Wave Propagation In Beam Research Articles

Wave propagation and absorption of sandwich beams containing interior dissipative multi-resonators

In this study, a sandwich beam with periodic multiple dissipative resonators in the sandwich core material is investigated for broadband wave mitigation and/or absorption. An analytical approach based on the transfer matrix method and Bloch theorem is developed for both infinite and finite sandwich structures. Wave attenuation constants are theoretically obtained to examine the effects of various system parameters on the position, width and wave attenuation performance of the band gaps. The wave absorption coefficient of the sandwich beam is quantitatively studied to distinguish wave attenuation mechanisms caused by reflection and absorption. It is numerically demonstrated that a transient blast-induced elastic wave with broadband frequencies can be almost completely mitigated or absorbed at a subwavelength scale. The results of this study could be used for developing new multifunctional composite materials to suppress impact-induced and/or blast-induced elastic waves which may cause severe local damage to engineering structures.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation.

A novel polarization splitter based on dual-core photonic crystal fibers

In this paper, we propose and numerically demonstrate the operation of a new type of polarization splitter based on the photonic crystal fiber technology. Both the full-vector plane wave method and beam propagation method with anisotropic perfectly matched layers are employed to design and investigate the properties of the splitter. Numerical results show that the polarization splitter possesses extremely short length of 0.7322mm and high extinction ratio of ⿿32dB at the wavelength of 1,550nm. Moreover, the polarization splitter is proposed to achieve extinction ratio better than ⿿10dB and a bandwidth of 15.6nm. The novel structure is compact in size and easy to fabricate, making it prospecting for miniaturized complex communication devices.

Non-reciprocal elastic wave propagation in spatiotemporal periodic structures

We study longitudinal and transverse wave propagation in beams with elastic properties that are periodically varying in space and time. Spatiotemporal modulation of the elastic properties breaks mechanical reciprocity and induces one-way propagation. We follow an analytic approach to characterize the non-reciprocal behavior of the structures by analyzing the symmetry breaking of the dispersion spectrum, which results in the formation of directional band gaps and produces shifts of the first Brillouin zone limits. This approach allows us to relate position and width of the directional band gaps to the modulation parameters. Moreover, we identify the critical values of the modulation speed to maximize the non-reciprocal effect. We numerically verify the theoretical predictions by using a finite element model of the modulated beams to compute the transient response of the structure. We compute the two-dimensional Fourier transform of the collected displacement fields to calculate numerical band diagrams, showing excellent agreement between theoretical and numerical dispersion diagrams.

The analysis of optical wave beams propagation in lens systems

In this paper some aspects of the formation and propagation of optical wave beams in lens systems were considered. As an example, the two-lens optical information processing system was considered. Analysis of the two-lens optical circuit has been made with a systems approach perspective. As part of the radio-optical analogies had been applied certain provisions of the theory of dynamical systems to the spatial optical system. The lens system is represented as a simple series-connected optical elements with known spatial impulse response. General impulse response of such a system has been received, as well as consider some special cases of the impulse response. The question of the relationship between the parameters and the size of the input aperture lenses for undistorted transmission of the optical signal has been considered. Analysis of the energy loss resulting from the finite aperture of the lens. It's based on an assessment of the fraction of radiation that propagates beyond the lens. Analysis showed that the energy losses depend explicitly on the following parameters: radiation wavelength, distance between input aperture and lens, and ratio of the input aperture and lens aperture. With the computer help simulation the dependence of losses was shown on the above parameters

Development of scattering suppression technique for optical trasillumination image using equation for beam wave propagation

Development of scattering suppression technique for optical trasillumination image using equation for beam wave propagation

Wave propagation in periodic buckled beams. Part II: Experiments

Buckled periodic beams possess a geometrically nonlinear, load–deformation relation and intrinsic length scales such that stable, nonlinear waves are possible. In part I of this paper, a model has been derived that predict compressive/rarefaction, supersonic/supersonic solitary waves, varying the level of compression and the support type (guided or pinned). Although this work has been validated by simulating the structure with finite-elements, in the present paper, investigations are done experimentally, focusing on the guided-supported, slightly-buckled beam.

Wave propagation in periodic buckled beams. Part I: Analytical models and numerical simulations

Periodic buckled beams possess a geometrically nonlinear, load–deformation relationship and intrinsic length scales such that stable, nonlinear waves are possible. Modeling buckled beams as a chain of masses and nonlinear springs which account for transverse and coupling effects, homogenization of the discretized system leads to the Boussinesq equation. Since the sign of the dispersive and nonlinear terms depends on the level of buckling and support type (guided or pinned), compressive supersonic, rarefaction supersonic, compressive subsonic and rarefaction subsonic solitary waves are predicted, and their existence is validated using finite element simulations of the structure. Large dynamic deformations, which cannot be approximated with a polynomial of degree two, lead to strongly nonlinear equations for which closed-form solutions are proposed.

