One-dimensional Beam Research Articles

Robust adaptive boundary control of a disk–beam–mass system under unknown distributed disturbance

This paper focuses on the boundary stabilization control of a rotating disk–beam–mass system (DBMS), comprised of a one-dimensional flexible beam perpendicularly affixed to a rotating rigid disk at its lower boundary and a payload, conceptualized as a tip mass at its opposite end. We posit that the boundary control, which includes an external torque acting on the disk and an external force acting on the tip mass, is subject to an undefined time-varying disturbance. Concurrently, the flexible beam experiences an undefined spatiotemporal-varying distributed disturbance. Firstly, we employ Hamilton’s principle to elaborate on the mathematical model that describes the motion of DBMS. Subsequently, an adaptive boundary control is designed to stabilize the beam’s transverse displacement and regulate the disk’s angular velocity to track a predetermined value asymptotically. Applying the theory of Lyapunov, we demonstrate that uniform and ultimate boundedness under distributed disturbance can be achieved. Finally, we conduct several numerical simulations to showcase the applicability and efficacy of our proposed adaptive boundary controller.

Vibration analysis of rotating pre-twisted composite beams through isogeometric-based dimensional reduction method

The free vibration analysis of rotating pre-twisted composite beams with arbitrary cross-section geometry is investigated using an isogeometric-based dimensional reduction method. The three-dimensional beam problem is decomposed into a two-dimensional cross-sectional analysis and a one-dimensional beam problem, significantly reducing the numerical cost compared to three-dimensional finite element method. The simultaneous influences of pre-twist and rotational speed are carefully studied for various composite beams. This approach benefits from the numerical advantages of isogeometric analysis, with results showing better agreement with three-dimensional finite element method than other studies in the literature.

Physics-informed neural networks approach for one-dimensional beams

Physics-informed neural network (PINN) is a machine learning technique where the physics of the problem is embedded into the loss function. The straightforward approach is to define the loss function using the problem governing differential equations and its boundary/initial conditions in a sort of collocation method. In general, the hyperparameters of neural networks for each problem at hands are defined via a grid search-like procedure, or simply by trial and error. In this paper, the application of PINNs is illustrated for one-dimensional beam problems, and the influence that the network weights initialization procedure has on the training is investigated. The code was built using SciANN, a Python package that uses TensorFlow and Keras for scientific computing and physics-informed deep learning employing artificial neural networks.

Asymptotic Homogenization Method with fictitious multilayers applied to the mesoscale characterization of concrete beams

The escalating complexity of engineering challenges necessitates the utilization of increasingly efficient materials, often met through the adoption of composite materials as a viable solution. Concrete stands out as one of the most prevalent composite materials in civil engineering, evolving through alterations in its constituent components as researchers pursue enhanced durability, workability, and sustainability. However, traditional theories treating concrete as a homogenous isotropic material prove inadequate for predicting the mechanical properties of these innovative concretes, primarily due to the excessive costs associated with experimental analyses. Consequently, this study introduces a high-order zig-zag multilayer theory incorporating the asymptotic homogenization method. The variational formulation of a unified beam kinematics was used to carry out a multiscale analysis through the asymptotic expansion of the unknown variables. This methodology facilitates the transformation of a beam composed of heterogeneous materials into an equivalent homogeneous. The findings of the formulation proposed agree with established numerical and experimental formulations documented in the literature, even when employing a one-dimensional beam theory.

Two-dimensional synchrotron beam characterization from a single interferogram

Double-aperture young interferometry is widely used in accelerators to provide a one-dimensional beam measurement. We improve this technique by combining and further developing techniques of nonredundant, two-dimensional, aperture masking, and self-calibration from astronomy. Using visible synchrotron radiation, tests at the ALBA synchrotron show that this method provides an accurate two-dimensional beam transverse characterization, even from a single 1 ms interferogram. The nonredundancy of the aperture mask in the technique enables it to be resistant to spatial phase fluctuations that might be introduced by vibration of optical components or in the laboratory atmosphere. Published by the American Physical Society 2024

Wide-field large-angle beam splitters based on polarization-insensitive coding metasurfaces

