Dimensional Beam Research Articles

Warren truss inspired hierarchical beams for three dimensional hierarchical truss lattice materials

Networks of beams are a subject of increasing interest to create architected materials with exceptional mechanical properties and low density. This paper investigates the mechanical properties of one dimensional (1D) hierarchical beams for the development of three dimensional (3D) truss lattice materials. These 1D hierarchical beams are constructed in two configurations by placing axial and inclined struts in single and double laced Warren truss patterns in each side of a beam with polygon cross section. Analytical and numerical analyses have been used to characterize their mechanical properties, including the elastic modulus, second moment of area, and shear stiffness of hierarchical beams drawn from a broad design space. Also, the failure limits of the beams with respect to parent material failure and various buckling modes are probed. Finally, the hierarchical beams have been implemented as the constituent members of Kelvin and octet lattices, and the elastic modulus and failure boundaries of the second-order hierarchical lattices are evaluated. The investigation reveals the competition between the elastic properties in the individual hierarchical beams based on different combinations of the design variables. The stiffness of the designs under compression and bending is found to be a function of the axial member size and cross sectional shape of the hierarchical beam. On the other hand, the shear stiffness of hierarchical beam designs is a function of the inclined member size and their inclination angle. It is demonstrated that incorporating hierarchy in the Kelvin and octet truss lattices can enhance the load bearing capacity of designs at low relative densities when compared to their hollow counterparts. Also, it is shown that second-order hierarchical stretching and bending-dominated lattices incorporating first-order hierarchical beams, can not only achieve but also surpass the strength and stiffness scaling relations established for first-order lattices. This becomes particularly noteworthy when considering bending-dominated lattices, as the hierarchy can drive their stiffness toward the boundaries, enabling them to outperform their equivalent stretching-dominated rivals.

Analytic solution for two dimensional beam problems: Pure displacement boundary conditions

The present manuscript delineates the derivation of strong solutions for the linear elasticity problem in a two dimensional rectangular beam. The materials under consideration can exhibit either isotropic or orthotropic properties. Additionally, the analysis is not restricted to slender beams because the ratio between the length and the height of the beam can be arbitrary. The boundary conditions fall into the Dirichlet category, implying that both horizontal and vertical displacements are specified on all four surfaces. The sole requirement is that these surface displacements are continuous functions, although they may not necessarily be smooth. Since the displacements at the surfaces can be arbitrary, there is no need to consider approximations, such as those concerning local (small) boundaries in slender beams. Nonetheless, it is demonstrated that an equivalent principle to the Saint-Venant principle exists for pure displacement boundary conditions. The partial differential equations are solved through the separation of variables method, leading to the identification of two solution types, encompassing both cosine and sine Fourier series. Particular emphasis is placed on evaluating the convergence of these solutions. For two distinct and general examples, it is confirmed that the solutions indeed exist.

Ultrasound-based jawbone surface quality evaluation after alveolar ridge preservation.

Bone readiness for implant placement is typically evaluated by bone quality/density on 2-dimensional radiographs and cone beam computed tomography at an arbitrary time between 3 and 6months after tooth extraction and alveolar ridge preservation (ARP). The aim of this study is to investigate if high-frequency ultrasound (US) can classify bone readiness in humans, using micro-CT as a reference standard to obtain bone mineral density (BMD) and bone volume fraction (BVTV) of healed sockets receiving ARP in humans. A total of 27 bone cores were harvested during the implant surgery from 24 patients who received prior extraction with ARP. US images were taken immediately before the implant surgery at a site co-registered with the tissue biopsy collection location, made possible with a specially designed guide, and then classified into 3 tiers using B-mode image criteria (1) favorable, (2) questionable, and (3) unfavorable.Bone mineral density (hydroxyapatite) and BVTV were obtained from micro-CT as the gold standard. Hydroxyapatite and BVTV were evaluated within the projected US slice plane and thresholded to favorable (>2200mg/cm3; >0.45mm3/mm3), questionable (1500-2200mg/cm3; 0.4-0.45mm3/mm3), and unfavorable (<1500mg/cm3; <0.4mm3/mm3). The present US B-mode classification inversely scales with BMD. Regression analysis showed a significant relation between US classification and BMD as well as BVTV. T-test analysis demonstrated a significant correlation between US reader scores and the gold standard. When comparing Tier 1 with the combination of Tier 2 and 3, US achieved a significant group differentiation relative to mean BMD (p=0.004, true positive 66.7%, false positive 0%, true negative 100%, false negative 33.3%, specificity 100%, sensitivity 66.7%, receiver operating characteristics area under the curve 0.86). Similar results were found between US-derived tiers and BVTV. Preliminary data suggest US could classify jawbone surface quality that correlates with BMD/BVTV and serve as the basis for future development of US-based socket healing evaluation after ARP.

