Straight Beam Research Articles

Development of an equivalent model of a damping elastic ring considering elastic contact on bulges

The study introduces a model of an elastic ring that takes into account contact conditions on bulges. The model represents the elastic damping ring as a series of straight beams connected by hinges. The methodology proposed herein calculates the average weighted stiffness of sections of the ring containing bulges and a smooth elastic part, which is essential for determining the overall stiffness of the entire ring.

Geometrically engineered mass sensing CMOS-MEMS resonators for temperature compensation via folded anchors

We present, for the first time, a single-layer plate resonator with specific folded anchors capable of reducing the temperature coefficient of frequency (TCF) by two orders of magnitude compared to straight beams. Folded anchors provide differential strain through either compressive or tensile thermal stress depending on the anchor design and, in turn, allow for positive and negative temperature-induced frequency change components. With a nominal 2 MHz frequency, we experimentally report a frequency shift of 2500 ppm over a temperature span from 0ºC to 90ºC using an optimal anchor folding aspect ratio. The frequency-temperature curve exhibits a turnover point at 27ºC granting a unique opportunity to, in a future application, complement this passive strategy with an active micro-oven for negligible TCF. The proposed approach main advantage relies on its mechanical design-level implementation exploiting a geometrical engineering strategy than can be directly extended to other topologies. This technique reveals as particularly suited for ultra-sensitive mass sensing applications based on microelectromechanical systems (MEMS) resonators where single-layer resonators are optimal thanks to their minimum footprint, attaining minimum mass structures. Results demonstrate that adoption of the proposed folded anchors strategy decreases effectively the thermally induced frequency fluctuations within the system intrinsic noise level.

Perspectives on the generalized modeling of six beam theories: A unified dynamic stiffness matrix

High-precision, efficient and streamlined methods for the dynamic modeling and analyzing of engineering structures have consistently captured attention of designers and researchers. This paper addressed this increasing demand by presenting a generalized modeling and analyzing method. Specially, a unified model was proposed to integrate six beam theories into a single formula. Upon this model, a unified dynamic stiffness matrix was derived, serving as an elemental building block for formulating the transfer matrix, frequency-dependent mass and stiffness matrices as well as further integrating finite element method, dynamic stiffness matrix method and transfer matrix method. Through this transition, challenges associated with transcendental eigenvalue in dynamic stiffness matrix method and transfer matrix method was effectively resolved and the advantages of transfer matrix method in handling complex structure were maximized. Given the widespread utilization of curved beams in buildings, bridges, robotics and sensors, the proposed method was validated through comparative analysis with other methods, focusing on both curved and straight beams. Furthermore, this study delineated applicability scopes of different beam theories and provided the strategic approach for curved and straight beams. The feasibility of this strategy was demonstrated through an investigation involving a corrugated structure comprising both straight and curved beams.

Research on Computer Aided Deformation Control Strategy for Welding of Large Long Straight Beams

<p>Long straight string beams are often used as supporting structures in large equipment. Due to the large size of string beams, welding technology is generally used to complete their production. This article first constructs the finite element model and heat source model of the chord beam based on the structure of the long straight beam, and then obtains the distribution and evolution law of the temperature field, as well as the temperature rise law of the temperature field under dynamic simulation. Based on this law data, an improved BP neural network model is used to predict the deformation of the beam. In order to verify the authenticity of the prediction results, the article finally builds a Matlab simulation experimental environment and conducts simulation experiments on the welding deformation prediction of the beam.</p> <p> </p>

Design and fabrication of a novel all-quartz resonant pressure sensor with continuously variable section of DETF