Metasurfaces have been used to make various optical devices such as beam splitters because of their excellent capability to control light. The most recent work on metasurface beam splitters focused on realizing one-dimensional beam splitting. Based on generalized Snell’s law, we designed the beam splitters using a coding strategy by phase gradient metasurfaces, which can divide vertically incident light into two-dimensional space. Meanwhile, the beam splitters are polarization-insensitive because highly rotationally symmetric nanorods are used as structure units. Using different code groups, especially applying 0 and π binary phases, the proposed beam splitters have various functions such as beam deflection, two-beam splitting, and multi-beam splitting. The flexible design of the coding maps allows the light transmission to cover a full-view field. The maximum splitting angles in two-beam and multi-beam splitters are 35.7° and 28.3°, respectively. All the designed beam splitters have a power efficiency of over 80%. The beam splitters have the advantages of small size, easy integration, large beam splitting angle, wide beam splitting area, and high efficiency. They could be applied to many optical systems, such as multiplexers and interferometers in integrated optical circuits.

Development of the 1-D X-ray beam diffuser for multilayer monochromator and its application to X-ray phase tomography

Abstract The one-dimensional (1-D) X-ray beam diffuser was developed to reduce horizontal stripe-shaped intensity irregularities on the beam from a multilayer monochromator while keeping the horizontal spatial coherence of the beam required for phase measurements using a grating interferometer. The diffused beam showed a smoothed beam profile without degrading the visibility of Moiré fringes in the grating interferometer. In the X-ray phase tomographic measurement, a sectional image with the beam diffuser showed clear structure without artifacts while the sectional image without the diffuser suffered from the remaining striped-shaped artifacts.

Generalized fractional one-dimensional Hermite-Gaussian beams

Generalized fractional one-dimensional Hermite-Gaussian beams

A one-dimensional higher-order dynamic modeling method for thin-walled beams with circular cross-sections

This paper addresses the construction of a dynamical model for a thin-walled beam with circular cross-section in the framework of one-dimensional higher-order beam theory. And a method for pattern recognition of circular thin-walled structures is proposed based on principal component analysis. Initially, a set of equal length linear segments are defined to discretize the mid-line of a circular section. Preliminary deformation modes of thin-walled structures, defined over the cross-section through kinematic concept, are parametrically derived through changing the discretization degree of the section. Next, the generalized eigenvectors are derived from the governing equations, and the characteristic deformation modes of circular sections with different discretization degrees are solved based on principal component analysis. In addition, a reduced higher-order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The features include further reducing the number of degree of freedoms (DOFs) and significantly improving computational efficiency while ensuring accuracy. For illustrative purposes, the versatility of the procedure is validated through both numerical examples and comparisons with other theories.

Framework of Physically Consistent Homogenization and Multiscale Modeling of Beam Structures

In this work, a framework of physically consistent homogenization and multiscale modeling (PCHMM) is developed to analyze complex slender structures with homogenized one-dimensional beam models. Firstly, it is highlighted that periodic boundary conditions are not valid for the representative volume element (RVE)-based homogenizations if a shear-deformable beam model is to be obtained. Addressing this issue, physically consistent boundary conditions (PCBCs) are discussed in detail, which accounts for the influence of shear forces on the behavior of the slender structure and the corresponding RVE. A procedure of enforcing such boundary conditions is also given, applying sectional stresses to the RVE with fictitious DoFs. Additionally, we introduce a newly developed correct formula to calculate effective sectional properties which guarantee the cross-scale energy conservation though a modified Hill’s condition. The PCHMM framework, with homogenization/dehomogenization procedures using PCBC and the modified Hill’s condition, is also conveniently integrated into a commercial finite element software. The correctness and effectiveness of the developed framework of homogenization and multiscale analysis are demonstrated through several numerical examples, including lattice beams, twist-morphing metamaterial spars, and a realistic wing. The extension of this theory to plate/shell structures will be presented in our future work.

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

A 27 ​GHz, simple 2-bit 1×8 phased array

This study demonstrates a simple 2-bit phased array operating at 27 ​GHz that supports one-dimensional beam scanning with left-handed circular polarization (LHCP). The antenna is constructed using a compact four-layer printed circuit board (PCB) structure, consisting of a 90° phase shifter layer with microstrip structures, a ground (GND) layer, a direct current (DC) control layer, and a circularly polarized annular radiation patch layer with 1-bit phase shifting. Based on the proposed unit structure, a 1×8 array with half-wavelength inter-element spacing was designed and validated. Experimental results show that the array achieves a peak gain of 10.23 dBi and is capable of beam scanning within ±50°.