Stabilization of hollow Gaussian beams in nonlinear metamaterial waveguides

Hollow Gaussian beams which possess the dark hollow spatial intensity distribution were found to have interesting applications in trapping nano-sized particles and free-space optical communication. Many applications demand stable dynamics of higher dimensional beams. Here we theoretically study the dynamics of hollow Gaussian beams in cubic and quintic nonlinear negative index metamaterial. We adopt Lagrangian variational analysis and explore the parametric regions characterizing the metamaterial in which the hollow Gaussian beam can execute stable dynamics as well as it can undergo filamentation due to intrinsic collapse. We confirm the analytical results obtained through variational analysis by direct numerical analysis based Crank Nicolson method implemented in Python programming.

The preliminary in vitro study and application of deep learning algorithm in cone beam computed tomography image implant recognition

To properly repair and maintain implants, which are bone tissue implants that replace natural tooth roots, it is crucial to accurately identify their brand and specification. Deep learning has demonstrated outstanding capabilities in analysis, such as image identification and classification, by learning the inherent rules and degrees of representation of data models. The purpose of this study is to evaluate deep learning algorithms and their supporting application software for their ability to recognize and categorize three dimensional (3D) Cone Beam Computed Tomography (CBCT) images of dental implants. By using CBCT technology, the 3D imaging data of 27 implants of various sizes and brands were obtained. Following manual processing, the data were transformed into a data set that had 13,500 two-dimensional data. Nine deep learning algorithms including GoogleNet, InceptionResNetV2, InceptionV3, ResNet50, ResNet50V2, ResNet101, ResNet101V2, ResNet152 and ResNet152V2 were used to perform the data. Accuracy rates, confusion matrix, ROC curve, AUC, number of model parameters and training times were used to assess the efficacy of these algorithms. These 9 deep learning algorithms achieved training accuracy rates of 100%, 99.3%, 89.3%, 99.2%, 99.1%, 99.5%, 99.4%, 99.5%, 98.9%, test accuracy rates of 98.3%, 97.5%, 94.8%, 85.4%, 92.5%, 80.7%, 93.6%, 93.2%, 99.3%, area under the curve (AUC) values of 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00, 1.00. When used to identify implants, all nine algorithms perform satisfactorily, with ResNet152V2 achieving the highest test accuracy, classification accuracy, confusion matrix area under the curve, and receiver operating characteristic curve area under the curve area. The results showed that the ResNet152V2 has the best classification effect on identifying implants. The artificial intelligence identification system and application software based on this algorithm can efficiently and accurately identify the brands and specifications of 27 classified implants through processed 3D CBCT images in vitro, with high stability and low recognition cost.

UAV-Assisted Wideband Terahertz Wireless Communications with Time-Delay Phased UPA under Beam Squint

