Oblique incidence properties of locally resonant sonic materials with resonance and Bragg scattering effects

A locally resonant sonic material （LRSM） is an elastic matrix containing a periodic arrangement of identical local resonators （LRs）, which can reflect strongly near their natural frequencies, where the wavelength in the matrix is still much larger than the structural periodicity. Due to the periodic arrangement, an LRSM can also display a Bragg scattering effect, which is a characteristic of phononic crystals. A specific LRSM which possesses both local resonance and Bragg scattering effects is presented. Via the layered-multiple-scattering theory, the complex band structure and the transmittance of such LRSM are discussed in detail. Through the analysis of the refraction behavior at the boundary of the composite, we find that the transmittance performance of an LRSM for oblique incidence depends on the refraction of its boundary and the transmission behaviors of different wave modes inside the composite. As a result, it is better to use some low-speed materials （compared with the speed of waves in surrounding medium） as the LRSM matrix for designing sound blocking materials in underwater applications, since their acoustic properties are more robust to the incident angle. Finally, a gap-coupled LRSM with a broad sub-wavelength transmission gap is studied, whose acoustic performance is insensitive to the angle of incidence.

Response Characteristics of Position Sensitive Detector under Oblique Incidence Condition

Based on Lucovsky equation,the response solution of 1-D position sensitive detector(PSD) is given under the condition of parallel light oblique incidence and Gaussian beam oblique incidence,and the response characteristics are analyzed by numerical calculation. The relation between oblique incident angle and output current is introduced and illustrated.

Design of wideband graded-index antireflection coatings at oblique light incidence

We suggest a design method of graded-refractive-index （GRIN） antireflection （AR） coating for s-polarized or p- polarized light at off-normal incidence. The spectrum characteristic of the designed antireflection coating with a quintic effective refractive-index profile for a given state of polarization has been discussed. In addition, the genetic algorithm was used to optimize the refractive index profile of the GRIN antireflection for reducing the mean reflectance of s- and p-polarizations. The average reflectance loss was reduced to only 0.04% by applying optimized GRIN AR coatings onto BK7 glass over the wavelength range from 400 to 800 nm at the incident angle of θo = 70°.

Analysis of shielding effectiveness and mechanical properties of metal matrix composite AL6061 reinforced with Al_(2)O_(3) and fly ash for oblique incidence of EM wave

fields such as lightning strike susceptibility,electromagnetic energy from radar,airborne radio frequency transmitter.To provide high-intensity radiated field protection(HIRFP)for the electric and electronic aircraft system and defied the EMI effect on it,metal matrix composite was conquered.To provide the dynamic everincreasing requirement of industries,it is necessary that Al6061 metal matrix composite assisted with AL2O3 and fly ash is used to construct the aircraft to provide HIRFP.The thickness of the material can be maintained as low as possible to use it as a coating material for the aircraft surface.X-band for oblique incidence is used to measure electromagnetic and mechanical safeguarding properties of composites.Design/methodology/approach-Day by day,the applications of aerospace are becoming digital and automated.Proper shielding techniques are required to operate digital electronic devices without electromagnetic interference.It leads to a rapid rise in temperature,thermal ablation,delamination,and adverse effects on the electric and electronic aircraft system.Fly ash,a metal matrix material composite AL6061 with different percentages of reinforcement of Al_(2)O_(3),was contemplated and experimented with for mechanical properties like tensile strength,density and hardness.Findings-The obtained results compared with adjusted values and an improvement of 0.19,0.18,0.14 g/cm3 for density of MMC-1,MMC-2,MMC-3.31,11 MPa for tensile strength of MMC-1,MMC-2.24,27,23 BHN for hardness of MMC-1,MMC-2,MMC-3.With regard to the shielding effectiveness the results compared with adjusted values and obtained 11.36,14.56,19.47 dB better value than it.According to the above results,fabricated MMC’s provide superior results for a defined application like HIRFP(Surface material of aircraft).Practical implications-It can be used to protect electronic devices under a high-intensity radiated field,mainly in aircraft design to protect from lightning effect.Originality/value-For a better approximation of the signal toward the practical case,the oblique incidence was considered with a different combination of Al_(2)O_(3)and fly ash,reinforced to pure AL6061 to get better shielding and mechanical properties.

Absolute surface form measurement of flat optics based on oblique incidence method

In this Letter, a test method based on oblique incidence is practically implemented in the interferometric measurement process. Three sets of wavefront data are achieved through cavity interference measurement with a Fizeau interferometer and one oblique incidence measurement. An iterative algorithm is applied to retrieve the absolute surface shape of the test flat. By adding two sets of measurements, the absolute surface error of the interferometer＇s reference flat can be obtained. The new method can not only calibrate the reference flat error of interferometer, but also provide the absolute measurement method for high precision optical components applied in high power laser systems.

Photoinjector beam quality improvementby shaping the wavefront of a drive laser with oblique incidence

To increase the quantum efficiency （QE） of a copper photocathode and reduce the thermal emit- tance of an electron beam, a drive laser with oblique incidence was adopted in a BNL type photocathode rf gun. The disadvantageous effects on the beam quality caused by oblique incidence were analyzed qualitatively. A simple way to solve the problems through wavefront shaping was introduced and the beam quality was improved.

