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This research article investigates the effects of object's vibration and fluid movement on the acoustics of subsonic flows, specifically focusing on the scattering of acoustic waves by a vibrating rigid plate submerged in uniform flow. The acoustic plane wave that impacts the plate, coupled with its oscillatory motion, causes a disruption in the fluid medium. This disturbance, in turn, gives rise to a Rayleigh wave that propagates along the boundary separating the plate and the fluid. The study uses the Wiener‐Hopf technique to analytically model the acoustic scattering by a rigid barrier of finite dimensions and analyze the relationship between acoustics and structures. The method involves applying Fourier transformations to the governing boundary value problem and resolving the Wiener‐Hopf equations using the factorization theorem, Liouville's theorem, and analytical continuation. The integral equations of scattered potential computed asymptotically are used to describe the acoustic characteristics of structures and their interaction with fluid flow in subsonic conditions. The findings of the study reveal the sharp peaks of the scattered potential at certain angles with more oscillation in high subsonic flow. Also, increasing the frequency of the vibrating plate increases the amplitude of the scattered potential but is attenuated in mean flow whereas enhancing plate vibrations amplifies the scattered sound, and it is more vibrant in high subsonic flow than mean flow and no fluid flow. This research has applications in noise reduction, aeronautical engineering, and the detection of underwater structures using acoustic waves and micropolar elastic media. [ABSTRACT FROM AUTHOR]

In this study, we are analyzing the effect of the Hilbert Transform (HT) on diffraction of a plane wave by an oscillating half-plane. Both the incident wave and oscillating half-plane have different oscillating frequencies. After the necessary mathematical computations for several types of time-dependent oscillating functions, it is verified graphically that the HT induces a shift of 90 ∘ , which can be observed from the flipping effect in the magnitude of the sinusoidal components occurring in their respective diffracted fields. Graphical illustrations presenting the effects of the HT are presented and discussed. [ABSTRACT FROM AUTHOR]

We verify the recently developed method by Kisil (Kisil 2024 SIAM J. Appl. Math. 84, 464-476 (doi: 10.1137/23M1562445)) through its application in the study of the anti-plane dynamic response of an elastic square-cell lattice quadrant having a free lateral boundary that is subjected to a sinusoidal point load. The vertical boundary of the quadrant is assumed to be either fixed or free. The approach adopted utilizes the discrete Fourier transform in both principal lattice directions to reduce the governing equations to a functional equation linking both the bulk and boundary response of the system. For both problems, this functional equation is shown to reduce to scalar Wiener-Hopf equation whose solution can be exploited to determine the full response of the lattice system. The analytical solutions based on the Wiener-Hopf method are also implemented in numerical investigations that demonstrate the lattice response to various positions and frequencies of the load. In particular, this study includes dynamic regimes induced by the load that possess strong anisotropy and shows how the associated waveforms interact with the boundaries of the quadrant. [ABSTRACT FROM AUTHOR]

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The propagation of shear waves inside/at the Earth’s crust during earthquake may cause the progression of punch in the rock medium. In this study, the movement of semi-infinite punch due to the propagation of the shear wave in a pre-stressed vertically transversely isotropic poro-viscoelastic medium has been analyzed. Based on Wiener–Hopf technique and two-sided Fourier integral transformations, the dynamic stress concentration due to moving punch is determined in closed form. The significant effects of various affecting parameters viz. velocity of moving punch, horizontal initial stress, vertical initial stress, anisotropy parameter, porosity, and viscoelasticity on dynamic stress concentration have been discussed. It is noteworthy that as the punch propagates with higher velocity, dynamic stress concentration in the considered poro-viscoelastic medium escalates. It is also found that horizontal tensile and vertical compressive initial stresses have an adverse impact on the dynamic stress concentration. On the other hand, the horizontal compressive and vertical tensile initial stresses have a favorable influence on the dynamic stress concentration. Also, its values increase with the increase of porosity, while it gets decreased as anisotropic parameter prevails in the considered medium. The behavior of dynamic stress concentration in three different types of pre-stressed vertically transversely isotropic poro-viscoelastic media viz. sandstone (a sedimentary rock), granite (an igneous rock), and marble (a metamorphic rock) has been compared. From this comparison, it is obtained that the dynamic stress concentration attains maximum value if the rock medium is marble and minimum value if the rock medium is sandstonel. Some graphical illustrations and numerical computations have also been established. Furthermore, some important properties are identified from the obtained dynamic stress concentration expressions. [ABSTRACT FROM AUTHOR]

