Modeling of transient ultrasonic wave propagation using the distributed point

Transient ultrasonic waves in a fluid medium generated by a flat circular and a point-focused transducer of finite size are modeled by the distributed point source method (DPSM). DPSM is a Green's-function-based semi-analytical mesh-free technique which is modified here to incorporate the transient loading from a finite-sized acoustic transducer. Conventional DPSM solves acoustic problems in steady-state frequency domain. Here, DPSM is extended to the time domain without the fast Fourier transform (FFT) but using the Green's function in the time domain. This modified method is denoted t-DPSM. Harmonic point sources of DPSM are replaced by time-dependent point sources in t-DPSM. Generated t-DPSM results are compared with the finite element (FE) results for both focused and flat circular transducers. The developed method is used to solve the transient problem of wave scattering by an air bubble in a fluid as the bubble is moved horizontally or vertically from the focal point of the focused transducer. The received energy signal is compared for different eccentricities.     

Lagrangian finite element method for solitary wave propagation

A finite element method for a study of the propagation of solitary waves has been presented using the Lagrangian formulation. In this method, the computation of the convection terms can be avoided in the basic iteration procedure and the determination of the free surface position is automatically performed. To obtain the velocity and pressure, the velocity correction method is effectively used based on the correction potential. To overcome the distortion of the configuration of finite elements, the rezoning technique has been effectively used. The wave propagation analysis has been carried out and the validity of the present method has been demonstrated.     

Lamb波在复合材料板中传播的谱有限元建模和仿真

基于谱有限元对Lamb波在复合材料层合板中的传播进行了模拟。结合Gabor小波分析对谱有限元及传统有限元模拟结果与理论结果进行了对比, 并对相控阵法结构探伤的扫描过程进行了模拟和分析, 给出了Lamb波的传播和扫描图像。结果表明, 在得到更精确模拟结果的同时, 谱有限元较传统有限元法能大大缩短计算时间, 证实了该方法在模拟Lamb波在复合材料板中的传播方面的优越性。同时, 谱有限元法能很好地模拟相控阵法探伤的扫描过程, 模拟结果与实际结果吻合, 证实了本文建模方法的可行性和精确性。      

Control of wave propagation response using quasi crystals: A formulation based on spectral finite element

This paper presents wave propagation studies in quasi crystal structures and quasi crystal reinforced aluminium structures. The analysis is performed using frequency domain spectral finite element formulation. The analysis considers different 2-D decagonal and 3-D icosahedral quasi crystals. First, wave propagation analysis of quasi crystal structure alone is performed and the propagation of phonon and phason modes for different quasi crystals are studied. The study includes the propagation of axial and transverse wave responses in these quasi crystals. The study has found that the amplitude of the phason modes is very small compared to the phonon modes and the increase of the phason mode content (through increase in R) increases the phason mode amplitude, without affecting the phonon mode amplitudes. It is shown that the dominant axial phonon mode is non-dispersive and the dominant flexural phonon mode is dispersive. In the next study, the aluminium beam structure is reinforced with different quasi crystals in different configurations and the wave propagation of axial and transverse responses are studied. For all the combinations of quasi crystal aluminium beam combination, there is substantial suppression of responses both for the axial and the bending responses. Unsymmetrical configuration produces substantial non-dominant phonon modes which propagate dispersively. It is found that for a symmetric bi-morph configuration, the response is reduced significantly, about 68% and 75% for axial loading and 80% and 78% for flexural loading, respectively, for the 2-D decagonal quasi crystal and the 3-D icosahedral quasi crystal.     

Thermoelastic wave with a finite heat propagation velocity

It is shown that, when the velocity of heat propagation is considered, the thermoelasticity problem with instantaneous heating of a surface does not have a solution. A method is proposed for determining the amplitude of a thermoelastic wave from the initial conditions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 176–180, July, 1971.     

Transmission line interpretation of the finite element mesh for a wave propagation problem

A one-dimensional exterior electromagnetic scattering problem is formulated using a differential equation approach followed by a finite element discretization. By interpreting the resulting linear algebraic equations as node voltage equations for a transmission line, a boundary element is obtained which satisfies the requirement of no wave reflection at the edge of the finite element region. Numerical results which show the elimination of non-physical standing waves from the scattered field are presented and discussed.     

