Rectangular Irregularities Research Articles

Dynamics of irregular hyperelastic substrate under the impact of moving load

This work delves into the study of stresses induced in a non-homogeneous pre-stressed nearly incompressible elastic substrate with irregularity as a result of a normal load moving on its rough surface. The irregularity on the free surface of the substrate is considered in the form of parabolic irregularity. The solution methodology features the applicability of perturbation method along with substitution method to obtain the displacement components. The expressions of the induced shear and normal stresses have been established in closed form, and their expressions for special cases of the considered problem have also been deduced, which concur well with the existing literature. The influences of affecting parameters viz., non-homogeneity, frictional coefficient, irregularity factor, irregularity depth, hydrostatic stress and depth of the substrate on shear and normal stresses have been depicted graphically by means of numerical computation. The computational results have been manifested for distinct cases of irregularity zone involving parabolic as well as rectangular irregularities present in the considered geometrical model. It has been figured out that the presence of non-homogeneity in the irregular substrate has significant impact on the developed stresses.

Rigidity and Irregularity Effect on Surface Wave Propagation in a Fluid Saturated Porous Layer

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations. It can be seen that the phase velocity is strongly influenced by the wave number, the depth of the irregularity, homogeneity parameter and the rigid boundary. The dimensionless phase velocity is plotted against dimensionless wave number graphically for different size of rectangular irregularities and homogeneity parameter with the help of MATLAB graphical routines for both free and rigid boundaries for several cases. The numerical analysis of dispersion equation indicates that the phase velocity of surface waves decreases with the increase in dimensionless wave number. The obtained results can be useful to the study of geophysical prospecting and understanding the cause and estimating of damage due to earthquakes.

Scattering of the electromagnetic wave by a layer with one-dimensional rectangular irregularities

Multiple scattering of a plane electromagnetic wave by a layer with random one-dimensional rectangular irregularities of the permittivity is studied. The dependence of the mean scattered intensity on the parameters of the irregularities is obtained. It is established that the mean intensity of the field oscillates as a function of the mean width of irregularities. The conditions for a substantial increases or decrease in the mean intensity of the wave in the layer are determined.

Influence of rectangular and parabolic irregularities on the propagation behavior of transverse wave in a piezoelectric layer

PurposeThe purpose of this paper is to theoretically analyze the propagation of Love-type wave in an irregular piezoelectric layer superimposed on an isotropic elastic substrate.Design/methodology/approachThe perturbation technique and Fourier transform have been applied for the solution procedure of the problem. The closed-form expressions of the dispersion relation have been analytically established considering different type of irregularities, namely, rectangular and parabolic for both the cases of electrically open and short conditions.FindingsThe study reveals that the phase velocity of Love-type wave is prominently influenced by wave number, size of irregularity, piezoelectric constant and dielectric constant of an irregular piezoelectric layer. Numerical simulation and graphical illustrations have been effectuated to depict the pronounced impact of aforementioned affecting parameters on the phase velocity of Love-type wave. The major highlight of the paper is the comparative study carried out for rectangular irregularity and parabolic irregularity in both electrically open and short conditions. Classical Love wave equation has been recovered for both the electrical conditions as the limiting case when both media are elastic and interface between them is regular.Practical implicationsThe consequences of the study can be utilized in the design of surface acoustic wave devices to enhance their efficiency, as the material properties and the type of irregularities present in the piezoelectric layer enable Love-type wave to propagate along the surface of the layer promoting the confinement of wave for a longer duration.Originality/valueUp to now, none of the authors have yet studied the propagation of Love waves in a piezoelectric layer overlying an isotropic substrate involving both parabolic and rectangular irregularities. Further, the comparative study of rectangular irregularity and parabolic irregularity for both the cases of electrically open and short conditions elucidating the latent characteristics is among the major highlights and reflects the novelty of the present study.

Shear Wave Propagation in Multilayered Medium including an Irregular Fluid Saturated Porous Stratum with Rigid Boundary

The present investigation is concerned with the study of propagation of shear waves in an anisotropic fluid saturated porous layer over a semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformation. Numerically, the effect of irregularity present is analysed. It is seen that the phase velocity is significantly influenced by the wave number and the depth of the irregularity. The variations of dimensionless phase velocity against dimensionless wave number are shown graphically for the different size of rectangular irregularities with the help of MATLAB.

Enhancing rigid frame porous layer absorption with three-dimensional periodic irregularities

This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.

Analysis of the responses of termites to tunnel irregularity

Subterranean termites build extensive underground galleries consisting of elaborate tunnels and channels to forage food resources. Diverse soil conditions surrounding the tunnels, such as soil density, may cause irregularities in the size and shape of the tunnels, and termites are likely to encounter a number of tunnel irregularities while traveling. Considering the tunnel length, how termites respond to an irregularity is likely to affect their movement efficiency, and this in turn is directly correlated to their foraging efficiency. To understand the response of termites, we designed an artificial linear tunnel with rectangular irregularities in a 2-D arena. The tunnel widths, W, were 3 and 4 mm. The rectangular irregularities were 2 mm in width and of varying heights H (2, 1, 0, −1, and −2 mm). The positive and negative sign of H represents a convex and concave structure, respectively. We systematically observed the movement of termites, Coptotermes formosanus Shiraki, at the irregularity and quantified the time needed, τ, for a termite to pass the irregularity. The time τ was shorter for (W, H) = (3, 0) and (3, −1) than for (W, H) = (3, 1), (3, 2), and (3, −2). The time τ was longer for (W, H) = (4, −1), and (4, −2), than for (W, H) = (4, 0), (4, 1) and (4, 2). Four types of behaviors explained the response to the irregularity. The implications of these findings are briefly discussed in relation to termite foraging efficiency.