This paper reports a novel piezoelectric quartz crystal pressure sensor with a double-ended tuning fork (DETF) resonator. The key design is the resonator beams with a continuously variable section shape. Different from the traditional DETF with straight beams or the one with variable sections with steps, this design can improve sensitivity effectively. Theoretical analysis indicates that the sensitivity will increase with a decrease in beam width. Resonant pressure sensors with three different DETFs are designed and analyzed by finite element analysis software. Simulation results show that the sensitivity of this design is 162.27 Hz/MPa. This sensor has a typical structure, which includes three parts: the diaphragm, DETF resonator, and back-cavity structure. Quartz MEMS processes have been used in fabrication. The three parts are bonded together by vacuum glass frit sealing process. Test results of this sensor show that the natural frequency is 44.709 kHz with a quality factor of 12 717. The sensitivity is 155.6 Hz/MPa in the pressure range of 0–20 MPa. The results indicate that this novel design has advantages in sensitivity and fabrication processes. It will be a benefit for a high-performance and low-cost pressure measurement.

Exploring Tunable Torsional Mechanical Properties of 3D‐Printed Tubular Metamaterials

Additive manufacturing has proven to be a reliable and quick method for creating devices and tools. One example is 3D‐printed nasal swabs that require robust mechanical strength while maintaining adequate flexibility. However, there is a lack of detailed understanding on the mechanical response of tubular structures under torsion loading. The goal of this work is to understand the torsional behavior of a group of 3D‐printed tubular metamaterials. The idea of mechanical metamaterials is used and it is started with a rectangular lattice. Two main design methods are used: reinforced lattices and compliant lattices. First, diagonal reinforced beams are added to enhance the torsional rigidity. Furthermore, pre‐buckling is added to the straight beam, creating a flexible structure that increases the maximum torsional resistance. The experiments demonstrate that the sponge‐inspired design exhibits enhanced stiffness approximately 21 times that of baseline tubular designs. Moreover, the strength and toughness of the sponge‐inspired design are approximately 2.5 and 3 times higher. By curving the beam, compliant tubulars are created. The torsional angle is increased by at least 2.7 times, while the torsional toughness can reach up to 17 times. Using these two design strategies helps in creating tubular metamaterials with varied applications.

Short-term behavior of glass fiber-polymer composite bending-active elastica beam under service load application

Bending-active elastica beam is a structural configuration that is based on the elastic deformation of an initially straight beam. This deformation occurs when horizontal displacements are applied to a sliding support, causing the beam to bend into an arched shape. Previous research has focused on the stability of small-scale bending-active structures, thus not considering material strength, which is crucial in real-scale applications and structural design. This paper investigates the short-term structural behavior of bending-active elastica beams using pultruded glass fiber-polymer composite profiles, as used in real-scale structures. A series of short-term bending and service load application experiments were performed considering different bending degrees and loading scenarios. These results were used to validate finite element modeling. They demonstrated that steeper bent beams experience material failure, while shallower ones exhibit snap-through buckling. Material failure initiates on the tensile side of the beams, with cracks initiating at locations of maximum curvature. Higher bending degrees and symmetric loading result in higher maximum loads than lower bending degrees and asymmetric loading. A strain-based failure criterion, which can serve for structural design, is derived.

Enabling the transfer matrix method to model serial–parallel compliant mechanisms including curved flexure beams

AbstractCompliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces, low stress levels, and flexible design parameters, which have attracted considerable attention in precision engineering, metamaterials, robotics, and so forth. However, serial–parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design. Here, the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial–parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods. Consequently, serial–parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step‐by‐step procedure. Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach. In conclusion, the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial–parallel compliant mechanisms and beam structures, including curved flexure hinges and irregular‐shaped rigid bodies.

Bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness

In this paper, the boundary-based finite element method (BFEM) is developed for the bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness. The curved beams are discretized into a series of uniform straight segments. Based upon the first order shear deformation theory and the reciprocal theorem of Betti and Rayleigh, the boundary integral equations (BIEs) associated with each beam segment are derived and expressed in explicit form. The fundamental solutions required in the BIEs are obtained explicitly from the associated Green’s function. Since no singular integrals, numerical integrations and function interpolations are involved in the BIEs, our proposed BFEM provides an exact solution for a straight beam with uniform thickness, and only one single element with two end nodes is required for our analysis. Even only an approximate solution is provided for a curved beam with non-uniform thickness, BFEM converges faster than the conventional finite element method, and the results are in well agreement with those obtained by the commercial finite element software. Through the illustrated numerical examples, its generality is shown by: (1) stacking sequence of laminates: symmetric or unsymmetric; (2) beam geometries: straight, stepped, or curvilinear with uniform or non-uniform thickness; (3) loading types: axial force, transverse force and/or bending moment; distributed or concentrated; and (4) supporting conditions: clamped, simply supported, or free; with or without internal supports.

