Nonhomogeneous Beam Research Articles

Estimating the Optically Pumped Threshold Fluence of Thin‐Film Gain Media Using Arbitrary Excitation Beams

Optically pumped threshold fluences are a widely reported metric to benchmark the performance of thin‐film gain media and lasers. Estimating the threshold fluence for nonhomogeneous beams, such as a circular Gaussian excitation, is not trivial since the average fluence depends on the estimated spot diameter. Using an exemplary lead halide perovskite film, the inversion volume at different pump energies is mapped. It is shown that the peak fluence of an arbitrary spatial beam profile is more relevant at the threshold, as it provides an upper bound to the threshold fluence. Also, simple conversion factors to estimate the peak fluence using Gaussian excitation beams are provided and the methodology to arbitrary profiles is extrapolated. Furthermore, it is advocated for using flat‐top or uniform stripe excitations to unambiguously extract the threshold fluence, since these excitations display minor discrepancies between the average and peak fluence, and keep the inversion volume relatively constant during the measurement.

Asymptotic evolution of speckle patterns to synthesize non-homogeneous string beams

We analyze the evolution of the speckle pattern subjected to a compression showing that the spatial evolution of the probability density function satisfies a non-linear diffusion equation. Its asymptotic solution corresponds to a non-homogeneous wave with string-shape. During the compression, an irradiance interaction is generated between the speckles. The interaction satisfies a type-logistic equation. The electric field components associated with the speckles present a random behavior, however, during the compression process, the transversal components cancel each other, and the resulting light presents a state of polarization parallel to the propagation coordinate, justifying the non-homogeneous behavior. Computer simulations are presented.

Interaction of inhomogeneous warm electron beam with collisional cold plasma

The linear interaction of a warm non-homogeneous electron beam (EB) with a non-homogeneous, unmagnetized, collisional cold plasma is investigated. The inhomogeneity and warmness of beam which leads to electric field amplification have no effect on the dielectric of the unmagnetized plasma. The study revealed that the dielectric constant remains unaffected by the warmness of the beam whereas the amplification of the electric field is affected by the warmness of the beam.

SPIDER, the Negative Ion Source Prototype for ITER: Overview of Operations and Cesium Injection

An overview of the recent operations and the main results of cesium injection in the Source for the Production of Ions of Deuterium Extracted from Rf plasma (SPIDER) negative ion source are described in this contribution. In experiments without cesium injection, all SPIDER plants were tested to verify the basic expectations on the operational parameters (e.g., electron cooling effectiveness of magnetic filter field) and to determine its operational region. For beam properties, it was shown that the current density varies across the beam in the vertical direction. In preliminary cesium experiments, the expected increase of negative ion current and simultaneous decrease of co-extracted electrons were found, along with the influence of the control parameters (polarization of the plasma electrodes, magnetic filter field) on the SPIDER beam uniformity in the horizontal and vertical directions. It was shown that non-Gaussian tails can be identified in the angular distribution on the plane perpendicular to the beam propagation direction. Stray particles, nonhomogeneous beam and large divergence might result in unexpected heat and particle loads over ITER neutral beam injector (NBI) accelerator grids; it is the goal of SPIDER to assess and possibly to identify suitable methods for controlling these beam features. A major shutdown, planned for late 2021, to solve the issues identified during the operation and to carry out scheduled modifications, is outlined. Such improvements are expected to allow SPIDER to pursue the ITER requirements in terms of negative ion current, electron-to-ion ratio, and beam duration.

Precise integration solutions for the static and dynamic responses of axially graded solid beams

By virtue of the scaled boundary finite element method (SBFEM), the precise integration solutions (PIS) to deflections, stresses and transverse vibration parameters of the functionally graded solid beams are provided. It is worth to note that the mechanical parameters of the graded beams are altered across the x-axis according to power-law, exponential, trigonometric or other arbitrary theories. In SBFEM, the in-homogeneous beam is simplified into the one-dimensional model and just two high-order linear spectral elements are exploited to discretize the axially non-homogeneous beam. Nevertheless, the high accuracy can be ensured. It is essential to remind that the displacement-based beam spectral element is characterized by owning only two degrees of freedom. Additionally, the changing patterns of the displacement and stress field through the transverse direction can be expressed as an analytical matrix exponent. Aided by the two-dimensional fundamental equations of elastic materials and the employed scaled boundary coordinate, the governing equation of the axially graded solid beam is derived in the form of second order ordinary differential equation. Furthermore, the stiffness matrix and PIS of displacements and stresses are acquired from evaluating the governing equation by means of the dual vector technology and precise integration methodology (PIM). Applying the kinetic energy theory constructs the mass matrix of the axially heterogeneous beam. Afterwards the PIS to natural frequencies are obtained according to solving the eigenvalue equation. Finally, numerical exercises are presented to portray the excellent agreement and fast convergence ratio of the introduced PIS and discuss influences of supported conditions, gradient exponents, length-to-thickness ratios and formulae of gradation functions on the flexural behaviors and free vibration responses of the axially graded elastic beams.

