Showing 12 results for Wave Propagation
Volume 13, Issue 2 (5-2013)
Abstract
It is well known that ground surface with irregular topographic features causes complicated seismic responses. The complex seismic response is mainly caused by wave scattering. In this study, for a homogeneous, isotropic, linearly elastic half-space, the formulation of a two-dimensional SH-wave field based on the direct boundary element method and Neumann series expansion is developed. By discretizing the ground surface to boundary elements, the boundary integral equation is formulated into a general matrix form. This general matrix form is then reduced to a more efficient form, which considerably reduces the size of the computational matrices using Neumann series expansion. For this purpose, a Fortran computer program is developed, whose accuracy and feasibility in the frequency domain is shown by some numerical analyses conducted for grounds with semicircular convex and concave, and symmetrical V-shaped canyon topographical configurations. Comparing the results of the present study with those available in the literature shows the accuracy of the present study by just considering two first terms of Neumann series expansion. The minor differences of the results of the present research with other reseach results may be assigned to the number of terms of Neumann series expansion and the order of used boundary elements. In other words, if the number of terms of Neumann series expansion and the order of used boundary elements incease, the accuracy of the numerical results may enhance. Based on the results of the present research for various parameters of different two-dimensional canyons, the following conclusions may be obtained: When the exciting frequency increases, the wave-length decreases. As a result, the violence effects of incident wave due to canyon effects may be significant for a given canyon. Moreover, the displacement field of various canyon points follows more complicated pattern. On the other hand, for smaller exciting frequencies with larger wave-lengths, the canyon effects as the main cause of disturbation source are not so remarkable, and the displacement field of various canyon points are smoother. The effects of incident wave angle is also remarkable on the disturbation patterns of displacement field of different canyon points. When the angle increases, the triangle canyons experience more complicated patterns compared to semicircular canyons. Analyses'''' results show important effects of shape and depth of various canyons. These effects are more considerable when depth''''s variations are remarkable in comparison with the wave-length of incident wave. Furthermore, the mentioned effects are functions of frequency and angle of incident wave.
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Volume 13, Issue 15 (3-2014)
Abstract
The work is dedicated to the elastic wave propagation in particulate composite with random distribution of soft and stiff inclusions. The multiple scattering theory of Waterman-Truell in combination of static generalized self-consistent model is used to formulate the Dynamic Generalized Self-Consistent Model which is used because of its precision in modeling of high volume fraction and high frequency waves. The model has been described and two different cases containing of soft and stiff inclusions are considered. The propagation behavior such as normalized wave propagation, normalized attenuation and the dynamic effective properties are studied. Investigation is carried on long and intermediate wave-length regime and different values of volume fraction for longitudinal (P) and shear (S) elastic waves. The results indicate that the propagation properties are strongly affected by aforementioned parameters.
Mehran Kadkhodayan, Hassan Zafarmand,
Volume 14, Issue 11 (2-2015)
Abstract
In this paper the three dimensional dynamic analysis and stress wave propagation in thick functionally graded plate subjected to impact loading is studied. Material properties (elasticity modulus and density) are assumed to vary continuously through the thickness direction of the plate according to a simple power law distributions and the Poisson’s ratio is assumed to be constant. The equations of motion are based on three dimensional theory of elasticity. The three dimensional Graded Finite Element Method (GFEM) based on Rayleigh-Ritz energy formulation and Newmark direct integration method has been applied to solve the equations in time and space domains. It is assumed that in dynamic loading the upper surface of the plate is subjected to a pressure load that varies linearly with time, and suddenly is unloaded at a specified time. This unloading acts as an impact loading. Afterward, the time histories of displacement through the thickness, stresses in three dimensions and velocity of stress wave propagation for different values of power law exponents, various boundary conditions and thickness to length ratios have been investigated. The obtained results are in agreement with available data in literature.
