统的频率响应曲线具有多值性和跳跃性.     

广义兰姆波的积累二次谐波发生研究

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。     

Evolution equation for nonlinear Scholte waves

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.     

二维非线性单原子正方晶格色散摄动分析

声子晶体的色散关系决定弹性波在其中的传播方式。从二维无限周期结构的波动方程出发,提出了一种分析非线性离散型声子晶体的色散关系的一阶近似摄动法。通过引入Bloch理论与小参数摄动展开法,得到了一阶近似的色散关系与频散曲线,以分析不同方向上的阻抗配置与非线性系数对频散及群速度的影响。以二维单原子正方晶格为例,得到了其一阶频散曲线。色散结果显示带隙及传播方向与波幅相关。最后模拟了晶格对点谐波激励的响应,以验证摄动分析有效性。     

Second harmonic generation of shear waves in crystals

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.     

Supercritical parametric wave phase conjugation as an instrument for narrowband analysis in ultrasonic harmonic imaging

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.     

非线性声波方程的几种解法对比

在医学诊疗领域及微、介观损伤的无损检测行业中,经常需要对介质的材料非线性系数进行表征,以得到局部区域更加精细的力学性能变化.文章在简述各向同性固体和理想流体介质中的非线性声波方程的基础上,证实了它们具有相同的形式,这表明它们的解也应具有相同的形式和性质.介绍了求解非线性声波方程的五种方法,包括有限差分、有限元、摄动法、...     

Computer model for harmonic ultrasound imaging

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.     

纹影法在超声场成像中的应用

纹影法成像系统具有分辨率高、成像速度快等特点,可以实现稳态声场分布以及声波传播的瞬态过程快速成像。将纹影法应用于瞬态声传播特性以及声子晶体声场的成像研究。在瞬态成像时,记录了单脉冲辐照固体表面产生的泄漏瑞利波和泄漏纵波的传播过程,并且与仿真结果进行比较,两者的泄漏波辐射角较一致。在声子晶体声场的成像中,通过改变入射频率,观察到了声子晶体在其工作频率时背表面的稳态声场,为其俘获颗粒能力的研究与分析提供了直观的实验依据。     

超声造影剂微泡非线性声学特性的数值仿真

以空气泡为例,采用描述气泡半径运动的Rayleigh-Plesset方程,对其在高频声压辐照下的非线性振荡,散射声场和散射截面进行理论和数值研究,为获取更清晰的图像提供理论依据。结果表明:激励声压的频率在微泡的固有谐振频率附近时,可以产生强的二次谐波散射声压。同时,提高入射声强可以增大二次谐波散射截面,但不能改变基波散射截面。