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

NUMERICAL ANALYSIS OF AN INNOVATIVE ENERGY DISSIPATION DEVICE

Application of systems for passive vibration control is an efficient way for seismic protection of structures. Systems for passive vibration control consist of seismic isolation devices and energy dissipation devices. Base isolation of structures is a concept where devices for passive vibration control are placed in foundations of buildings. Various energy dissipation devices have been developed and tested so far, while metallic dampers represent a significant class. Those devices dissipate energy through the yield of metal material which they are made of. The metallic dampers have often been used because of their main advantages reflected in stable hysteretic behavior and well-known models for analytical prediction of the dissipated energy and structural response. Most of the metallic dampers have been developed for application in the beam-column joints or in the bracing system. The innovative energy dissipation device named multi-gap multi-level multi-directional seismic energy absorber, intended for the application in the horizontal seismic dilatation in the system of base isolation, has been developed recently by the group of the authors among whom is one of the authors of this paper. The main parts of the absorber are vertical components with linearly changeable circular cross-section. Due to the lateral displacements of the isolated structure the vertical components bend and energy dissipation is provided by yielding of the steel material they are made of. According to the previous experimental and numerical study of the absorber’s vertical components, three-dimensional finite element model of the absorber has been developed and presented in this paper. The aim of the numerical analysis is to determine mechanical properties of the absorber based on the lateral force-displacement diagram. Furthermore, a simplified numerical model using one-dimensional beam finite elements has been proposed. The performance of the absorber has been determined using the available semi-analytical solution for elastoplastic deflection of non-prismatic cantilever beams previously developed by the first author as well. The obtained results have been compared and it has been concluded that all three modelling approaches provide reliable mechanical properties of the absorber necessary for dynamic analysis of structures in engineering practice.

Optimized analysis and reinforcement design model for RC/SCC box-section bridges using developed advanced design framework

In recent years, there has been a significant rise in the construction of reinforced concrete (RC) and steel-concrete composite (SCC) box-section bridges. However, design codes do not provide specific design methods for the RC plates of such bridges where the plates experience both intricate forces and moments. The current design approaches are primarily based on conventional one-dimensional beam element theory, which neglects the complex spatial force characteristics of the structural elements, potentially leading to unsafe design. Therefore, it is imperative to address this issue. To bridge this gap, a comprehensive analysis and reinforcement design procedure named as the developed advanced design framework (DADF) is proposed in this study. The spatial analysis of bridges was performed using a refined numerical model, called the spatial grid model (SGM), to consider the structural spatial effects with limited model scales. Subsequently, the internal force corresponding matrix (IFCM) was implemented through Python scripts to determine the most critical internal force combination for an RC plate element. Additionally, the three-layered sandwich model (T-LSM) was employed with limit analysis to automatically design reinforcement for all elements, serving as a practical tool for design. This research demonstrates that the implementation of the DADF can significantly reduce steel reinforcement in the RC plates of such bridges by up to 48 %, and 23 % in total, showcasing the efficiency of the developed framework. Overall, the findings emphasize that the proposed DADF offers a robust procedure for steel reinforcement design of RC/SCC box-section bridges.

Multi-segmented fifth-order polynomial–shaped shells under hydrostatic pressure

The design and construction of submerged complex shells for new applications in offshore structures are increasingly popular. Therefore, the purpose of this study is to present the analytical model and Lagrange multipliers associated with the constraint equation for large displacement analysis of a fifth-order polynomial–shaped shell under hydrostatic pressure for the first time. The shell geometry can be computed using differential geometry with a fifth-order polynomial. The energy functional of the fifth-order polynomial–shaped shell is derived based on the principle of virtual work and written in the appropriate form. The nonlinear static responses of the fifth-order polynomial–shaped shell under hydrostatic pressure can be calculated using the nonlinear finite element method via the fifth-order polynomial shape function. This study develops the model using one-dimensional beam elements divided along the shell radius. To avoid the slope of a meridian curve at the equatorial plane approaching infinity, the shell is divided into two regions defined by different surface parameters. At the junction of two adjacent regions, the continuity requirements are established as the constraint conditions using Lagrange multipliers. The numerical results from the proposed methods are demonstrated and discussed, along with the effects of varied seawater depth, thickness, and elastic modulus on the deformed configuration and principal curvature at the deformed state. The results show that the nonlinear displacement is higher than the linear one in the case of the hydrostatic pressure, whereas the case of the internal pressure has an opposite result. For principal curvatures at the apex, the principal curvatures increase as the seawater depth increases, whereas the principal curvatures decrease when the thickness and elastic modulus increase.