Reza Rajabiehfard, Abolfazel Darvizeh, Mansoor Darvizeh, Reza Ansari, Hamed Sadeghi,
Volume 15, Issue 2 (4-2015)
Abstract
In this paper, the dynamic plastic buckling of axisymmetric circular cylindrical shells subjected to axial impact is investigated. The von Mises yield criterion is used for the elastic-plastic cylindrical shell made of linear strain hardening material in order to derive the constitutive relations between stress and strain increments. Nonlinear dynamic circular cylindrical shell equations are solved with the finite difference method for three types of boundary conditions and two types loading. Two types of loading are stationary cylindrical shells impacted axially and traveling cylindrical shells impacted on a rigid wall. The growth and improvement of axial and lateral strains and buckling shapes of cylindrical shells are investigated for different boundary and loading conditions, from the viewpoint of stress wave propagation. It is found that the total length of cylindrical shell is affected by the plastic deformation when the plastic wave reaches unimpacted end. Also it is found that shortening and energy absorption are independent of loading and boundary conditions. The buckling shapes are affected by loading and boundary conditions; also peak loads at impacted and unimpacted ends are affected by loading conditions and are independent of boundary conditions. The presented theoretical results are compared with some experimental results and good agreement is obtained.
Azadeh Goodarzi, Hossein Mohammadi Shodja, Behdad Hashemian,
Volume 15, Issue 8 (10-2015)
Abstract
In the present work, the elastodynamic field of scattering of an anti-plane high frequency elastic shear wave due to an embedded nano cylindrical cavity in an infinite elastic medium is obtained by considering the effects of couple-stresses. In the theories accounting the effects of couple-stresses in their formulations, a new characteristic length of material is introduced into the formulations, and so, these are capable to capture size effect at micro and nano scales. Also, in contrary to classical continuum theory which has difficulties in describing dispersion of wave at high frequencies, observed dispersive wave in experiments can be explained in the framework of these theories. In this work, the analytical expressions of elastodynamic fields around the cavity are obtained by considering equation of motion, dispersion relation and appropriate boundary conditions in the framework of two theories considering couple-stresses. Also, the dynamic stress concentration factor around the cavity within these theories is obtained, and, as a limiting case, the results of two cases of dynamic stress concentration factor in classical theory as well as static stress concentration factor in couple stress theories are recovered. In the framework of these theories, by several examples, the effects of frequency of incident wave and the ratio of couple stress characteristic length to the size of the cross section of the cavity on the displacement field, stress field and dynamic stress concentration factor around the cavity are studied, and the results are compared with the corresponding classical solutions.
Shahram Yareiee, Mohammad-Reza Sayyed Noorani, Ahmad Ghanbari,
Volume 16, Issue 6 (8-2016)
Abstract
Ultrasonic Phased Arrays are an emerging technology in nondestructive testing and evaluation. Some important factors affecting on the performance of these probes include, positioning elements in probe, number of elements, distance between two elements, elements length, and time delays to excite probe elements. The type of linear phased array probes is a prevailing type in which elements placed side by side and longitudinally. In this paper based on analyzing the existent laws in design and performance of the phased array probes related to the propagation of ultrasonic waves, an improved dimensional design for ultrasonic linear phased array probes, as well as improvement of the sequence of time delays to excite the probe elements are done. In order to evaluate the performance of the probe with improved design in comparison with a similar ordinary probe, an ultrasonic phased array test is simulated using FEM-based ABAQUS software. By numerical simulations, the performance of the probe with improved design versus the ordinary probe for propagating the guided waves in a thin square aluminum plate is compared. In first part, the attenuation coefficient of the received signals of reflected wave is evaluated, and in second part, the performance of the probes for radial scanning is compared. Results of both simulations confirm that the performance of the probe with improved design is much better than the similar ordinary one. Specially, the probe with improved design propagates the ultrasonic waves with the maximum head wave energy, and steers them with higher accuracy towards a determined direction.