Future Unmanned Aerial Vehicle (UAV)-assisted wireless communication systems are expected to utilize wide bandwidths available at terahertz (THz) frequencies to enhance system throughput. To compensate for the severe path loss in the THz band, it is essential to have a multitude of antennas in the UAV to generate narrow beams for directional transmission. However, narrow beams severely limit its spatial coverage, which greatly affects the efficiency of large-scale access UAV-assisted THz systems. Moreover, the combination of massive antennas and large bandwidth at THz makes the misalignment of the beams caused by beam squint non-negligible and also high energy consumption. UAV-assisted communication technology can effectively increase spatial coverage and provide reliable LoS communication links. In addition, reducing the number of radio frequency (RF) chains while ensuring the number of transmitted data streams and space division multiplexing capability is also an effective way to reduce energy consumption in the UAV communication. In this paper, a single RF chain uniform planar array (UPA) with true-time-delays (TTDs) is equipped on the UAV to achieve two dimensional (2D) beams and split spatial beams to improve transmission efficiency. We analyze the 2D beam squint of the UPA and design a time-delay phased UPA for UAV-assisted THz communication systems. By introducing TTDs between the single RF chain and phase shifters, the beam squint can be controlled flexibly by introducing the delay between each antenna. When TTDs are arranged in both the horizontal and vertical dimensions, the coverage of the beams becomes more complicated compared to uniform linear arrays (ULA). Simulation results show that the proposed time-delay phased UPA can achieve better performance in both single-beam and multi-beam modes for single user and multi-user scenarios compared with conventional phased UPA, respectively. In addition, we propose frequency division beam multiple access (FDBMA) multi access technology, which achieves more efficient multi access by reusing resources from different frequency beam pairs. Finally, the results also show that the enlargement of the beamwidth through the proposed FDBMA strategy can also increase the performance in multi-user scenarios.

Manipulating self-focusing beams induced by high-dimensional parabolic umbilic beams

The excellent property that the intensity of autofocusing beams in the focal plane increases exponentially, makes them especially beneficial for biomedical treatment. We experimentally generate tunable (2+1)-dimensional circular parabolic umbilic beams (CPUBs) for the first time based on the high-dimensional diffraction catastrophe integral, which is determined by the potential function. Such CPUBs have circular and symmetrical intensity distributions in space through radial symmetry transformation. Due to the flexibility of high dimensionality, these light beams have rich light field structures and self-focusing property. Where, the maximum intensity suddenly increases by orders of magnitude in the focal plane. Unlike the classical circular Airy beams, CPUBs exhibit multiple self-focusing points along the optical axis and a needle-like structure during propagation, which can be affected by manipulating the control parameters. The rich properties provide a new perspective for exploring the novel physical mechanisms and phenomena in autofocusing beams. The experimental results verify the correctness of the numerical simulations. CPUBs greatly enrich the autofocusing beam family and will be advantageous for medical treatments, optical micromanipulation, and microscopic imaging.

On‐Chip Electrically Driven Tunable Meta‐Lens for Dynamic Focusing and Beam Steering

AbstractThe on‐chip meta‐lenses consisting of subwavelength slot arrays with lateral gradients have shown great potential for parallel signal processing and optical computing. The dynamic tuning mechanisms which are necessary steps toward exploiting the applications of the on‐chip meta‐system have been rarely mentioned yet. Here, a free‐form functional microheater via topology design is proposed to manipulate the refractive index distribution, allowing for flexible optical wavefront shaping. For a proof‐of‐concept, wide range of dynamic focusing and beam steering are demonstrated via a tunable meta‐lens on silicon photonic platform. The continuous scanning of the focused beam is experimentally achieved with a maximum travel range of 100 µm in the longitudinal direction (≈95 nm mW−1) and 25 µm in the lateral direction (≈20 nm mW−1). The thermal‐optic tuning elements can response the electrical control within ≈41.2 µs. A waveguide array at the focal plane is used to characterize the device. The on‐chip loss of the tunable meta‐lens is measured to be &lt;1 dB including the coupling loss from slab to single‐mode waveguide. The proposed tunable meta‐lenses are fabricated via a standard silicon photonic process and allow for arbitrarily two dimensional (2D) beam steering. It offers great versatility for on‐chip meta‐systems with a wider scope of functionalities and applications.

Free form shape optimization of three dimensional beams using cross section analysis

We introduce an efficient method for shape optimization of three dimensional beams that is based on free-form design of the beam’s cross section. The cross section boundary of each beam segment is parameterized by a closed, unclamped B-spline curve, whose control points’ coordinates serve as design variables. The response of the beam is evaluated globally as a one-dimensional entity using 3D beam finite elements, while each cross section is modeled locally using cross section analysis following anisotropic beam theory. A fully consistent analytical sensitivity analysis is derived to account for the relation between the control points and the beam cross-sectional properties and design updates are performed using gradient-based optimization. The proposed method is applied to several test cases, aiming at minimization of compliance or maximization of the fundamental frequency. The numerical results and a comparison to other methods for beam optimization show that the method can generate highly competitive designs. A consistent quantitative comparison to high resolution continuum topology optimization shows that a performance which is only slightly inferior can be achieved, for only a small fraction of the computational effort.