Modeling of ultrasonic wave propagation in integrated piezoelectric structures under residual stress

The objective of this study is to understand the role of residual stress in piezoelectric layers in order to predict the performance of integrated structures. This is of particular importance in thick or thin film technology. Considering a bulk piezoelectric material, the Christoffel equation for a piezoelectric material is modified to take into account a uniform residual stress on a given cross section. A numerical study of its influence is carried out on the slowness curves and coupling coefficients of a lithium niobate material. In a second part, modified Christoffel tensor is used to calculate the dispersion curves of Lamb waves in a piezoelectric plate. The Lamb modes are found to be sensitive to the residual stress. In particular, it is shown how the behavior of the first Lamb modes is modified with residual stress. In a third part, these results are extended to a piezoelectric film laid down on a substrate in order to model the importance of these phenomena on the behavior of an integrated structure. The numerical study of guided waves in a lithium niobate plate is performed first, then the case of a lithium niobate film laid down on a silicon substrate is considered.     

Thermoelastic wave characteristics in a hollow cylinder using the modified wave finite element method

This paper represents a modified formulation of the wave finite element (WFE) method for propagating analysis of thermoelastic waves in a hollow cylinder without energy dissipation. The 2D-high-order spectral element with the Gauss–Legendre–Lobatto integration is applied into the WFE method, which produces the diagonal mass matrix. Based on the assumption of harmonic displacement fields by Fourier series expansion, the general discretization wave equation is simplified from the 3D problem to 2D. Dispersion properties of elastic wave propagation in the hollow cylinder are computed considering the choice of the spectral element orders, and the results indicate the high efficiency and high accuracy of the modified formulation compared with that of the software Disperse. Then, using the modified formulation, the thermoelastic dynamic equation of the cylinder is derived from the generalized thermoelasticity theory. The propagation of the thermoelasticwave (including two kinds of wave modes) in the cylinder without energy dissipation is discussed in differentcases. Finally, wave structures along the radial direction of thermoelastic wave modes are shown at thenondimensional frequency 1.25, which can be used for the recognition of different modes.     

Two step explicit finite element method for tsunami wave propagation analysis

Numerical analysis of tsunamis applying the finite element method is presented based on the shallow water wave equation. To discretize time, a two step explicit method is used. The scheme is the extension of the Lax-Wendroff finite difference method. The present finite element method is used for the analysis of the Tokachi-oki Earthquake tsunami problem and compared with the tide gauge records. The conclusion of this paper is that the present method is suitable for the prediction of the tsunami wave propagation problem.     

Convergence criteria for scattering models of ultrasonic wave propagation in suspensions of particles

Scattering models used to simulate the attenuation and phase velocity of an ultrasonic wave propagating through a suspension of particles involve the summation of an infinite series of partial waves. The accuracy of computation is influenced by the number of terms included in the harmonic series, and the number of terms required depends upon the scatterer size compared with wavelength. It is shown that the errors in modelled attenuation and phase velocity resulting from premature truncation can be significant when modelling higher values of particle diameter-frequency product. A useful and simple heuristic is presented, in which the number of terms in the summation of the infinite series needed for satisfactory convergence to a final value is a function of the particle diameter-frequency product and of the compressive wave velocity in the continuous phase     

基于谱元法的复合材料裂纹梁Lamb波传播特性研究

基于谱元法提出了一种弹簧元来模拟复合材料梁由于横向裂纹导致的轴弯耦合效应,分析复合材料裂纹梁中Lamb波的传播特性。由断裂力学的相关知识求得弹簧元的刚度,建立复合材料裂纹梁的损伤谱元模型。通过模拟复合材料裂纹梁内Lamb波传播,并和传统的有限元结果进行比较,验证了所提出模型的可行性和有效性。推导了频域内Lamb波各模态的能量计算公式,裂纹处的能量守恒证明了所提出模型的正确性,同时计算表明复合材料梁中裂纹处反射与透射的Lamb波各模态能量随着裂纹深度的变化规律具有单调性,结论可以为定量识别复合材料梁裂纹提供实用依据。     

Modelling of ultrasonic consolidation using a dislocation density based finite element framework

A dislocation density based constitutive model has been developed and implemented into a crystal plasticity quasi-static finite element framework. This approach captures the evolution of dislocations and grain fragmentation at the bonding interface when boundary conditions pertaining to the Ultrasonic Consolidation process (UC) are prescribed.

The model is initially calibrated using experimental data from published refereed literature for simple shear deformation of a single crystal pure aluminum and uniaxial tension of a polycrystalline Aluminum 3003-H18 alloy. The model has then been extended to predict the results of an Al 3003- H18 alloy undergoing UC. Good agreement between the experimental and simulated results has been observed for the evolution of linear weld density and embrittlement due to grain substructure evolution. For computational time efficiencies, a novel time homogenisation approach has been followed which significantly reduces the computational overhead.     