Flapwise bending vibrations of rotating axially functionally graded variable section beams

Free flapwise bending vibrations of rotary axially functionally graded (FG) beams with non-uniform cross-section are presented according to the Euler-Bernoulli beam theory. The dynamic equations are derived from the second-kind Lagrange's equations, in which the potential and kinetic energy functions are described by using a set of hybrid deformation variables. The modal characteristics are calculated from the dimensionless eigenvalue equation by the assumed mode approach. The accuracy and effectiveness of the proposed approach are confirmed by comparative and convergence studies. The effects of dimensionless parameters, such as the taper ratios of height and breadth,the hub radius ratio, the angular velocity, and the material gradient parameter, on mode shapes and natural frequencies of tapered rotary beams with axially varying Young's modulus and mass density are studied in detail. The numerical results presented in this work are benefit to the optimization design of rotating tapered non-homogeneous beams.

Development of a cross-sectional finite element for the analysis of thin-walled composite beams like wind turbine blades

A method for structural analysis of thin-walled composite beams like wind turbine blades is presented. This method is based on the Nonhomogeneous Anisotropic Beam Section Analysis (NABSA) which consists in discretizing the beam cross section using finite elements. The proposed implementation uses 3-node line cross-sectional finite elements with nodes having rotational degrees of freedom to describe the cross-sectional warping displacements. Solutions obtained using this approach were verified against the corresponding analytical or numerical solutions. Agreement was very good to excellent for the computation of cross-sectional properties and distribution of stresses, strains and warping displacements for a broad range of possible composite beam behaviors including geometric and material couplings, open sections, multicell sections, and arbitrary laminates. For thin-walled layered structures, the proposed method provides models with fewer degrees of freedom than equivalent models based on a two-dimensional discretization of cross sections using triangular or quadrilateral elements such as conventional NABSA or VABS which suggests that computation time could be reduced.

Thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation

In this paper, thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation is investigated. For this purpose, at first, Euler–Bernoulli beam theory is used and the governing differential equations are obtained by using Hamilton’s principle. The nonlocal strain gradient theory is implemented to capture the small scale effects. Adomian decomposition Method (ADM) and Homotopy Perturbation Method (HPM) are used to obtain the frequencies of vibration. Also, the nonhomogeneous beam model has been considered, where Young’s modulus and density of the beam vary linearly and quadratically with respect to longitudinal direction of the beam for three different boundary conditions: simply supported, clamped, and clamped simply supported.

Modeling and analysis of energy harvester based on galloping considering the non-homogeneous beam

ABSTRACT This paper proposes a piezoelectric energy harvester based on non-homogeneous beam, which is employed to capture wind energy by galloping. A distributed parameter model of piezoelectric energy harvester with the nonuniformity of cantilever beam is developed. The quasi steady state approximation is used to simulate the fluid force. The model is verified by the experimental results reported previously. The influences of load resistance, the position of piezoelectric patch, and the size of beam on the output power are studied. Finally, a set of optimization parameters are generated to study the performance of the energy harvester. The results show that compared with rectangular beam, the output power of piezoelectric energy harvester with non-homogeneous beam can be increased by 32%.

