Wave Propagation In Orthotropic Media Research Articles

A comparative study of guided wave propagation in timber poles with isotropic and transversely isotropic material models

Guided wave (GW) has been used for many years in non-destructive testing (NDT). There are various ways to generate the guided wave, including impact or impulse either manually or using devices. Although the method of impact or impulse is considered to be simple and practical in guided wave generation, it produces waves with broadband frequencies, which often make analysis much more difficult. The frequency bandwidth produced by manual impacts is usually at the low end, and is therefore justified when dealing with one dimensional wave propagation assumption in low strain integrity testing of cylindrical structures. Under such assumption if the velocity is known accurately, NDTs can produce reasonably good results for the condition assessment of the structure. However, for guided wave propagation in timber pole-like structures, it is rather complicated as timber is an orthotropic material and wave propagation in an orthotropic medium exhibits different characteristics from that in isotropic medium. It is possible to obtain solutions for guided wave propagation in orthotropic media for cylindrical structures, even though the orthotropic material greatly complicates GW propagation. In this paper, timber has been considered as a transversely isotropic (i.e. simplified orthotropic) material and a comparative study of GW propagation in a timber pole is conducted considering isotropic and transversely isotropic modelling. Phase velocity, group velocity and attenuation are the main parameters for this comparative study. Moreover, traction-free situation and embedded geotechnical condition are also taken into consideration to evaluate the effect of boundary. Displacement profile, wave propagation pattern and power flow at particular frequency are utilized to determine different displacement components of longitudinal and flexural waves along and across the timber pole. Effect of temperature and moisture content (in terms of modulus of elasticity) in timber pole is also compared to show the variation in phase velocity.

Stability analysis of second- and fourth-order finite-difference modelling of wave propagation in orthotropic media

The stability of the finite-difference approximation of elastic wave propagation in orthotropic homogeneous media in the three-dimensional case is discussed. The model applies second- and fourth-order finite-difference approaches with staggered grid and stress-free boundary conditions in the space domain and second-order finite-difference approach in the time domain. The numerical integration of the wave equation by central differences is conditionally stable and the corresponding stability criterion for the time domain discretisation has been deduced as a function of the material properties and the geometrical discretization. The problem is discussed by applying the method of VonNeumann. Solutions and the calculation of the critical time steps is presented for orthotropic material in both the second- and fourth-order case. The criterion is verified for the special case of isotropy and results in the well-known formula from the literature. In the case of orthotropy the method was verified by long time simulations and by calculating the total energy of the system.

Comparative study on orthotropic solid waves by time-domain BEM and dynamic photoelasticity

Experimental research and numerical analysis are two basic tools in the study of wave propagation problems in orthotropic media. In this paper, an experimental method, namely dynamic orthotropic photoelasticity, which studies the dynamic behavior of orthotropic materials on a macroscopic scale by employing orthotropic birefringent materials, is established. Meanwhile, a numerical method, namely time domain boundary element method (BEM) for wave propagation in orthotropic media, is also presented. The two methods are used together in the analysis of semi-infinite orthotropic plates with and without a circular hole modeled by a unidirectional fiber-reinforced composite under impact loading. The propagation, reflection and diffraction of stress waves in the orthotropic media are recorded experimentally and investigated. Time histories of birefringent fringe orders or stresses for specific points of the plates are obtained, respectively, from the two methods and compared with each other. The comparative study demonstrates the applicability and accuracy of the two methods for wave propagation problems in orthotropic media.

Analytical and experimental study on wave propagation problems in orthotropic media

Wave propagation problems in orthotropic media are studied jointly by analytical and experimental methods in this paper. Dynamic orthotropic photoelasticity, which studies experimentally the dynamic behavior of orthotropic materials on a macroscopic scale by employing orthotropic birefringent materials, is established. A dynamic stress-optic law for orthotropic birefringent materials is postulated and practical methods of calibrating dynamic mechanical constants and dynamic stress-fringe values are proposed. Meanwhile, time domain boundary element method (BEM) for wave propagation in orthotropic media, is also presented based on the theory of elastodynamics. A scheme of stress calculations that is necessary for strength analysis is established. The paper stresses on the applications in wave propagation problems in orthotropic media by demonstrating three examples. The semi-infinite orthotropic plates with and without a circular hole modeled by a unidirectional fiberreinforced composite under impact loading are analyzed. Time histories of birefringent fringe orders or stresses for specific points of the plates are obtained respectively from the two methods and compared with each other. Based on the above comparative study, the dynamic response of an underground workshop under seismic waves is studied by time domain BEM. The responses of displacements and stresses are solved. The effects of angle and frequency of incident waves and the degree of media anisotropy on dynamic response of the underground workshop are investigated.

Ultrasonic reflection and guided wave propagation in biaxially laminated composite plates

This paper presents the results of numerous ultrasonic reflection measurements on plates of laminated composites in which the angle of incidence of a finite-aperture acoustic wave and its frequency have been varied. These experiments have been carried out on biaxially laminated graphite–epoxy specimens utilizing water as a fluid-coupling medium. The stacking sequence of the individual laminae is restricted such that in each layer a principal material axis lies in the incident plane of the acoustic wave. The data are compared to the results of a recent theoretical analysis based on an analytical treatment of wave propagation in orthotropic media in conjunction with a transfer matrix approach. Reflection and transmission coefficients are derived from which the characteristic behavior of the system is identified. Results are presented both as reflection spectra and dispersion curves. In general, very good agreement is found between prediction and experiment. Moreover, significant changes in the reflection spectra are observed, depending on the layer ordering in the composite plates.