In this work, the influences of nonlocal interactions on the growing inclusion are studied which are embedded in an elastic wave metamaterial with local resonators. The nonlocal interactions between main resonators are considered as linear springs connected to the second nearest neighboring ones. In addition, the inclusion is supposed that particle masses change along a straight line. Based on the Wiener–Hopf method, the ratio of the tip to end displacements of the inclusion is derived. Furthermore, the dynamic effective mass and stop band frequency are discussed. Numerical results show that in comparison with the system without nonlocal interactions, the new periodic structure can make the displacement ratio tend to the case of homogeneous lattices for high-speed regions. It indicates that more powerful resistance can be created by nonlocal springs during the inclusion growth. [ABSTRACT FROM AUTHOR]

In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics.

In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics. [ABSTRACT FROM AUTHOR]

The problem of elastic SH-wave diffraction from a finite interface defect formed on the boundary of the rigid joint between a layer and a half-space is considered. The model of the defect is an impedance strip on the surface of the joint with a given impedance boundary condition. Using the Wiener–Hopf technique the problem is reduced to an infinite system of linear algebraic equations. Its solution is used to study the behavior features of the displacement field on the surface of an elastic layer which is free from the stresses. [ABSTRACT FROM AUTHOR]

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail. [ABSTRACT FROM AUTHOR]

The article deals with the study of a moving interfacial semi-infinite crack situated between two orthotropic strips of different composite materials. The crack surface is under the shear wave disturbance. The governing equations have been solved by applying the Fourier transform technique to get the desired standard form of the Wiener–Hopf equation, which is further solved by using the Wiener–Hopf method. The analytical asymptotic expressions for physical quantities like stress intensity factor (SIF) and crack opening displacement (COD) for the crack have been obtained. The nature of SIF and COD for different combinations of composite materials and also for various depths of the semi-infinite strips has been depicted graphically. [ABSTRACT FROM AUTHOR]

The electromagnetic wave diffraction from perfectly conducting truncated wedges is considered on the rigorous level in cylindrical coordinates. An analytical regularization method is developed to obtain mathematically accurate problem solutions. The solution method is based on the unknown field representation through the principal value Kontorovich–Lebedev integral and the eigenfunctions series. We analyze the scattering from the semi-infinite truncated wedge, which consists of two non-parallel and non-intersecting perfectly conducting and infinitely thin half-planes, and develop this technique for analysis of more complicated problems of wave diffraction from the truncated wedge of finite length. The problems are reduced to the infinite systems of linear algebraic equations (ISLAE) of the first kind. The convolution type operators and their inverse ones are used to reduce them to the ISLAE of the second kind applied to the analytical regularization procedure. Two versions of the procedure, such as left- and right-sides regularization, are considered. The developed technique is compared with the Wiener–Hopf method. The numerical examples of wave scattering from the truncated wedge, including its well-known geometries as the semi-plane and the slit in the infinite plane, are analyzed. [ABSTRACT FROM AUTHOR]

The results of the theoretical and experimental study of the effect of the wing-setting angle on the far acoustic field associated with the wing trailing edge scattering of hydrodynamic near-field perturbations of a turbulent subsonic jet are presented. For a model in which the scattering surface is simulated by a half-plane, the analytical dependence of the principal characteristics of the scattering field on the setting angle of the scattered surface is obtained using the Wiener–Hopf technique. An experimental study of the sound field of the "nozzle–plate" configuration using a movable azimuthal microphone array is carried out in TsAGI AC-2 anechoic chamber and a good agreement between the theoretical model and the measurement data is shown. [ABSTRACT FROM AUTHOR]