Ali Mansouri, Hossein Ghaffarzadeh, Majid Barghian, Morteza Homayoun Sadeghi,
Volume 16, Issue 11 (1-2017)
Abstract
A variety of numerical methods were developed for the wave propagation analysis in the field of structural health monitoring. In this framework, meshless methods are suitable procedure for the analysis of problems such as damage initiation and its propagation or the fracture of materials. In this study, Hermit-type radial point interpolation method (HRPIM) is investigated for the numerical modeling of flexural wave propagation and damage quantification in Euler-Bernoulli beams using MATLAB. This method employs radial basis function (RBF) and its derivatives for interpolation which leads to Hermitian formulation. The evaluation of performance and capability of HRPIM is based on the comparison between the captured HRPIM ang benchmark signals using the root mean square error (RMSE) and reflection ratio from damage. The algorithm of damage quantification is the analytical solution which relates the reflection ratio to the damage extent. In this study, Gausian-type RBF is utilized and the number of field nodes, the size of support domain, shape parameters of RBF, the number of polynomials in the interpolation formula, the arrangement of background cells and the number of Gaussian points in damage length are the effective parameters on results. Based on the evaluation, the acceptable values and range of theses parameters are presented for correct modeling.
Sadegh Moodi, Hossein Mahdizadeh, Mehdi Azhdary Moghaddam,
Volume 17, Issue 4 (6-2017)
Abstract
Accurate investigation of physical phenomena is one of the important challenges in engineering fields. The present study is about a wet tank which entrance of water is investigated in three cases. When the water wave moves into a tank, complex flow regimes are created. This complexity is mainly associated with different flow mechanisms during the entrance of water and propagation of waves at the bottom bed that should be modelled by means of Navier-Stokes equations with free-surface capability and in 3D phase. Due to complexity and time consuming of Navier-Stokes equations modelling, Shallow water equations are used with the assumption of hydrostatic pressure. First case is about efflux over a wet bed. Second, water influx from the middle top is investigated and then influx from top edges is modelled. A dimensionless number is introduced for each case based on water velocity, gap length and drop height which shows acceptable domain for appropriate compatibility between results. Finally, results of numerical modelling are compared with Navier-Stokes solutions which are obtained from STAR-CD software. Results show admissible compatibility with each other based on observations and inspections.
Mohsen Mirzajani, Naser Khaji,
Volume 17, Issue 5 (7-2017)
Abstract
In this paper, the Wave Finite Element Method (WFEM) is developed for modelling of stress wave propagation in one-dimensional problem of nonhomogeneous linear, anisotropic micropolar rod of variable cross section. For this purpose, the WFEM equations are developed based on the micropolar theory of elasticity. Two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational Degree of Freedom (DOF) is considered besides the classical elasticity’s DOF. The method proposed in this paper is implemented to solve the wave propagation and impact problems in micropolar rods with different layers. The results of the proposed method are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.
Sadegh Moodi, Hossein Mahdizadeh,
Volume 18, Issue 6 (10-2018)
Abstract
In this paper a modified Godunov-type wave propagation algorithm is utilised for the modelling of falling water wave over a dry bed. The defined numerical model is well-balanced and is capable to treat the influx/efflux source terms and also the friction term within the flux-differencing of the finite volume neighbouring cells. Additionally, the method employs a rather simple HLLE wave speed for the propagation over dry-state. First the efflux flow from the bed of a reservoir is analyzed. Then, the entrance of falling water wave from the middle and edge sides of the reservoir over a dry bottom is simulated. In order to validate the achieved numerical results for the non-hydrostatic pressure situations a dimensionless number based upon the inflow velocity, the slot length and the falling height is introduced. The obtained results of the defined numerical solver are then compared with the numerical prediction of the STAR-CD which is a commercial Navier-Stokes package. The numerical results demonstrate that the introduced flux-wave solver is able to simulate the falling water waves over the dry-state for a given range of the dimensionless number.
