Theoretical Wave Velocities Research Articles

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints. In this study, numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method (FEM) with the intrinsic cohesive zone model (ICZM). Then, the uniaxial compressive and wave propagation simulations were performed. The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models. The uniaxial compressive strength (UCS) and wave velocity of rock masses decrease monotonically as the joint number increases. However, the wave velocity grows monotonically as the joint dip angle increases. When the joint dip angle is 45°–60°, the UCS of the rock mass is lower than that of other dip angles. The wave velocity parallel to the joints is greater than that perpendicular to the joints. When the dip angle of joints remains unchanged, the UCS and wave velocity are positively related. When the joint dip angle increases, the variation amplitude of the UCS regarding the wave velocity increases. To reveal the effect of the joint distribution on the velocity, a theoretical model was also proposed. According to the theoretical wave velocity, the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results. Furthermore, a theoretical indicator (i.e. fabric tensor) was adopted to analyze the variation of the wave velocity and UCS.

Laser-Generated Scholte Waves in Floating Microparticles.

This study aims to demonstrate the generation and detection of Scholte waves inside polystyrene microparticles. This was proven using both experimental analysis and COMSOL simulation. Microspheres of different sizes were excited optically with a pulsed laser (532 nm), and the acoustic signals were detected using a transducer (40 MHz). On analyzing the laser-generated ultrasound signals, the results obtained experimentally and from COMSOL are in close agreement both in the time and frequency domain. A simplified analysis of Scholte wave generation by laser irradiation for homogeneous, isotropic microspheres is presented. The theoretical wave velocity of the Scholte wave was calculated and found close to our experimental results. A representation of pressure wave motion showing the Scholte wave generation is presented at different times.

Application of impact-echo method for rockbolt length detection

This study examines the spectral responses resulting from the use of the impact-echo method for rockbolt length detection. A rockbolt is a thin long member that is often used in tunnels or slope protection works to fasten structures and soil/rock mass tightly together. It involves embedding a long steel bolt fully anchored to the original structure to resist strong pulling forces and stabilize the original structure or serve as a connecting member between two materials. Inadequate embedment length or poor grouting can prevent rockbolts from serving the function they were designed for and result in rockbolt failure. This study employed finite element analysis to conduct numerical simulation analyses of the stress wave signals in rockbolts and then used the impact-echo method to measure rockbolt length and grout integrity. Our results indicate that the impact-echo method can be used to determine rockbolt length but requires prior knowledge of whether the rockbolt is grouted. If not, then its detection signals will be similar to those of a bare steel bar. The rockbolt length can then be calculated using the theoretical wave velocity in a steel bar and the fundamental frequency derived from measurements. If the rockbolt is grouted, then the wave velocity in the grout material must be known so that the accurate length of the rockbolt can be derived.

Modelling and Validation of a Guided Acoustic Wave Temperature Monitoring System.

The computer modelling of condition monitoring sensors can aide in their development, improve their performance, and allow for the analysis of sensor impact on component operation. This article details the development of a COMSOL model for a guided wave-based temperature monitoring system, with a view to using the technology in the future for the temperature monitoring of nozzle guide vanes, found in the hot section of aeroengines. The model is based on an experimental test system that acts as a method of validation for the model. Piezoelectric wedge transducers were used to excite the Lamb wave mode in an aluminium plate, which was temperature controlled using a hot plate. Time of flight measurements were carried out in MATLAB and used to calculate group velocity. The results were compared to theoretical wave velocities extracted from dispersion curves. The assembly and validation of such a model can aide in the future development of guided wave based sensor systems, and the methods provided can act as a guide for building similar COMSOL models. The results show that the model is in good agreement with the experimental equivalent, which is also in line with theoretical predictions.

Influence of 3D printing stress wave on residual stress

As a popular rapid manufacturing technology, three-dimensional printing (3D printing) has been widely adopted in medical, automotive, aerospace, construction and other industrial fields. The stereo lithography apparatus (SLA) is an effective 3D printing method for ceramic printing. However, shrinkage from monomer to polymer and laser stress wave cause residual stress in the formed parts during SLA. Serious quality defects including cracks, warpage and deformation caused by residual stress have remained to be a problem. Basically, the laser stress wave plays an important role in the generation of 3D printing residual stress. In this work, to investigate the propagation mechanism of the laser stress wave, the finite element method was adopted to simulate the SLA process of zirconia. The influence of 3D printing factors on the residual stress was obtained, and we found that the wave velocity of the stress wave obtained by the simulation model was highly consistent with the theoretical wave velocity. Meanwhile, the attenuation formula of the stress wave in the 3D printing process was obtained by fitting to investigate its attenuation law. Based on the above results, the attenuation law of the 3D printing stress wave has a direct influence on the development and variation trend of its residual stress.