Effects of axial load and structural damping on wave propagation in periodic Timoshenko beams on elastic foundations under moving loads

The propagation and attenuation properties of waves in ordered and disordered periodic composite Timoshenko beams, which consider the effects of axial static load and structural damping, resting on elastic foundations are studied when the system is subjected to moving loads of constant amplitude with a constant velocity. The transfer matrix methodology is adopted to formulate the model in a reference coordinate system moving with the load. The localization factor is calculated to determine the wave velocity pass bands and stop bands. The interactions between the static axial load and moving load, structural damping and disorder on the bands are analyzed.

Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach

Abstract This paper presents the wave propagation approach for analyzing the free vibration and wave reflection in carbon nanotubes. The propagation and reflection matrices obtained by the wave propagation method are useful for the analysis of mechanical energy transmission and reflection in micro/nano devices. These matrices can also be used for obtaining the natural frequencies of carbon nanotubes. Firstly, the obtained natural frequencies by this method are compared with the results in the literature. Then, the effect of small scale on the reflected power of an incident wave upon different boundary conditions is studied in details. It was found that the reflected power of an incident wave upon a simply supported boundary is independent of the small scale, incident wave frequency, material and geometrical parameters of the carbon nanotubes while the reflected power of a wave upon clamped and free boundary conditions depends on the small scale, incident wave frequency, material and geometrical parameters.

Remote Detection of Concealed Radioactive Materials by Using Focused Powerful Terahertz Radiation

This review paper summarizes the results of studies of a novel concept of the remote detection of concealed radioactive materials by using focused high-power terahertz (THz) radiation. The concept is based on the known fact that the ambient electron density in air is low (one to three free electrons per cubic centimeter). These electrons can serve as seed electrons from which an avalanche breakdown in strong electromagnetic fields starts. When a powerful THz radiation is focused in a small spot, the breakdown-prone volume can be much smaller than a cubic centimeter. So, the probability of having some free electrons in this volume and, hence, the probability of breakdown are low in the absence of additional sources of air ionization. However, in the vicinity of radioactive materials (10–20 m), the electron density can be higher, and, hence, there are always some seed free electrons from which the avalanche ionization will start. Thus, the breakdown rate in this case can be close to 100 %. Realization of this concept requires studies of various physical and technical issues. First, it is necessary to develop a high-power source of (sub-) THz radiation whose power, frequency, and pulse duration are sufficient for realizing this goal. Second, it is necessary to analyze numerous issues important for realizing this concept. Among these issues are (a) enhancement of the ionization level of air molecules in the presence of hidden radioactive materials, (b) estimating the minimum detectable mass of radioactive material, (c) formation of breakdown-prone volumes in focused THz wave beams, and (d) effect of atmospheric conditions on the propagation and focusing of THz wave beams and on the optimal location of the breakdown-prone volume between a container with hidden radioactive material and a THz antenna. The results of these studies are described below.

Wave propagation in beams with anti-symmetric piezoelectric shunting arrays**Project supported by the National Natural Science Foundation of China (Grant No. 51322502).

Piezoelectric shunting arrays are employed to control the wave propagation in flexible beams. Contrary to conventional symmetric configuration, a substrate beam with anti-symmetric shunting arrays is investigated by adapted transfer matrix method. Compared with symmetric scheme, the anti-symmetric one demonstrates some distinctive characteristics. Primarily, the longitudinal and flexural waves are coupled, so they are correlated and must be considered simultaneously. Moreover, the attenuation of flexural wave is much stronger in anti-symmetric scenario, while the longitudinal wave demonstrates the converse side. As a result, the anti-symmetric scheme can be utilized to improve the vibration isolation capability of shunting arrays. Finally, the theoretical analyses are validated by finite element simulations.

An Adaptive Physics-Based Method for the Solution of One-Dimensional Wave Motion Problems

In this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). The solution of the problem includes two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, adaptive points are determined using the wavelet theory. This part is done employing the Deslauries-Dubuc (D-D) wavelets. By solving the problem in the first step, the domain of the problem is discretized by the same cells taking into consideration the load and characteristics of the structure. After the first trial solution, the D-D interpolation shows the lack and redundancy of points in the domain. These points will be added or eliminated for the next solution. This process may be repeated for obtaining an adaptive mesh for each step. Also, the smoothing spline fit is used to eliminate the noisy portion of the solution. Finally, the results of the proposed method are compared with the results available in the literature. The comparison shows excellent agreement between the obtained results and those already reported.