Effect of size factor and tapered angles on the shear behavior and strength of haunched beams reinforced with basalt fiber reinforced polymer rebars: Experimental and analytical study

Haunched beams are beams that exhibit varying effective depth over their span. This study includes an experimental and analytical analysis aimed at investigating the influence of size factor on the shear behavior of tapered beams reinforced with basalt fiber reinforced polymer BFRP bars. The main focus of this study revolves around investigating the effects of both inclination angle and size factor as key variables. In this study, a total of eight simply supported beams were tested. The beams were longitudinally reinforced with a 1% ratio of BFRP reinforcement, and separated into two equal groups. Each group consisted of one straight beam and three haunched beams. The haunched beams had varied tapering angles, namely 4⁰, 7.96⁰, and 11.86⁰. The first group is designated for the allocation of large beams, while the second group is designated for the allocation of small beams, which have a cross-section that is one-fourth the size of the large beams. The test results indicate that an increase in tapered angles leads to an increase in shear strength. Additionally, it was observed that smaller beams exhibited a greater normalized shear strength compared to larger beams with a significant rate as compared with straight beams. Subsequently, two equations were developed using the tested data, whereby one of them represents an optimal equation including a logical safety margin, while the other equation is characterized by a conservative equation, providing a substantial safety margin for predictions.

Modeling and design of a SMA self-actuating bistable beam

Bistable beams with implanted actuators show the self-actuating ability that further improve performance of the system. In this paper, a novel self-actuating bistable mechanism coupled by elastic straight beam and SMA curved beam was designed and tested. Snap-back behavior of the presented system was triggered by SMA curved beam actuator, which generated actuation moment and rotation angle at the end of flexible beam. The bistable mechanism was modeled through nonlinear governing equation of large deflection beam. A solution strategy that considered multiple inflection points was developed to solve the governing equation. Loading path, deflection curves, and energy landscape of bistable beam were illustrated and further analyzed. Moreover, parameters of SMA curved beam actuator were determined by a simplified model. A prototype of the self-actuating bistable beam was fabricated and the snap-back phenomenon was observed on the test bench. Accompanied by the snap-back, a 44% decrease of axial load could be reached. It was also found that the bistable beam could be reset by applying vertical concentrated force. Reciprocating snap-back tests were conducted to confirm that point. Possible applications of the presented bistable beam could be variable load mechanisms and novel flexible switches.

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators.

Synchronization in microstructures is a widely explored domain due to its diverse dynamic traits and promising practical applications. Within synchronization analysis, the synchronization bandwidth serves as a pivotal metric. While current research predominantly focuses on symmetric evaluations of synchronization bandwidth, the investigation into potential asymmetries within nonlinear oscillators remains unexplored, carrying implications for sensor application performance. This paper conducts a comprehensive exploration employing straight and arch beams capable of demonstrating linear, hardening, and softening characteristics to thoroughly scrutinize potential asymmetry within the synchronization region. Through the introduction of weak harmonic forces to induce synchronization within the oscillator, we observe distinct asymmetry within its synchronization range. Additionally, we present a robust theoretical model capable of fully capturing the linear, hardening, and softening traits of resonators synchronized to external perturbation. Further investigation into the effects of feedback strength and phase delay on synchronization region asymmetry, conducted through analytical and experimental approaches, reveals a consistent alignment between theoretical predictions and experimental outcomes. These findings hold promise in providing crucial technical insights to enhance resonator performance and broaden the application landscape of MEMS (Micro-Electro-Mechanical Systems) technology.