Scattering of forward bulk magnetostatic waves by a defect of the surface of a ferromagnetic film magnetized at an arbitrary angle

The solution for the diffraction problem of scattering of magnetostatic waves by an arbitrary shallow defect situated under the surface of a ferromagnetic film magnetized at an arbitrary angle is obtained in the quasi-static approximation. Expressions for the energy flux density of scattered magnetostatic waves in the far-field zone are found. The results of computations of the time-averaged flux density of bulk magnetostatic waves reflected from rectangular and circular shallow irregularities are presented.

Total absorption peak by use of a rigid frame porous layer backed by a rigid grating.

The acoustic properties of a low‐resistivity porous layer backed by a rigid plate containing periodic rectangular irregularities, creating multicomponent diffraction gratings, are investigated. Numerical and experimental results show that the structure possesses a total absorption peak at the frequency of the modified mode of the layer when designed as proposed in the article. These results are explained by an analysis of the acoustic response of the whole structure and especially by the modal analysis of the configuration. When more than one irregularity per spatial period is considered, either additional higher frequency peaks or additional total lower frequency peaks are observed.

Total absorption peak by use of a rigid frame porous layer backed by a rigid multi-irregularities grating

The acoustic properties of a low resistivity porous layer backed by a rigid plate containing periodic rectangular irregularities, creating a multicomponent diffraction gratings, are investigated. Numerical and experimental results show that the structure possesses a total absorption peak at the frequency of the modified mode of the layer, when designed as proposed in the article. These results are explained by an analysis of the acoustic response of the whole structure and especially by the modal analysis of the configuration. When more than one irregularity per spatial period is considered, additional higher frequency peaks are observed.

Initiation of detonation in a tube with parabolic contraction and conic expansion

On the basis of results of two and threedimensional numerical simulation, we proposed for the firsttime to use the profiling of axisymmetrictube walls inthe shape of parabolic contraction and conic expansion for initiating the detonation by means of a relatively weak shock wave. The detonation initiationmechanism is revealed, and its basic stages are analyzed. For simulating the propane–air mixture, wefound the paraboliccontraction shape and selectedthe conicexpansion parameters providing the initiation of detonation for the Mach number of an originalshock wave equal to 2.65.According to the theoretical results of V.P. Korobeіnikov, V.A. Levin, and V.V. Markov, the externaldisturbance of a reacting flow can become the cause offormation of a selfsustained detonation [1, 2]. Thesedisturbances can result in substantially nonlinearoscillatory processes due to the instability of the exothermicreaction front. Apparently, only detailednumerical experiments can provide the solution of theproblem under consideration on detonation initiationand indicate ways of its practical realization.Two processes at which the detonation wave can begenerated are wellknown and used in practice; theseare the direct initiation [1] and deflagrationtodetonation transition [3]. In [4] we proposed, investigated,and justified an original approach to shock detonationinitiation with the help of a regular shaped obstacles inplanar channel in which the leading shock wave(LSW) propagates. On the basis of numerical investigations and experiments, we showed that the regularparabolic structure of walls of the channel makes itpossible to reduce considerably the time and the distance before detonation initiation in comparison withthe wall structure in the shape of rectangular irregularities. The subsequent numerical investigation of theshocktodetonation transition (SDT) in an axisymmetric tube with the geometry of the walls investigatedin [4] for the planar case showed that for the Machnumbers in the initiating shock wave (ISW) importantfrom the viewpoint of practical applications, the process differs from that in the planar channel. It provedto be that the local explosion occurs in the region offocus of already the first parabolic element of thestructure instead of in the vicinity of the fifth one asoccurred in [4] for

Behavioral response of termites to tunnel surface irregularity

Subterranean termites construct underground tunnels, tens to hundreds of meters in length, in order to search for and transport resources. Diverse soil conditions surrounding the tunnels, such as soil pores and differing moisture concentrations, may cause different sized- and shaped-irregularities in the tunnels. To understand how individual termites respond to the irregularities, the present study monitored the movement of termites, Coptotermes formosanus Shiraki, in artificially excavated tunnels with rectangular irregularities of varying sizes in two-dimensional sand substrates. Termites tunneled at some of the irregularities and not at the others. The tunneling or non-tunneling behavior resulted from four different responses. The non-tunneling response may result from a behavioral adaptation that allows termites to avoid wasting energy that may be used in foraging.

Diffusion Properties of Various Irregular Panels

An experimental study has been made of the angular distribution of scattered sound energy from several types of 8-ft by 8-ft wall panels used in room construction. The measurements were made using pulse type transmission with carrier frequencies from 500 cps to 4000 cps. The various panels studied were flat transite, corrugated transite, triangular splayed panels, panels with rectangular irregularities, and polycylindrical panels. The paper will present some of the experimental data on scattering together with a comparison of data obtained from full scale panels to that reported from model studies.