The 2-D diffraction of a pulsed electromagnetic (EM) plane wave by a semi-infinite sheet with conductive and dielectric properties is analyzed analytically with the aid of the Wiener–Hopf technique and the Cagniard–DeHoop technique. Novel exact analytical expressions describing the time-domain (TD) EM field in the presence of the conductive half-plane are derived. Moreover, closed-form approximate TD expressions are arrived at via Koiter’s approximate method of factorization. Illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper (Galyamin et al., 2021) where a simpler case of uniform dielectric filling has been considered. Here we use the same analytical approach based on Wiener–Hopf–Fock technique and deal with more complicated case of a layered dielectric filling which is closer to potential applications. The latter are connected with analytical description of electromagnetic processes involving open-ended waveguide structures prospective due to the modern trends in beam-driven radiation sources (mainly in the terahertz (THz) frequency region) and THz-based bunch manipulation. [ABSTRACT FROM AUTHOR]

Radiation of sound waves by a coaxial duct is considered. The coaxial duct has an inner rigid wall which is infinite, while the outer wall is rigid for z < 0 and perforated for z > 0 which makes the problem more interesting. Applying the Fourier transform technique, the mixed boundary value problem is described by a Wiener–Hopf equation and then the solution of the problem is found by means of the Wiener–Hopf (WH) technique. The influence of the parameters of the problem like inner and outer duct radii, frequency and porosity on the sound pressure level is displayed graphically. This study is important because of its applications in noise reduction in modern aircraft jet and turbofan engines. The current problem is also compared with subproblems with and without perforated and very good agreement is observed. [ABSTRACT FROM AUTHOR]

In the current discussion, we have carefully analyzed the interaction of the incident wave field on a finite symmetric plate under the assumption of Neumann boundary conditions in the presence of cold plasma. The boundary value problem is established after implementing the Fourier transform on the Helmholtz equation. The Wiener-Hopf analysis is utilized to sort out the problem proposed for this model. The separated field is evaluated and its graphical analysis is presented to further study the effects of various physical parameters in the presence of cold plasma. [ABSTRACT FROM AUTHOR]

We solve the problem of diffraction of elastic SH-waves on a defect formed on the interface of an elastic layer rigidly joined with a half space. The defect is modeled by a semiinfinite plane with given mixed-type impedance boundary conditions. By using the Wiener–Hopf technique, we obtain the rigorous solution of the problem. This solution is used to study the behavior of the coefficients of transformation of the modes of scattered waves at the tip of the defect, as well as the energy reflection and transmission coefficients of waves for various subdomains of the structure as functions of the geometric and physicomechanical parameters of the problem. In order to perform the diagnostics of the edge of the analyzed defect, we carried out the physical analysis of the formation of the field of displacements on the free surface of the layer. [ABSTRACT FROM AUTHOR]

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail.

Radiation of sound waves by a semi-infinite circular cylindrical pipe with non-uniform lining is analyzed by using the Jones' method in conjunction with the mode matching technique. This mixed method of formulation gives rise to a scalar Wiener–Hopf equation. The inner surface of the duct is coated by acoustically absorbing different linings. In the present study, different linings with partial rigidity make the problem more interesting when it is compared with the uniform lining. The solution of the considered problem involves three infinite sets of coefficients satisfying three infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the radiation phenomenon are shown graphically. The solution is compared graphically with a similar study existing in the literature. A perfect agreement is observed between the both results. [ABSTRACT FROM AUTHOR]

Wiener–Hopf Equations are of the form u (t) = f (t) + ∫ 0 + ∞ k (t − τ) u (τ) d τ , t > 0. These equations arise in many physical problems such as radiative transport theory, reflection of an electromagnetive plane wave, sound wave transmission from a tube, and in material science. They are also known as the renewal equations on the half-line in Probability Theory. In this paper, we present a method of deriving asymptotic expansions for the solutions to these equations. Our method makes use of the Wiener–Hopf technique as well as the asymptotic expansions of Stieltjes and Hilbert transforms. [ABSTRACT FROM AUTHOR]

The exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition of solutions for two modes of loading: (i) symmetrically applied moments; (ii) symmetrically applied transverse forces with compensating moments. The exact expressions for stress intensity factor (SIF) have been obtained. Due to symmetry only the opening mode of SIF is present for each case of loading. For both cases of loading the stress states are determined by two dimensionless parameters composed by four elastic constants. Expression for SIF for the case of loading with symmetrically applied moments is obtained in terms of elementary functions and coincides with the elementary solution due to beam theory. Expression for SIF for the case of loading with symmetrically applied transverse forces with compensating moments has been obtained in terms of one function of one of the parameters expressed as a single integral, multiplied by a power function of the second parameter. The solution for this case demonstrated good agreement with the existing numerical solution for the range of parameters, for which the latter had been obtained. The obtained solution covers all possible range of parameters.