SKAO H i intensity mapping: blind foreground subtraction challenge

ABSTRACT Neutral Hydrogen Intensity Mapping (H i IM) surveys will be a powerful new probe of cosmology. However, strong astrophysical foregrounds contaminate the signal and their coupling with instrumental systematics further increases the data cleaning complexity. In this work, we simulate a realistic single-dish H i IM survey of a 5000 deg2 patch in the 950–1400 MHz range, with both the MID telescope of the SKA Observatory (SKAO) and MeerKAT, its precursor. We include a state-of-the-art H i simulation and explore different foreground models and instrumental effects such as non-homogeneous thermal noise and beam side lobes. We perform the first Blind Foreground Subtraction Challenge for H i IM on these synthetic data cubes, aiming to characterize the performance of available foreground cleaning methods with no prior knowledge of the sky components and noise level. Nine foreground cleaning pipelines joined the challenge, based on statistical source separation algorithms, blind polynomial fitting, and an astrophysical-informed parametric fit to foregrounds. We devise metrics to compare the pipeline performances quantitatively. In general, they can recover the input maps’ two-point statistics within 20 per cent in the range of scales least affected by the telescope beam. However, spurious artefacts appear in the cleaned maps due to interactions between the foreground structure and the beam side lobes. We conclude that it is fundamental to develop accurate beam deconvolution algorithms and test data post-processing steps carefully before cleaning. This study was performed as part of SKAO preparatory work by the H i IM Focus Group of the SKA Cosmology Science Working Group.

Effects of chemical degradation on longitudinal fracture of non-homogeneous beams: an analytical study

An analytical study of the chemical degradation of the material and its effects of on longitudinal fracture behaviour of continuously non-homogeneous cantilever beam is carried-out. The chemical degradation is described by decreasing of the elasticity modulus of the non-homogeneous material with time. The fracture is studied by analyzing of the strain energy release rate. For this purpose, the strain energy release rate is derived as a function of time with taking into account the chemical degradation and the non-homogeneity of the material. The time-dependent fracture is analyzed also by applying the J-integral with considering the chemical degradation for verification. The variation of the strain energy release rate with the time due to the chemical degradation is studied and discussed in detail.

Delamination analysis of multilayered viscoelastic beam exposed to chemical degradation

Delamination of multilayered viscoelastic non-homogeneous beam structure subjected to chemical degradation is analysed in this paper. The creep behaviour is treated by using a linear viscoelastic model. The influence of chemical degradation is taken into account by decreasing the elasticity modulus and the coefficient of viscosity with time. The time-dependent delamination fracture under chemical degradation is studied by analysing the strain energy release rate. The strain energy is used to obtain the strain energy release rate that accounts for the creep and for the chemical degradation. The solution is verified by applying the compliance method with considering of the chemical degradation.

Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method

This paper presents the dynamic responses of a fiber-reinforced composite beam under a moving load. The Timoshenko beam theory was employed to analyze the kinematics of the composite beam. The constitutive equations for motion were obtained by utilizing the Lagrange procedure. The Ritz method with polynomial functions was employed to solve the resulting equations in conjunction with the Newmark average acceleration method (NAAM). The influence of fiber orientation angle, volume fraction, and velocity of the moving load on the dynamic responses of the fiber-reinforced nonhomogeneous beam is presented and discussed.

Nonhomogeneous multicolor laser beams optimization to obtain a stronger intensity single harmonic radiation path

Abstract How to obtain the high signal intensity harmonic spectra with the single harmonic radiation path contribution becomes an important issue in the investigations of the high-order harmonic generation and attosecond science. In this paper, through the nonhomogeneous multicolor laser beams optimization, the best time-spatial laser waveforms, including the positive and negative time-spatial waveforms, to produce the harmonic spectra can be found. As a result, the harmonic plateaus with the single harmonic radiation path contribution and with the enhancement of several orders of magnitudes can be obtained, which can support the generation of the isolated pulses with the durations of 29 as. The physical mechanism behind the improvement of the harmonic spectra is given by the time-spatial profile analyses of the laser pulses and the harmonic spectra.

Conservation Integrals in Nonhomogeneous Materials with Flexoelectricity

The flexoelectricity, which is a new electromechanical coupling phenomenon between strain gradients and electric polarization, has a great influence on the fracture analysis of flexoelectric solids due to the large gradients near the cracks. On the other hand, although the flexoelectricity has been extensively investigated in recent decades, the study on flexoelectricity in nonhomogeneous materials is still rare, especially the fracture problems. Therefore, in this manuscript, the conservation integrals for nonhomogeneous flexoelectric materials are obtained to solve the fracture problem. Application of operators such as grad, div, and curl to electric Gibbs free energy and internal energy, the energy-momentum tensor, angular momentum tensor, and dilatation flux can also be derived. We examine the correctness of the conservation integrals by comparing with the previous work and discuss the operator method here and Noether theorem in the previous work. Finally, considering the flexoelectric effect, a nonhomogeneous beam problem with crack is solved to show the application of the conservation integrals.