A Novel Straight Beam Element for Lateral-Distortional Deformation Analysis of Frames and Curved Beams Made of Monosymmetric I-Sections

Conventional beam elements ignoring distortion may overestimate the lateral resistance of frames and curved beams made of monosymmetric I-sections. This paper introduces two new distortional modes represented by mechanical couples relative to twisting and shearing of the two flanges that are opposite in directions but unequal in magnitudes. A straight beam element with nine degrees of freedom (DOFs) per node, including the conventional three translations, three rotations, warping and the new two distortions, is newly derived. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping–distortion compatibility problem that occurs in frames and curved beams is resolved. In the numerical examples, the results produced by the present beam element is demonstrated to agree excellently with the shell-element solutions for the lateral-distortional deformation of the angled frame and curved beam. It is observed that the cross-sectional distortion effect becomes extremely significant for angled frames of short unbraced length and for curved beams of high curvature.

A conical spiral piezoelectric energy harvester with parallel beams for all-directional flow energy harvesting

Piezoelectric energy harvesting technology using flow-induced vibration is a type of interference-resistant and miniaturizable power generation technology, which is promising on powering the wireless micro electromechanical system in flow filed. However, the flow direction of the natural flow field is changeable while most existing flow-induced piezoelectric energy harvesters (PEHs) are limited by their working direction. In this paper, we propose a conical spiral piezoelectric energy harvester with parallel beams (CSPEH-PB) that can collect energy under flow excitation in all directions. Based on the multi-dimensional vibration analysis of conical spiral structure, we investigate the resonance mode and effective flow velocity range of the CSPEH-PB through numerical analysis. In comparative experiments with a bimorph flat PEH, we verify the effective flow velocity range and voltage of the CSPEH-PB and polyvinylidene fluoride (PVDF) films attached. The results demonstrate that the CSPEH-PB generates an effective voltage greater than 0.53 V through the PVDF films under any direction of the water flow, and has a wider resonance bandwidth than PEH with straight beam. This study provides a practical solution for adapting PEHs to changeable flow direction.

Structural Behavior of a Fixed-End Arched Cellular Steel Beam without Lateral Support

The arched cellular beam has the advantages of both the solid-web arch and the straight beam with web opening, and has become increasingly admired by architects in recent years. In this paper, four arched cellular beam specimens are designed using an orthogonal test method (OTM) with a three-factor and two-level approach. Firstly, the static loading test is carried out to analyze the mechanical response of the arched cellular beam under concentrated load. Then, a numerical analysis based on ABAQUS finite element (FE) software is carried out. The results show that the simulation results agree well with the test results, which indicates the accuracy of the simulation analysis method. Finally, the buckling load of the arched cellular beam under three different loads is calculated using the variable parameter FE analysis. Combined with the range analysis in the OTM, the influence of the target factor on the buckling load of the arched cellular beam is determined. The results show that the order of the factors affecting the out-of-plane elastic buckling is rise–span ratio > web height–thickness ratio > diameter–depth ratio.

Microphone array based on tangent line method.

The tangent line method (TLM) was originally proposed for loudspeaker arrays to generate curvilinear acoustic beams. In this study, the TLM was applied to a microphone array. Based on reciprocity, the TLM-based microphone array can be used to form curvilinear beams. A curvilinear beam is produced as an envelope for the tangent lines. Tangent lines, which are straight beams with different angles, are generated by applying a delay-and-sum (DAS) beamformer. Because the envelope length is specified, the distance discrimination in the sensitivity is better using the TLM than the DAS beamformer. Case studies have indicated that directivity is better in the former TLM than in the latter. The TLM is realizable with fixed delay times for each microphone unless the formation of curvilinear trajectory is altered according to reproduction frequencies. Hence, the same simplicity of implementing the DAS beamformer can be achieved by optimizing the curvilinear trajectory based average frequency. Optimization is conducted such that the acoustic contrast between the focal point and elsewhere is maximized. In summary, the frequency-averaged optimal TLM can be a fixed beamformer with better performance than and the same simplicity as the DAS beamformer.