An elegant and convenient rigorous approach for solving canonical circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener–Hopf–Fock equation and leads to an infinite linear system for reflection coefficients (S-parameters) of the waveguide, and the latter can be efficiently solved numerically using the reducing technique. As a specific example directly applicable to beam-driven radiation sources based on dielectric-lined capillaries, diffraction of a slow TM symmetrical mode at the open end of a circular waveguide with uniform dielectric filling is considered. A series of such modes forms the wakefield (Cherenkov radiation field) generated by a charged particle bunch during its passage along the waveguide axis. Calculated S-parameters were compared with those obtained from COMSOL simulation and an excellent agreement was shown. This method is expected to be very convenient for analytical investigation of various electromagnetic interactions of terahertz (THz) waves (both free and guided) and charged particle bunches with slow-wave structures perspective in context of modern beam-driven THz emitters, THz accelerators, and THz-based bunch manipulation and bunch diagnostic systems. [ABSTRACT FROM AUTHOR]

Approximate analytical solution of point source diffraction from a strip satisfying a recently introduced boundary condition is presented in this paper. Both separated and interacted fields are computed separately and then related transformations are applied to obtain the field diffracted from a strip satisfying non-reciprocal boundary condition. The correctness of mathematical results is also verified graphically and a good agreement with the existing literature is observed. [ABSTRACT FROM AUTHOR]

Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov's method. These configurations are: (i) the wedges forming a half-plane; (ii) the wedges forming a plane; (iii) one of the wedges being a half-plane. In all cases, the external boundaries are supposed to be free of stresses. By applying Mellin's transform for all three configurations the problem has been reduced to vector Riemann's problem, and the matrix coefficient has been factorized for the case of the mentioned restrictive condition. The first configuration, i.e. the problem of an inclined edge crack located along the boundary separating two wedges of different elastic isotropic materials forming a half-plane is considered in more detail. The solution has been obtained for both uniform (corresponding to remote loading) and non-uniform (loading applied at the crack faces) problems. Numerical results are presented and compared with the available results obtained by other authors for particular cases. The obtained solutions appear especially valuable for analysing extreme cases of parameters. [ABSTRACT FROM AUTHOR]

In the present work, the radiation of sound waves from a coaxial duct is considered. This coaxial duct has an inner wall which is infinite and has piecewise acoustically absorbent material, while the outer wall is semi-infinite and rigid. The analytical solution of the problem is found by means of the Wiener-Hopf technique. Applying the Fourier transformation to the boundary value problem, the explicit expression for the scattered field is obtained. In the end, some numerical results are displayed for different parameters and compared to rigid case. [ABSTRACT FROM AUTHOR]

In the present work, the band-pass filter characteristics of a coaxial waveguide with an impedance coated groove on the inner wall and perfectly conducting outer wall is analyzed rigorously through the Wiener–Hopf technique. By using the direct Fourier transform, the related boundary value problem is reduced to the Wiener–Hopf equation whose solution contains infinitely many constants satisfying an infinite system of linear algebraic equations. These equations are solved numerically and the field terms, which depends on the solution obtained numerically, are derived explicitly. The problem is also analyzed by applying a mode-matching technique and the results are compared numerically. Besides, some computational results illustrating the effects of parameters such as depth of the groove, surface impedances and radii of the walls are also presented. [ABSTRACT FROM AUTHOR]

Analytical solution is studied for a rigid circular waveguide which has a finite gap on its outer wall. Following the Wiener-Hopf technique, problem is formulated as a Fredholm integral equations. Asymptotic evaluations of integrals are carried out and the field terms are determined explicitly. Finally, the influence of the different parameters (gap length, width of the waveguide, etc.) on the radiation are illustrated numerically. [ABSTRACT FROM AUTHOR]