Global eigenmodes of thin liquid sheets by means of Volume-of-Fluid simulations

The unsteady dynamics of planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is numerically investigated by means of the Volume-of-Fluid (VOF) technique for supercritical regimes. The global behavior of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively small amplitude, thereby exciting sinuous modes. To gain more physical insights into the fluid system, a theoretical linear one-dimensional model is also developed. A physical interpretation of this model relates the sheet dynamics to transverse vibrations of tensional string forced by terms containing the lateral velocity and subjected to a total damping coefficient, which can assume negative values. The VOF simulation satisfactorily confirms that the velocity impulse perturbation splits into two wave fronts traveling downstream with the theoretical wave velocities. A good agreement is found in comparing the crossing times over the entire domain length of such waves with the almost constant spacing between the frequencies of the eigenvalue spectrum. Surface tension plays a stabilizing role, and for relatively high values of density ratio rρ of gaseous-to-liquid phases, the sheet becomes unstable. It is argued that the distribution of transverse velocity component of the gaseous phase represents the forcing term, which leads the system toward the instability when, for relatively high rρ, the total damping becomes negative. An analogy seems to exist between the global unstable behavior exhibited by the liquid sheet as rρ increases and the shear-induced global instability found by Tammisola et al. [Surface tension-induced global instability of planar jets and wakes,” J. Fluid Mech. 713, 632–658 (2012)] in the presence of surface tension. However, for the gravitational sheet, the surface tension is stabilizing.

Propagation characteristics of ship waves in navigation tunnel and its influence on continuous navigation safety of ship

In parallel to the construction of navigable tunnels which is gradually put on the agenda in China, more and more navigable tunnels are bound to be built. However, the relevant technical support is still extremely lacking. The existing engineering design and construction only refer to the construction experience of various traffic tunnels or the inland waterway navigation regulations, which in turn creating a limitation that the influence of navigable hydrodynamic environment is not considered. Therefore, to fill in the gaps in the research on key technologies of ship navigation safety in navigable tunnels, the open-source package FUNWAVE-TVD based on completely nonlinear Boussinesq equation has been used to establish a numerical model, demonstrating ship travelling wave motion in navigable tunnels in linear canals. The model can help to determine the ship model by pressure source terms. The model size and research conditions are determined according to the inland river navigation code and existing engineering examples. The accuracy of the model is evaluated using numerical verification, grid convergence analysis and ship travelling wave stability. The temporal and spatial distributions of height and velocity of the solitary wave induced by ships in navigable tunnels are analyzed. The safety impact of ship travelling wave in navigable tunnels on continuous navigation is discussed. The results show that the model has a great ability to capture the propagation and evolution process of ship travelling wave in navigable tunnels. It is pointed out that large fluctuations are easily formed on both sides of the quay wall of the navigation tunnel and in the middle part. The multiple nonlinear regression equation containing the maximum solitary wave height η max, ship draught P , Fr , water depth, width of navigation tunnel and ship type is obtained. The equation shows that the maximum solitary wave height gradually increases with the increase of ship draught and Fr , but vice-versa with the increase of water depth, width and section coefficient of navigation tunnel. It is found that the wave velocity of the front solitary wave surface is in good agreement with the theoretical solitary wave surface equation. Taking the theoretical wave velocity of the solitary wave as the propagation velocity, the safe sailing distance of the ship during the continuous navigation, especially under the conditions of large speed and draught in existing navigation tunnels, is obtained. The novelty of this paper is serving as a reference and basis for the design of navigation tunnels in single-line straight canals and playing a role as a theoretical foundation for the formulation of any key technical standards or specifications for navigation safety of ships in navigation tunnels.