Developments in ultrasonic modeling with finite element analysis

An overview is given of finite element analysis and its application to the modeling of ultrasonic nondestructive evaluation phenomena. Following a discussion of the underlying weighted residual methodology, a mass-lumping technique is described which results in an efficient computer implementation for 2D geometries. Code predictions are compared with both analytical and experimental results, and data from studies of attenuation, anisotropy, defect interactions, and surface waves are given. Initial results from a full 3D formulation are also shown.     

超声波化学反应器的温度场有限元模拟

文章基于有限元方法建立了超声波化学反应器的温度场模拟方法,并以超声波化学反应器内引发的苯乙烯分散聚合反应为例,利用ANSYS软件对超声波输出功率为400W时,不同时刻反应介质的温度场分布进行了模拟,研究结果表明超声波化学反应器内引发的分散聚合反应是分区域分阶段逐步进行的。     

A deep rod finite element for structural dynamics and wave propagation problems

In this paper, a new element for higher order rod (normally referred to as Minlin–Herrman rod) is formulated by introducing lateral contraction effects. The cross‐section is assumed to be rectangular. The stiffness and mass matrices are obtained by using interpolating functions that are exact solution to the governing static equation. The studies using this element for free vibration analysis show that lateral contractional inertia has a pronounced effect on the natural frequencies of the rod systems. The formulated element is not only able to capture the two propagating spectrums but also the dispersive effects in a deep rod. The results obtained from this element is compared with the previously formulated exact higher order spectral rod element. Copyright © 2000 John Wiley & Sons, Ltd.     

Simulations of piezoelectric Lamb wave delay lines using a finite element method

The method of piezoelectric finite elements was applied to the simulation of piezoelectric Lamb-wave delay lines with and without acoustical absorbers. In this finite-element analysis, free as well as electrically driven vibrations were computed. The shapes of the symmetric Lamb modes were determined by the solution of eigenproblems, and the transient mechanical build-up process was studied for a switched electrical sine wave excitation. The transfer function, the group delay time, and the impedance matrix of devices of different designs are calculated. The good agreement between simulation and experimental results indicates the suitability of the finite-element method for optimizing acoustic delay-line devices.     

Modelling crack propagation in reinforced concrete using a hybrid finite element–scaled boundary finite element method

A previously developed hybrid finite element–scaled boundary finite element method (FEM–SBFEM) is extended to model multiple cohesive crack propagation in reinforced concrete. This hybrid method can efficiently extract accurate stress intensity factors from the semi-analytical solutions of SBFEM and is also flexible in remeshing multiple cracks. Crack propagation in the concrete bulk is modelled by automatically inserted cohesive interface elements with nonlinear softening laws. The concrete–reinforcement interaction is also modelled by cohesive interface elements. The bond shear stress–slip relation of CEB-FIP Model Code 90 and an empirical confining stress–crack opening relation are used to characterise slip and split failure at the concrete–reinforcement interface, respectively. Three RC beams were simulated. The numerical results agreed well with both experimental and numerical results available in the literature. Parametric studies demonstrated the importance of modelling both slip and split failure mechanisms at the concrete–reinforcement interface.     

A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam

A new spectral element (SE) is formulated to analyse wave propagation in anisotropic inhomogeneous beam. The inhomogeneity is considered in the longitudinal direction. Due to this particular pattern of inhomogeneity, the governing partial differential equations (PDEs) have variable coefficients and an exact solution for arbitrary variation of material properties, even in frequency domain, is not possible to obtain. However, it is shown in this work that for exponential variation of material properties, the equations can be solved exactly in frequency domain, when the same parameter governs the variation of elastic moduli and density. The SE is formed using this exact solution as interpolating polynomial. As a result a single element can replace hundreds of finite elements (FEs), which are essential for all wave propagation analysis and also for accurate representation of the inhomogeneity. The developed element is used for eliciting several advantages of the gradation, including mode selection, mode blockage and smoothening of stress waves.     

Models of ultrasonic wave propagation in epoxy materials

This paper is concerned with modeling ultrasonic wave propagation in epoxy materials to better understand NDE procedures and to provide reliable input to more complex models of guided wave propagation in layered structures. Different physical models are considered in the context of how well they simulate the (known) linear relationship between bulk wave attenuation coefficients and frequency. The identified models are then extended to simulate wave propagation in materials with mechanical properties, which vary gradually in the spatial dimension. This is achieved using electric circuit transmission line analogs to the viscoelastic mechanical system. Verifying experimental results are included.