This investigation portrays the transient cylindrical wave diffraction by an oscillating strip. Mathematical analysis of the problem is carried out with the help of an integral transforms and the Wiener–Hopf technique. Using far zone approximation, the scattered field is evaluated by the method of steepest descent. This study takes into consideration the transient cylindrical source and an oscillating strip such that both the source and a scatterer have different oscillating frequencies ω 1 ′ and ω 0 ′ , respectively. The situation under consideration is well supported by graphical results showing the effects of emerging parameters. [ABSTRACT FROM AUTHOR]

The present research article presents the investigation of diffraction phenomenon of EM-plane wave by a non-symmetric plate of finite length under the influence of cold plasma. The Wiener–Hopf equation is formulated by boundary value problem related to this model and Fourier transform. The standard way of Wiener–Hopf procedure is used to tackle the resulting equation. Asymptotic expansion and modified stationary phase method are used to find the result for the diffracted wave by finite plate under the assumption of Neumann boundary conditions in an anisotropic medium. The case of an isotropic medium has been obtained by assigning the particular values to elements of permittivity tensor. The high-frequency signal can be assumed only when very large operating frequency is taken into account as compared to the cyclotron frequency. Various physical parameters for isotropic and anisotropic medium are discussed graphically. [ABSTRACT FROM AUTHOR]

• A hybrid method to predict the noise radiated from an unbaffled long enclosure. • Interaction between wavy micro-perforated absorbers and acoustic fields is studied. • Formation and suppression mechanisms of the radiated sound field are investigated. • Quasi-two-dimensional experiments are performed to validate the proposed model. The sound radiation control of an unbaffled long enclosure using wavy micro-perforated panel absorbers (WMPPAs) was numerically and experimentally investigated. First, a hybrid model based on the finite element method (FEM) and the Wiener-Hopf (W-H) technique was established to calculate the sound pressure level (SPL) radiated from an unbaffled long enclosure lined with MPPAs. Then, the hybrid model was validated, and the sound suppression performance of a single WMPPA was evaluated. The results demonstrate that the WMPPA exhibits better sound absorption properties than the flat and corrugated micro-perforated panel absorber (FMPPA and CMPPA), especially in the middle- to high-frequency range. To further enhance the sound attenuation performance, an array of WMPPAs was subsequently proposed to absorb higher-order acoustic modes inside the long enclosure so that broadband-radiated noise could be suppressed. The comparison results demonstrate that the WMPPAs can reduce the radiated SPL within a wide frequency range which is favourable for the suppression of environmental noise. In addition, the WMPPA array shifts the sound reduction curve towards a low-frequency range by approximately 500 Hz compared with that of a single WMPPA, which is promising for the reduction of broadband noise. After that, a mechanistic study was conducted to explain the sound reduction performance of WMPPAs from the perspective of modal contributions. In addition, the diffraction effect of sound waves at the sharp edge of a long enclosure was illustrated. Besides, the contribution of the wavy structure's scattering effect to the sound reduction performance of WMPPAs was analysed. Finally, the sound absorption abilities of the WMPPAs were examined using a quasi-two-dimensional (quasi-2D) experiment. The results show that the WMPPAs exhibit good sound reduction performance in the middle- to high-frequency range, which verifies the feasibility of applying WMPPAs to suppress the broadband noise radiated from long enclosures. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic fracture of a dissimilar chain composed of two different mass-spring chains and connected with other springs. The propagation of the fault (crack) is realized under externally applied moving forces. In comparison with a homogeneous double chain, the considered structure displays some new essential features of steady-state crack propagation. Specifically, the externally applied forces are of a different strength, unlike a static case, and should be appropriately chosen to satisfy the equilibrium of the structure. Moreover, there exists a gap in the range of crack speeds where the steady-state fracture cannot occur. We analyse the admissibility of solutions for different model parameters and crack speeds. We complement analytical findings with numerical simulations to validate our results. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'. [ABSTRACT FROM AUTHOR]