Investigation of mechanical properties for Non-Homogeneous by image tracking method

Abstract We have investigated new approach to predict mechanical properties for non-homogeneous materials. The investigation used copy paper 100 gsm as sampling object using image tracking method and based on bending of cantilever slender beam. The copy paper 100 gsm was shaped on non-homogeneous geometris than placing it with curvature angle variations (0°, 45° and 90°). We snapshot the copy paper sample using digital camera later tracked the coordinates at several points after divided the beam image into 16 segments. Futhermore, we calculated Modulus Young using elasticity equation for non-homogeneous beam. The results presented show that it is possible to obtain a good Modulus Young value due to approach Modulus Young value obtained by direct measurement using tensile strength device. This method is expected to become a reference for developing Modulus Young estimation for non-homogeneous geometry materials without direct contact.

Fracture analysis of a nonhomogeneous beam with two concentric cylindrical longitudinal cracks

This paper is concerned with the analysis of the fracture behaviour of a nohomogeneous cantilever beam with two concentric longitudinal cracks. The beam has a circular cross-section with linearly varying radius along the beam length. Moreover, the beam exhibits continuously varying material inhomogeneity in the radial direction. The fracture is analyzed in terms of strain energy release rate assuming nonlinear mechanical behaviour of the material. For this purpose, solutions for the strain energy release rate are derived by considering the energy balance. Two cantilever beam configurations with different lengths of longitudinal cracks are analysed. Moreover, the two cracks are arranged arbitrarily in the radial direction. The longitudinal fracture behaviour of the beam is also analysed by considering the complementary strain energy for verification. The strain energy release rate solutions are used to investigate the influence of varying radius of the cross section along the length of the beam on the longitudinal fracture behaviour. The effects of crack lengths and the location of the two concentric cracks in the radial direction on fracture are also studied. The influences of the loading conditions of the beam and the inhomogeneity of the material in the radial direction on the fracture behaviour are also evaluated.

1D-Hierarchical Ritz and 2D-GDQ Formulations for the free vibration analysis of circular/elliptical cylindrical shells and beam structures

The present paper proposes a comparison between two different computational techniques to evaluate the natural frequencies of some selected structural components. More specifically, three case studies are investigated: i) Isotropic circular and elliptical cylindrical shells; ii) Non-homogeneous circular cylindrical shell sectors; iii) Homogeneous and non-homogeneous rectangular beams. The 1D-Hierarchical Ritz Formulation (HRF) with 3D capabilities and the 2D-Generalized Differential Quadrature (GDQ) formulation (both in a weak- and a strong-form) are assessed by using a Finite Element Method (FEM) software. For both computational methodologies the Method of Power Series Expansion of the Displacement Components (MPSEDCs) has been employed. A parametric investigation is performed to study the sensitivity of the natural frequencies to some significant parameters, namely, the boundary conditions, the length-to-thickness ratio, as well as some material and geometrical properties. The main advantages of the proposed solution techniques are discussed in terms of convergence and accuracy, for each selected case study.

A damaged non-homogeneous Timoshenko beam model for a dam subjected to aging effects

A hemi-variational formulation for a damaged non-homogeneous Timoshenko beam is proposed here for the purpose of fast simulation of the properties of a dam. The dam is therefore modeled as a damaged non-homogeneous Timoshenko beam embedded in 2D space. The damage evolution and the mechanics of the beam are governed both by the hemi-variational principle and by the assumption on the form of the deformation energy functional, that comprehends the dissipative part owing to damage-aging effects. In the formulation, the Karush–Kuhn–Tucker (KKT) condition is derived and the damage, which locally decreases the stiffness (i.e., axial, bending, and shear stiffness) of the beam, becomes relevant once a measure of the elastic energy, called the normalized undamaged elastic energy, reaches a certain threshold that is constitutively prescribed ab initio. The aging effect is assumed by reducing such a threshold in the neighborhood of the bottom of the beam, where the concentration of the chemical and physical attacks is higher. As a result, we show a method for the calculation of the mechanical failure condition. In addition, we observe that, even though this threshold is assumed to decrease in a large region far from the bottom of the dam, the damage is confined at the bottom of it. Thus, we have proved that the trapezoidal shape that is used in the dam design is useful not only to decrease the state of stress in the elastic regime, but also to confine the effects of damage evolution owing to the aging effects.

On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.