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

The enabling emerging technologies such as nanotechnology increased the demand for small-size devices. The proper understanding of the nonclassical behavior of nanostructures is key for the design of these devices. As a result, the static and dynamic behavior of nanoscale beam structures has received a great attention in the past few years. This review aims at directing the light to research work concerned with bending, buckling, vibrations, and wave propagation of nanobeams modeled according to the nonlocal elasticity theory of Eringen. Due to the large body of references found in the literature, the authors chose to briefly present the key findings and challenges and direct light to possible future work. This review does not intersect with recent relevant reviews, which reflects its significance to readers.

Optimal beam focusing through turbulence.

Beam spread and beam wandering are the most perceptible effects of atmospheric turbulence on propagating laser beams. The width of the mean irradiance profile is typically used to characterize the beam spread. This so-called long-term (LT) statistic allows for a relatively simple theoretical description. However, the LT beam size is not a very practical measure of the beam spread because its measurements are sensitive to the movements of the source and detector, and to the large-scale variations of the refractive index that are not associated with turbulence. The short-term (ST) beam spread is measured relative to the instantaneous position of the beam center and is free of these drawbacks, but has not been studied as thoroughly as the LT spread. We present a theoretical model for the ST beam irradiance that is based on the parabolic equation for the beam wave propagation in random media, and the Markov approximation for calculation of the statistics of the optical field, and discuss an approximation that allows introduction of the isoplanatic ST point spread function (PSF). Unlike the LT PSF, the ST PSF depends on the overall beam geometry. This allows optimization of the initial beam field in terms of minimizing the ST beam size at the observation plane. Calculations supporting this conjecture are presented for the simple case of the coherent Gaussian beam, and Kolmogorov turbulence.

Numerical Algorithms with High Spatial Accuracy for the Fourth-Order Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions

In this paper, a compact algorithm for the fourth-order fractional sub-diffusion equations with first Dirichlet boundary conditions, which depict wave propagation in intense laser beams, is investigated. Combining the average operator for the spatial fourth-order derivative, the L1 formula is applied to approximate the temporal Caputo fractional derivative. A novel technique is introduced to deal with the first Dirichlet boundary conditions. Using mathematical induction method, we prove that the presented difference scheme is unconditionally stable and convergent by the energy method. The convergence order is $$O(\tau ^{2-\alpha }+h^4)$$O(?2-?+h4) in $$L_2$$L2-norm. The outline for the two-dimensional problem is also considered. Finally, some numerical examples are provided to confirm the theoretical results.

On three-dimensional internal gravity wave beams and induced large-scale mean flows

The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam–mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of Bordes et al. (Phys. Fluids, vol. 24, 2012, 086602).

Optical transillumination imaging of biological body at off-axis area of light beam using equation for beam wave propagation

Optical transillumination imaging of biological body at off-axis area of light beam using equation for beam wave propagation

Effects of the boundary conditions at fixed end on the flexural wave propagation in the periodic beam

The flexural wave propagation in a periodic beam is investigated using the method of multiple reflections. The effects of the clamped boundary condition and disturbance on the flexural wave propagation in the periodic beam are considered. A propagating disturbance is incident upon a discontinuity and gives rise to transmitted and reflected waves, and all of the transmitted and reflected waves of given flexural wave incident upon the beam at some location are found and superposed. The method is extended to the case of incident fading wave. The relation between the wave field of incident waves and the wave field of resulting waves on any segment is expressed. Much attention is devoted to the response in the frequency ranges with gaps in the band structure for the corresponding periodic beam. As an example, the application of the results to the analysis of a finite periodic beam with clamped-free boundary condition and a propagating disturbance is then demonstrated.

Wave propagation in beams with periodic arrays of airfoil-shaped resonating units

This paper presents an analytical and numerical study on the dispersion properties of an Euler–Bernoulli beam immersed in a steady fluid flow with periodic arrays of airfoil-shaped vibration absorbers attached to it. The resonance characteristics of the airfoils generate strong attenuation of flexural waves in the beam occurring at frequencies defined by the properties of the airfoils and the speed of the incident fluid. Analytical and numerical tools are developed to investigate the effects of the incident flow on the dispersion properties and the bandgaps of the system. Both steady and unsteady aerodynamic models are used to model the lift force and the pitching moment acting on the resonators and their effect on the dispersion relations of the system is evaluated. Finally, an effective medium description of the beam is developed to capture its behavior at long-wavelengths. In this regime, the system can be effectively considered as an acoustic metamaterial with adaptive dispersion properties.