Zero programming robotics in additive manufacturing repairs

This document explains the implementation of an integral additive manufacturing system at the Canadian Centre for Welding and Joining (CCWJ). Highlighting its use to remanufacture high-value components with a streamlined workflow using an optical coordinate measuring machine and parametric programming. The resultant output robot code is embedded with control of dimensional accuracy, laser power, beam velocity, and powder feed rate. This approach centers its attention on the remanufacturing of parts and their inherent complex surface as well as the time-consuming task of programming the robot to construct tool paths for the cladding strategy. These issues are solved using a set of topologies implemented in software and hardware that deliver a system that integrates the control parameters and the tooltip toolpaths into a highly automated system offering versatility, scalability, and reproducibility. The results show the capacity of the system to directly repair worn-out parts from a 3D scanner and deliver short-time programming sequences with integrated process constraints, precision, and high dimensional accuracy.

Experimental and numerical assessments of new concrete dry connections concerning potentials of robotic CNC manufacturing technique

Coinciding with new manufacturing methods such as robotic additive manufacturing techniques and the gradual transition in construction approaches, new structural elements should be developed that, against the classic approaches, can easily be manufactured by new additive manufacturing techniques. Concrete Dry connections are one of these discussed elements. Appropriate geometries of dry concrete joints, manufactured by robotic CNC technique, accelerate the construction process by eliminating the necessity of formwork, scaffolding and concrete injection. Furthermore, desirable connections with higher interlocking and resistance in different degrees of freedom can be developed by facing the difficulties of traditional construction methods. Through some examples, this paper initially discussed the possibility of constructing dry concrete joints by robotic 3D-printing and robotic milling/sawing methods, and their geometrical accuracy was measured. In addition, 9 geometries of dry concrete joints were proposed and produced by formwork. Then, the performances of the proposed post-tensioned dry joints were discussed and compared to similar monolithic elements. On this basis, certain dry joints, entirely and easily manufactured by additive manufacturing technology (robotic concrete printing and CNC), could achieve up to 64% of the flexural capacity of a dimensional similar monolithic beam.

2-Dimensional (2D) Beam Steering-Antenna Using Active PRS for 5G Applications.

This paper presents a compact coaxial-fed square microstrip patch antenna integrated with a beam-steering Partially Reflective Surface (PRS). The proposed design has a two-dimensional (2-D) Fabry-Perot Cavity (FPC) antenna acting as a radiator and the PRS as a beam-steering superstrate operating at 5.5 GHz. The PRS consists of 6 × 6 reconfigurable unit cells etched on Rogers 5880 with a thickness of 1.57 mm. By controlling the switching of PIN diodes in different sections of PRS, beam steering can be achieved up to ±47° in the azimuth plane with a gain of 9.1 dB and 10.2 dB and ± 15° steering in an elevation plane with a measured gain of 9.3 dB and 8.9 dB, respectively. The antenna prototype is 2.56 λ × 2.56 λ at 5.5 GHz, and the measured gain values are around 10 dBi for all the states. The beam is able to radiate at boresight or tilted to 42° in two azimuthal directions and 45° in elevation direction by adjusting the PIN diodes ON/OFF states. The 10 dB impedance bandwidth of 5.4-5.52 GHz is achieved.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

A hybrid collocation method for the computational study of multi-term time fractional partial differential equations

In this article, we focus on the numerical study of one and two dimensional higher order multi-term time fractional partial differential equations. In the adopted strategy, the temporal fractional derivative is replaced via well known L 1 formula and the integer order space derivatives are approximated by truncated one and two dimensional wavelet series. The fascinating nature of the scheme is to use collocation approach which convert the governing equations to the system of algebraic equations from which the wavelet coefficients can be calculated. Next, stability of the proposed scheme is investigated theoretically which is also the fundamental subject of the current work. Further computational convergence rate is computed which predicts that the order is approximately two. The scheme is applied to solve one dimensional beam models (fourth order partial differential equations) and two dimensional fissured rock models (Sobolev equations). Efficiency of the scheme is examined with the help of various error norms such as I ∞ , I r m s and I 2 . Simulations indicate pretty much good results from which we can say that the scheme is suitable and robust for both one and two dimensional problems.