Inverse design and optimization of a one-dimensional metagrating beam deflector by smart pattern search

This work introduces a fast semi-analytical algorithm for the inverse design and optimization of a one-dimensional beam deflector metagrating, utilizing Smart Pattern Search (SPS), an enhanced pattern search algorithm from MATLAB’s Global Optimization Toolbox. This algorithm demonstrates a significantly shorter processing time compared to machine learning based approaches for the same metagrating structure setup, parameters, and electromagnetic solver while achieving highly competitive efficiencies. At a wavelength of 1100 nm with angles of 60° and 70°, SPS even outperforms these methods. The SPS algorithm needs no state-of-the-art computers and completes the process in less than 27 min, while for counterpart methods at least several hours are needed on an Intel Core i7-3632QM CPU at 2.2 GHz, with 8 GB of DDR3 RAM.

An X-band beam-scanning reflectarray antenna stimulated using a spoof surface plasmon polaritons based low profile endfire MIMO antenna

A single-layer, low-profile beam scanning reflectarray (RA) fed by a spoof surface plasmon polaritons (SSPPs) based endfire MIMO antenna is proposed in this manuscript. The RA is based on a variable elliptical-shaped unit cell designed at 10.4 GHz. The unit cell has a low insertion loss of 2.3 dB and a reflection phase of 315.2°in the working frequency band from 9.52–11.23 GHz. The SSPPs based endfire MIMO antenna is used to mitigate the aperture blockage, achieve high isolation between the feed elements, and accomplish the continuous one-dimensional (1-D) beam scanning of ± 8°from the broadside. The maximum realized gain of the proposed reflectarray in the broadside direction is 22.6 dBi with a 3-dB beamwidth of 5.7°. The minimal beam switching loss is in the other direction, and the realized gain is 22.4 dBi with a 3-dB beamwidth of 5.8°. The 3-dB gain bandwidth (GBW) of 9.7 % of the proposed RA benefits nano-satellite applications. The fabricated prototype measurements in an anechoic chamber environment verify the simulated results.

Design and Measurement of a Two-Dimensional Beam-Steerable Metasurface for Ka-Band Communication Systems

This study introduces a steerable metasurface reflector designed for the Ka-band, enabling one-dimensional and two-dimensional beam steering. The paper elaborates on the design considerations, manufacturing process, and experimental findings. The unit cell design incorporates a Varactor diode as the tuning element, facilitating a dynamic phase range exceeding 300° with minimal metasurface beam steering losses. Notably, the experimental results are in good agreement with the simulation outcomes. The advantages of employing this metasurface reflector include rapid beam steering, cost-effective production implementation, support for both one-dimensional and two-dimensional beam steering, low reflection loss, high-resolution beam steering, and continuous beam steering capabilities.

Review of Vibration Analysis and Structural Optimization Research for Rotating Blades

AbstractBlades are important parts of rotating machinery such as marine gas turbines and wind turbines, which are exposed to harsh environments during mechanical operations, including centrifugal loads, aerodynamic forces, or high temperatures. These demanding working conditions considerably influence the dynamic performance of blades. Therefore, because of the challenges posed by blades in complex working environments, in-depth research and optimization are necessary to ensure that blades can operate safely and efficiently, thus guaranteeing the reliability and performance of mechanical systems. Focusing on the vibration analysis of blades in rotating machinery, this paper conducts a comprehensive literature review on the research advancements in vibration modeling and structural optimization of blades under complex operational conditions. First, the paper outlines the development of several modeling theories for rotating blades, including one-dimensional beam theory, two-dimensional plate–shell theory, and three-dimensional solid theory. Second, the research progress in the vibrational analysis of blades under aerodynamic loads, thermal environments, and crack factors is separately discussed. Finally, the developments in rotating blade structural optimization are presented from material optimization and shape optimization perspectives. The methodology and theory of analyzing and optimizing blade vibration characteristics under multifactorial operating conditions are comprehensively outlined, aiming to assist future researchers in proposing more effective and practical approaches for the vibration analysis and optimization of blades.