The Wiener-Hopf technique was used to obtain an analytical solution of the problem of waves produced in a fluid and an ice sheet by the uniform motion of a pressure region modeling an air-cushion vessel on the free surface of the fluid in an ice channel. Ice cover is modeled by two thin semi-infinite viscoelastic plates of constant thickness, floating on the surface of an ideal incompressible fluid of finite depth and separated by the free surface of the fluid. In the moving coordinate system, the plate deflection and fluid elevation are assumed to be steady-state. The wave forces, the elevation of the free surface of the fluid, and the deflection and deformation of the plates are investigated at different vessel speeds and ice sheet thicknesses. It is shown that for some values of the speed, ice sheet thickness, and current pressure, destruction of the ice sheet near the edge is possible. [ABSTRACT FROM AUTHOR]

The problem of waves generated in a fluid and an ice sheet by a pressure region moving on the free surface of the fluid along the edge of the semi-infinite ice sheet is solved using the Wiener–Hopf technique. The load applied in some region simulates an air cushion vehicle, and the ice sheet is modeled by a thin elastic plate of constant thickness on the surface of an ideal incompressible fluid of finite depth. In a moving coordinate system, the plate deflection and the fluid elevation are assumed to be steady. The wave forces, the elevation the fluid free surface, and the deflection and deformation of the plate at various speeds of the load are investigated. It is found that at near-critical load speeds, the ice sheet has a significant effect on the wave forces (wave resistance and side force) acting on the body moving on the free surface, and this effect is most pronounced at small distances from the edge. It is shown that for some values of the speed, ice thickness, and load pressure, breaking of the ice sheet near the edge is possible. [ABSTRACT FROM AUTHOR]

The problem of axially symmetric E-polarized electromagnetic waves diffraction from the circular cone formed by the junction of the perfectly electro-conducting (PEC) semi-infinite truncated cone and the perfectly magneto-conducting (PMC) finite cone is studied rigorously by applying the Kontorovich–Lebedev integral transformation technique, the mode-matching method, and the analytical regularization procedure. The convolution-type operator and its inverse operator are used to conduct the regularization procedure and to reduce the problem to the infinite systems of linear algebraic equations of the second kind. The left side and the right side of the regularization procedures are considered. Transition from the cone to the PEC plane with the circular magnetic window is analysed. The exact solution of the problem is obtained for the static limit, and the low-frequency approximate is derived. The Wiener–Hopf technique is also applied to obtain the solution. Both solutions obtained using the analytical regularization method and by the Wiener–Hopf technique are compared, and the relation between them is derived. Within the framework of the Macdonald's model, the solution is applied to analyse the far field scattered from the two partially absorbing conical scatterers; (1) the PEC semi-infinite cone with the "black" vertex; and (2) the semi-infinite PMC cone with the "black" truncated conical surface. [ABSTRACT FROM AUTHOR]

Numerous problems in thermal engineering give rise to problems with abrupt changes in boundary conditions particularly as regards structural and construction applications. There is a continual need for improved analytical and numerical techniques for the study and analysis of such canonical problems. The present work considers transient heat propagation in a two-dimensional half-space with mixed boundary conditions of the Dirichlet and the Robin (convective) type. The exact temperature field is obtained in double integral form by applying the Wiener-Hopf technique, and this integral is then efficiently evaluated numerically with the help of numerical algorithms developed for the present problem and by exploiting the properties of the integrand. The results are then compared to the numerical solutions using finite element methods, and excellent agreement is shown. Some potential application areas of the theory are also discussed, specifically in the regime where edge effects can influence thermal convection processes. [ABSTRACT FROM AUTHOR]

This investigation portrays the transient cylindrical wave diffraction by an oscillating strip. Mathematical analysis of the problem is carried out with the help of an integral transforms and the Wiener–Hopf technique. Using far zone approximation, the scattered field is evaluated by the method of steepest descent. This study takes into consideration the transient cylindrical source and an oscillating strip such that both the source and a scatterer have different oscillating frequencies ω 1 ′ and ω 0 ′ , respectively. The situation under consideration is well supported by graphical results showing the effects of emerging parameters.