High-frequency field intensity along focal point of a long metallic parabolic reflector coated by a magnetized plasma layer using oblique incidence

Theoretical analysis of the electromagnetic field distribution in the focal region of a long metallic parabolic reflector that has its surface covered with a magnetized plasma layer is derived. The incident wave is considered to be with a general oblique incidence for both parallel and perpendicular polarizations. The electromagnetic field intensity expressions along the focal region are obtained accurately using Maslov＇s method. The effects of plasma thickness on the reflected and transmitted field distributions are investigated. The effects of other physi- cal parameters such as the angle of incidence and the plasma and cyclotron frequencies on the transmitted field- intensity distribution along the focal region are also studied. The results obtained by Maslov＇s method and Kirchhoff＇s approximation are found to be in a good agreement.

Characterizing a liquid crystal spatial light modulator at oblique incidence angles using the self-interference method

The phase modulation characteristics of a reflective liquid crystal （LC） spatial light modulator （SLM） under oblique incidence are studied by using our proposed self-interference method. The experimental setup of the method is very simple and has good robustness to mechanical vibrations. By changing the gray value of the combined grayscale loaded on the LC-SLM, different sheared fringe patterns, generated by the interference between the constant phase-modulated beam and the ＋1-order diffracted beam of the blazed grating, can be obtained. The amount of phase modulation of the LC-SLM is obtained by subtracting the phase of the two side lobes in the frequency domain. By turning the turntable where the SLM is mounted, the phase modulation characteristics at different incident angles can be measured. The experimental results show that the phase modulation curves do not change significantly with the small angle. When the angle is large （i.e. larger than 10°）, the phase modulation curves become different, especially for the high gray levels. With the increase of the incident angle, the phase modulation depth is reduced. The results indicate that the incident angle plays an important role in the performance of the phase modulation of an LC-SLM.

Acoustic evaluation of cementing quality using obliquely incident ultrasonic signals

Ultrasonic cement bond logging is a widely used method for evaluating cementing quality. Conventional ultrasonic cement bond logging uses vertical incidence and cannot accurately evaluate lightweight cement bonding. Oblique incidence is a new technology for evaluating cement quality with improved accuracy for lightweight cements. In this study, we simulated models of acoustic impedance of cement and cementing quality using ultrasonic oblique incidence, and we obtained the relation between cementing quality, acoustic impedance of cement, and the acoustic attenuation coeffi cient of the A0-mode and S0-mode Lamb waves. Then, we simulated models of different cement thickness and we obtained the relation between cement thickness and the time difference of the arrival between the A0 and A0′ modes.

Interaction of Oblique Waves and A Rectangular Structure with An Opening Near A Vertical Wall

With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wall in oblique seas, in which the unknown coefficients are determined by the boundary conditions and matching requirement on the interface. The effects of the width of the opening and the angle of incidence on the hydrodynamic characteristics of a rectangular structure with an opening near a vertical wall are mainly studied. The comparisons of the calculation results with wall-present and with wall-absent are also made. The results indicate that the variation trends of the heave added mass and excitation force with wall-present are almost the same as those with wall-absent, and that the peak values in the former case are obviously larger than those in the latter due to the reflection of the vertical wall.

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.

The force of oblique incident wave on the breakwater with a partially perforated wall

Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-function expansion method is applied to expanding velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with other theories and a good agreement can be found between them. Experimental data have been compared with the present theoretical results. The effect of the traverse wall on wave forces has been discussed in detail. On the basis of the linear wave theory, it is shown that in the range Of engineering practice, the incident angle of wave has small influence on wave forces on the unit length of perforated caisson.

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed： Green＇s Function Approach

The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.

Properties of Ternary One Dimensional Plasma Photomic Crystals for an Obliquely Incident Electromagnetic Wave Considering the Effect of Collisions in Plasma Layers

An analytical study is presented on the modal dispersion characteristics, group velocity, and effective group, as well as the phase index of a ternary one dimensional plasma photonic crystal for an obliquely incident electromagnetic wave considering the effect of collisions in plasma layers. The dispersion relation is derived by using the transfer matrix method and the boundary conditions based on electromagnetic theory. The dispersion curves are plotted for both the normal photonic band gap structure and the absorption photonic band gap structure. It is found that the increase in the angle of incidence shifts the photonic band gap toward higher frequencies. Also, the cutoff frequency is independent of collisions.

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

Seismic response analysis of GRPS embankment under oblique incident P wave

In order to investigate the seismic performance of geosynthetic reinforced and pile supported(GRPS) embankment under seismic loads, an input method for three-dimensional oblique incidence of P wave was proposed. This method is based on the explicit finite element method while considering the viscous-spring artificial boundary(VSAB) condition. Using the proposed method, a numerical study was conducted, and the influence of oblique incidence on the seismic response of GRPS embankment under the oblique incident P waves was analyzed. The results indicate that in comparison with vertical incidence, the oblique incidence can significantly increase the displacement, velocity and acceleration of key locations in the GRPS embankment. The existence of geosynthetics can alleviate the impact of seismic load on the response of the embankment to a certain degree. Moreover, the number of reinforcement layers and modulus of geogrid also greatly influence the seismic performance of GRPS embankment.

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a nonviscous fluid

The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.

Oblique Wave Trapping by a Surface-Piercing Flexible Porous Barrier in the Presence of Step-Type Bottoms

The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.