KAM Tori for a Two Dimensional Beam Equation with a Quintic Nonlinear Term and Quasi-periodic Forcing

KAM Tori for a Two Dimensional Beam Equation with a Quintic Nonlinear Term and Quasi-periodic Forcing

Bending of optical solitonic beams modeled by coupled KMN equation

The dynamics of (2 + 1) dimensional optical solitonic beams modeled by coupled Kundu Mukherjee Naskar (KMN) equation are discussed by deriving one bright and one dark soliton solution. The arbitrary bending of solitonic beams of this coupled system has been described by exact curved soliton solutions having an arbitrary function. Such exact analytical results on the bending of solitonic pulse in a bimodal optical fiber system may pave new research directions in this field.

On the compressive strength of brittle lattice metamaterials

Lightweight architected materials made of a brittle parent solid have great potential for use in environments where extreme conditions occur due to their excellent strength-to-weight ratio and temperature resistance. In this study we combine experimental and modeling efforts to correlate the strength of three-dimensional lattice metamaterials to topological and microstructural characteristics, as well as the mechanical behavior of the base material. Three regular periodic lattices with varying rigidity, owing to their node connectivity, are additively manufactured using a brittle photopolymer and then tested to failure under compressive loads. Micromechanical models are developed to elucidate the experimental results and uncouple the effects of microstructure and strut failure on the resulting macroscopic strength. Our results indicate that stress concentrations at the nodes, where struts intersect, are significantly affecting brittle failure and need to be accounted for in predictive modeling frameworks. Towards this goal, both beam- and solid-based finite element models are considered and their efficacy in capturing the response and critical stresses is examined in detail. We finally show the dependence of lattice strength to relative density and compare the trends with well-known scaling formulas based on dimensional analysis and beam theory.

Manipulation and Improvement of Autofocusing Properties for Circular Butterfly Beams

AbstractA new class of (2+1)‐dimensional circular butterfly beams (CBBs) is first demonstrated based on high‐dimensional butterfly catastrophes. The intensity of CBBs increases abruptly by two orders of magnitude right before they propagate to the focal plane, implying that they possess an abruptly autofocusing (AAF) ability induced by accelerating properties. The autofocusing performance can be further improved by introducing vortices. Owing to the flexibility of high‐dimensional catastrophes, butterfly beams exhibit diverse optical light structures; thus, the focal length, focal intensity, and light field structures of CBBs are tunable. Experimental results are consistent with numerical findings. Therefore, CBBs enrich the family of AAF beams and will be advantageous for optical micromachining, medical treatments, optical tweezers, and nonlinear processes.

Vibration analysis of piezoelectric Kirchhoff–Love shells based on Catmull–Clark subdivision surfaces

AbstractAn isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialized to infinitesimal deformations and follow the Kirchhoff–Love hypothesis. Both the geometry and physical fields are discretized using Catmull–Clark subdivision bases. This provides the required ‐continuous discretization for the Kirchhoff–Love theory. The crystalline structure of piezoelectric materials is described using an anisotropic constitutive relation. Hamilton's variational principle is applied to the dynamic analysis to derive the weak form of the governing equations. The coupled eigenvalue problem is formulated by considering the problem of harmonic vibration in the absence of external load. The formulation for the purely elastic case is verified using a spherical thin shell benchmark. Thereafter, the piezoelectric shell formulation is verified using a one dimensional piezoelectric beam. The piezoelectric effect and vibration modes of a transverse isotropic curved plate are analyzed and evaluated for the Scordelis–Lo roof problem. Finally, the eigenvalue analysis of a CAD model of a piezoelectric speaker shell structure showcases the ability of the proposed method to handle complex geometries.

Two dimensional Airy beam soliton

We demonstrate the formation of a two dimensional Airy beam soliton in a photorefractive crystal. By simply varying the nonlinearity strength we identify several scenarios showing the coexistence between an Airy beam and the emerging soliton. The soliton output profile behaves according to the theoretical soliton existence curve and can be tailored by the nonlinearity strength even without modifying the input Airy beam shape. This last feature makes this Airy soliton distinct from the Gaussian beam generated photorefractive soliton.