On elastic waves in granular assemblies: From a continuumnization viewpoint

The characteristics of elastic waves in granular assemblies of spherical particles, which translate and spin, are analyzed by a continuumnization technique. The continuumnized governing equations for equal spheres in three-dimensional lattices are first obtained, accompanied by auxiliary tensors corresponding to the macroscopic material properties. The property tensors, i.e., the stiffness, coupling, and spinning tensors, given in neat analytical form, are solely determined by the micro-mechanics (the normal and tangential spring constants) and the microstructures of the lattices (the unit vectors connecting the centers of neighboring particles). The general formulas are then applied for two types of closest packed lattices. Theoretical wave velocities for p- and s-waves in such lattices are derived, together with the frequency for the pure spin mode and the group velocity for the spin motion coupled with s-waves. Two interesting findings of the physics of lattices of spheres are revealed: the s-wave coupled with spin motion in the lattices can be understood as acoustic and optical branches of waves in the diatomic model in solid-state physics; the anisotropic closest packed lattices would degenerate into a special isotropic state with zero Poisson’s ratio and a constant velocity ratio of 2 between p- and s-waves. How the wave velocities and the anisotropy are influenced by the spring constant ratios are also analyzed. The theoretical results obtained can be used for quantitative verification and for parameter calibration of discrete-element-method simulations using spherical particles.

花こう岩の異方弾性定数の評価法に関する研究

It is well known that granite has orthorhombic elasticity caused by the orientation distribution of the pre-existing microcracks. Measurements of P and S-wave velocities propagating in various directions are indispensable to determine these elastic constants, because the orthorhombic material has nine independent elastic constants.In this study, a new method to determine the elastic constants of granite is proposed. In this method, rock is assumed to be an elastic material which contains oriented cracks and random distributed cracks, and the effective elastic constants of rock are calculated by using New Self Consistent Scheme. From the calculated elastic constants, theoretical values of the elastic wave velocities are calculated and compared with measured values of them. The elastic constants can be back-analyzed by minimizing the difference between theoretical wave velocities and measured ones.The proposed method is applied to three kinds of granite. It is confirmed that the theoretical values of wave velocities agree well with the measured values, and that the elastic constants as well as the crack densities can be evaluated. Furthermore, it is pointed out that the elastic constants of granite can be evaluated by measuring P-wave velocities in three principal directions.

Wave-Mode Modification in Liquid Helium with Partially Clamped Normal Fluid

When the equations of first and second sound are modified to correspond to wave propagation in the presence of viscous forces on the normal fluid, two wave modes result. In the limit of large viscous forces, second sound becomes an overdamped thermal mode with zero velocity, and first sound becomes an undamped (acoustic) mode with wave velocity $v$ given to first order by ${v}^{2}={(\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}})}^{2}{{c}_{1}}^{2}+{(\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}})}^{2}{{c}_{2}}^{2}$ in terms of usual symbols. In this investigation, the onset of wave-mode modification has been examined as degradation of pure second-sound pulses and standing waves in the presence of barriers. Normal fluid was partially clamped in the interstices of emery powder or rouge, with viscous drag controlled by employing several packing densities. The velocity of thermal signals sent through chambers filled with these small particles decreases, and the damping increases with smaller interstices. The theoretical wave velocities of the thermal and acoustic modes are obtained, as functions of temperature and a viscosity coefficient, from the modified wave equations. For suitably chosen constant values of the viscosity coefficient, the theoretical velocity of thermal waves is in approximate quantitative agreement with the observed pulse velocities, and the observations are interpreted in this way. Qualitatively observed attenuation is shown to be in agreement with the same theory. The effect of capacitive thermal losses to the barrier particles, and consequent possible degradation of incipient wave modes to thermal diffusion, is also analyzed.

Theory of Breakdown Wave Propagation

The propagation of electrical breakdown waves in a gas is analyzed by assuming that the wave front of the breakdown wave is an electron shock wave. A simple three-fluid hydrodynamical model is used in which the partial pressure of the electron gas behind the shock zone is the primary source of the motion. A theoretical wave velocity of 2\ifmmode\times\else\texttimes\fi{}${10}^{7}$ m/sec is predicted for an applied field of ${10}^{4}$ V/m in ${\mathrm{H}}_{2}$ at a pressure of 0.2 mm Hg. Since the propagation mechanism of the breakdown wave is mechanical, the model explains propagation equally well into either a positive or negative electric field. Qualitative agreement between theoretical and experimental breakdown wave velocities is obtained.