Volume 22, Issue 4 (7-2022)
Abstract
Using modal analysis is a lot easier and more widespread among structures, but the important question is about the number of modes should be considered in the modal analysis method to reach an answer with an inevitable error but in logical tolerance. In this regard, the ratio of the dominant period of the earthquake to the main period of the structure is used as a criterion for selecting the number of modes in the modal analysis method. On the other hand, although the maximum displacement of the structure occurs above it, but when the period of the pulse is less than the main period of the structure, due to wave motion along the structure, the maximum shear strain can occur not only at the base but also in other places along the structure. In this paper, some limitations of modal analysis versus Dchr('39')Alembert solution have been studied in analysis of shear beam under impulsive loads. For this purpose, the structure is modeled with a shear beam with linear material and zero damping, and it is analyzed by discrete (modal analysis) and continuous (Dchr('39')Alembert solution) methods. The time response of modal analysis has been done by the fourth-order Runge-Kutta method. The shear beam is subjected to short, medium, and long period half-sine pulses, relative to the main period of the structure, as well as two near-field earthquakes with distinct pulse. The envelope of maximum induced displacement and shear strain (drift) along the beam have been selected to compare the two methods. The necessary number of modes in modal analysis are determined in such a way that its difference with the exact method (Dchr('39')Alembert solution) would be in acceptable range. For shear beam with linear material and zero damping, as it is expected, the results indicate that for convergence of shear strain (drift) response to the exact solution more number of modes are needed than convergence of displacement response in the modal analysis. Under short period pulse
, when the ratio of the period of the pulse or the predominant period of earthquake to the main period of the beam is less than
, if the minimum number of modes in modal analysis would be 20 and 50 modes for displacement and shear strain, respectively, then the percentage of error of envelope of maximum induced displacement and shear strain (drift) in beam, calculated by modal analysis, would be less than 10 percent, respect to Dchr('39')Alembert solution. Under medium period pulse
, when the ratio of the period of the pulse or the predominant period of earthquake to the main period of the beam is greater than
and less than
, for having ten percent difference between two methods of analyses, the necessary number of modes in modal analysis of beam would be
and
modes for displacement and shear strain, respectively. For the beam under long period pulse
, when the ratio of the period of the pulse or the predominant period of earthquake to the main period of the beam is greater than
, the necessary number of modes in modal analysis would be 1 and 5 modes for displacement and shear strain, respectively.
Volume 24, Issue 1 (4-2024)
Abstract
The most important point in performing the Pile Integrity Test (PIT) is the correct interpretation of the results. This insitu tests is very useful in the estimation of the pile length embedded in the soil or the control of the cross section of bored piled where the quility of the pile construction is in doubt. Two common defects of the bored piles are buldging and necking of the pile cross section which correspond to the over-size and narrowing of the pile diameter alonng the pile length. Thses two anolamies in the pile geometry inflence the pile functionality and an approperiate reaction is required. Correct identifications of the length and dpeth of an anomaly are among the factors that are influenced by the anomaly location and the interaction of the waves passing through the pile. In this research, an attempt is made to interpret the results of PIT by examining the dimensions and location of anomalies in different parts of the pile as well as the effect of the presence of soil on the obtained results. PIT is simulated by the numerical finite difference method and the results have been investigated. The pile head is loaded by a semi-sinusoidal impact which is defined as a compressive pressure over a circular region at the cross section centroid during a short period of time. The verification of the simulations is established by the compariosn of the results with those one-dimentional wave theory which is based on the arrival time of the impact wave to the reciever situated on the pile head. In addition, by changing the position of the wave vreciving in the numenrical mode, it was shown that the best place to install the accelerometer as the recivier would be at the distance of 0.6R from the pile center where R is the pile radius. This finding is consistent with the results of previous studies which confirms the validiy of the simulations. According to the results, the existance of the soil around the pile causes to deform the figure of the waves and it required to modify the records before a correct interpretation. The soil atound the pile plays a role of damper of the waves passing through the pile and it causes that the magnitude of the peaks observed in the records diminish and the interpretaion may not be so easy as that in a free pile. For the pile embeded in the soil, the closer the anomaly location is to the pile head, the less the damping effect of the soil is and thus, the wave forms are more similar to the free pile. Based on the findings of this study, to interprete correctly the PIT results, it is recommended to use the first peak of the recorded velocity if there is a necking defect, while the use of the second peak is recommneded for a buldging defect to estimate the anomaly depth based on the free pile diagrams.It is also seen that as the defect length increases to about twice the diameter of the pile, the peak value of the velocity changes (in most cases, it increases) and remains almost constant at larger lengths.