Abstract This work presents a Radon transform analysis of plane wave diffraction by an impedance step, such that the planes and the step have different impedances. Application of Radon transform on diffraction analysis is of vital importance in many real-time applications i.e., medical imaging, geosciences, astronomy, optics, stress analysis etc. Radon transform offers the advantage of introducing freedom in the usage of observer angle, during reconstruction of signal using plane wave diffraction. Radon transform along with Wiener–Hopf technique and asymptotic method of integration are used for computing the far field of the diffracted plane wave. The solution of plane wave diffraction by an impedance step consists of an infinite set of linear equations, which is obtained with the help of a software. Sinograms showing the effect of varying step height and impedance on the scattered field are plotted, compared and discussed. The mathematical analysis and graphical discussion show that Radon transform enables the observer angle to be varied between 0 to 2 π. The results are comparable to previous works on plane wave diffraction by an impedance step, when the observer angle is fixed. [ABSTRACT FROM AUTHOR]

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener-Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated. [ABSTRACT FROM AUTHOR]

This article examines sound radiation from a hard semi-infinite duct placed symmetrically inside an acoustically lined duct. We introduce a wake on right handed region of the duct configuration to analyze sound radiation process for the trailing edge situation. The integral transforms together with Wiener-Hopf techniques render the solution of underlying problem. However expressions for field intensity involve infinite sums/products that enable solution using truncation approach. The sound radiation analysis is then observed graphically while using different choice of some pertinent parameters. It is worth mentioning that results of leading edge situation can be recovered as a limiting case. [ABSTRACT FROM AUTHOR]

The problem of vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a time-periodic local load is solved analytically using the Wiener-Hopf technique. Ice cover is simulated by two thin elastic semi-infinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are considered. For the case of contact of plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that in the case of contact of two plates of different thickness, predominant directions of wave propagation at an angle to the crack can be identified in the far field. In the case of contact of plates of the same thickness with free edges and with free overlap, an edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given. [ABSTRACT FROM AUTHOR]

The acoustic properties of an area expansion are analyzed for frequencies where flow acoustic interaction may have a significant influence due to flow separation and vortex shedding. It is investigated why this interaction, which is seen in experimental data on a cylindrical duct as a resonance at a particular Strouhal number of order one, is present in rectangular but not in cylindrical modelling that would be expected to be more realistic; both models consider a plug flow. An analytic method that is suitable for identifying possible reasons for the discrepancies between the two geometries is used. The previously published rectangular model is generalized to the cylindrical case and both models are used to simulate results for all elements in the plane wave scattering matrix and for all parameters for which experimental results are available. The comparison between the two models and between models and measured data is thus not restricted to the flow acoustic induced resonance. The results show that the two geometries in general perform equally when compared with the experimental results, but that the rectangular modelling indeed performs better for some cases. This occurs around a critical Strouhal number, and for higher Mach number. Using the analytic form of the solution, it is shown that the observed discrepancy is related to interaction between the damped hydrodynamic mode and a downstream propagating higher order acoustic mode. Such interaction is not present in the corresponding quiescent duct, and is related to the presence of the shear layer. The analysis shows that the structure of the higher order acoustic modes is different for the cylindrical and rectangular case, respectively, causing the difference in resonant behaviour. [ABSTRACT FROM AUTHOR]

The analysis of a transition wave propagating in a finite heterogeneous discrete beam strip, composed of periodically placed masses and subjected to a harmonic load is presented. The load is assumed to be located sufficiently far away from the transition front. As waves propagate inside the structure, connections are broken and we investigate how this process evolves from the transient regime to the steady-state regime. It is found that the steady-state speed of this transition process, in the averaged sense, coincides with the predicted phase speed of the transition wave. For a given heterogeneity, we show that a transition wave can propagate steadily if the load amplitude and frequency are situated in a parameter subdomain. The steady-state regime does not exist outside of this domain. At a given load frequency, it is demonstrated that the average speed of fracture is independent of the load amplitude within a given steady-state domain and the number of such domains depends on the load frequency and structural heterogeneity. During the transition process, we identify several dynamic effects, including regimes where waves can be transmitted ahead of the front into the structure and the development of an inclination that follows the transition front in the steady-state regime. The occurrence of such effects and their behaviour also correspond to predictions from the theory. We show although the theoretical steady-state fracture regimes are realised globally, locally the fracture speed always behaves in a regular fashion. [ABSTRACT FROM AUTHOR]

The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.