Emittance Growth Study of an Electron Beam in a Double-Alpha Magnet Compressor Used in an Inverse Compton Scattering X-Ray Source

An Inverse Compton Scattering (ICS) X-ray source is under development at the ELSA (Electrons Laser X-Sources and Applications) electron RF linac of CEA DAM (Commissariat à l’Energie Atomique et aux Energies Alternatives, Direction des Applications Militaires). X-rays are emitted by the interaction of 30 MeV electron bunches with Nd:YAG laser pulses. The electron bunches duration is 30 ps rms before compression in two alpha magnets. In such a system, electron trajectories are curved with a short radius, resulting in a noticeable degradation of the beam emittance. In the specific case of strongly curved trajectories, the straight trajectory and beam shape assumptions used for space charge calculation in most simulation codes are questionable. Two different approaches to the simulation of electron beam dynamics within the alpha magnets are compared. A specific method to deal with changes from the reference particle frame to the laboratory reference frame, which does not imply any trajectory and beam shape assumptions, is proposed. Calculation results are presented. Along with an important emittance growth, they show that more physical effects can be taken into account in the latter simulation.

C-Shells: Deployable Gridshells with Curved Beams

We introduce a computational pipeline for simulating and designing C-shells , a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape. We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy. We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.

Study on the Influence Factors on Harvesting Capacity of a Piezoelectric Vibration Energy Harvesting System Covered on Curved Beam with Acoustic Black Hole

The acoustic black hole (ABH) structures have been shown to have great potential for energy harvesting. Within an ABH, the bending wave velocity decreases rapidly and the phase accumulates, resulting in localised energy accumulation. It is very significant that the energy can be harvested and power can be supplied for microelectronic devices. How to improve energy harvesting capacity is a problem that needs to be solved. Previous research on energy harvesting capacity of straight beams and flat plates with ABH has yielded a wealth of results. However, in practical engineering, curved beams are also commonly found. Given the differences in structure, it is of practical significance to study the influence factors on harvesting capacity of the piezoelectric vibration energy harvesting system covered on curved beam with acoustic black hole. First, the vibration characteristics of curved beam with ABH are analysed by the finite element method and localised energy accumulation is observed. Then, energy harvesting capacity is studied by means of the electromechanical coupling model in FEA; it has been found that energy harvesting capacity is lower in high frequency. The reason of this problem is analysed and solved by dividing the size of the piezoelectric sheet in an array layout. Based on this, the influence of array layout of piezoelectric cells on the energy harvesting capacity of the system is focused on. In addition, the influence of resistance value, material property, and curvature of curved beam on the energy harvesting capacity is analysed. Some meaningful results are obtained. These results provide the guidance to the design and optimisation for an energy harvesting system covered on curved beam with ABH.

Explicit analytical solutions for the full plane-stress field in sandwich beams under flexure governed by zigzag warping

We provide analytical solutions for the full stress field of straight sandwich beams with identical skins subject to linear elastic flexure governed by zigzag warping, where all layers obey Timoshenko’s kinematics. As a main novelty, we make use of an equilibrium equation for the Cauchy continuum to recover of the through-the-thickness normal stress component, σy. The new estimates are accurate for a wide range of relative stiffness between skins and core and suitable boundary conditions, as it can be demonstrated through the comparison with detailed finite element simulations where the sandwich is modelled as a two-dimensional continuum. As a main practical result concerned with the study of delamination, we find that at a core–skin interface of a cantilever sandwich subjected to a uniformly distributed load, in a region close to the fully-clamped cross-section, σy is a tensile stress of magnitude larger than that of the shear stress. On this basis, we infer that the availability of good estimates for σy, along with those for the longitudinal and shear stresses, may be important for the accurate design of sandwich panels.