Flexible Beam Research Articles

Model Reduction of a Continuous System with Friction-Induced Vibration Considering Separation and Re-Contact

The friction-induced vibration of a continuous system consisting of two flexible beams in sliding contact to represent a brake system is studied in this paper. Besides the motion of relative sliding when the two beams are in contact, the separation of beams may also happen in the system dynamics. The complex eigenvalue analysis for the stability of the steady sliding state and the transient dynamic analysis for the characteristics (intensity and periodicity) of the steady-state responses of the system are carried out. Moreover, the results obtained using different numbers of beam modes are acquired and compared. It is found that only a few low-order beam modes need to be incorporated to get accurate results of the stability of the steady sliding state and the steady-state responses of the continuous frictional system, which therefore theoretically justify the omission of high-order modes of continuous structures when investigating the friction-induced vibration of continuous systems and thereby greatly reduce the computational cost. Additionally, the inclusion of the separation and re-contact behavior has a significant effect on the number of required modes for accurate steady-state responses compared with that when no separation is considered, which also verifies the important role of the separation and re-contact behavior in the system dynamics. Besides, a reduced dynamic model that can produce identical dynamic behaviors to those of the continuous frictional system is constructed, with the structural parameters of the reduced model derived from the several key low-order modes of beams.

Dynamics modeling and simulation of steel cord conveyor belt based on dynamic elastic modulus

Steel cord conveyor belts are widely used in long-distance transportation of various materials. The steel cord belt is composed of rubber and steel cord core, exhibiting excellent viscoelasticity and complex dynamic characteristics during operation. The existing static elastic modulus cannot accurately reflect the real dynamic properties of the conveyor belt. In this paper, based on the catenary theory, the formula for the dynamic elastic modulus of the conveyor belt is derived by introducing the sag and elastic deformation of the steel cord conveyor belt on the basis of the static elastic modulus. The dynamic modeling of the steel cord conveyor belt is carried out using rigid belt block element + flexible beam method. Then, the RecurDyn software is used to establish the dynamic simulation system of the belt conveyor and conduct simulations, which are validated through a test bench. The results show that dynamics simulation based on the dynamic elastic modulus is closer to the real dynamic characteristics of the belt conveyor. Finally, the dynamic characteristics of belt conveyors under different start-up times, different start-up speeds, and idler spacing are analyzed using this modeling and simulation method. The results demonstrate that the dynamic elastic modulus can accurately reflect the real dynamic properties of the conveyor belt, providing a more accurate dynamic modeling and simulation method for the design of belt conveyors.

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.

Flexible manipulation terahertz beam based on an all-dielectric metasurface by utilizing addition and convolution algorithms.

The flexibly manipulated terahertz wave is currently a hot research topic. To address this challenge, we proposed an all-dielectric coding metasurface for shaping the terahertz wave including beam splitting, beam deflection, vortex beam generators, and a vortex beam and multi-beam splitting combination by combining addition with the convolution theorem. This work represents what we believe to be a new method of combining terahertz wave regulation with digital signal processing and opens up the versatile design ideas of multifunctional metadevices.

4D printing of customizable and reconfigurable mechanical metamaterials

Customizable and reconfigurable mechanical behavior is critical for self-adaptive low-frequency vibration isolators operating in dynamic environments. Herein, the mechanical metamaterials with customizable and configurable geometries, material stiffnesses, cushioning properties, and vibration isolation capabilities are fabricated using a 4D printed multi-material system. The metastructure is characterized by the connection of a flexural beam structure and a collapsible straw structure. At the unit level, the stiffness characteristics are analyzed by geometric and theoretical mechanical models. The effect of geometric parameters and material composition on the stiffness behavior of multi-material metamaterials is investigated. Metamaterials' customizable and configurable characteristics are examined by the quasi-static compression mechanical properties, cushion performances, and vibration isolation capabilities under varying geometric parameters and material compositions. Finally, the reprogrammable stiffness of the metamaterial is demonstrated through the modification of geometric parameters utilizing the shape memory properties in 4D printing. The customizable and configurable metamaterials inspire the next generation of cushioning and vibration isolators, holding significant promise for applications demanding superior vibration isolation performances in dynamic environments.

Stacked multi-wedge acoustic black holes for low-frequency attenuation of flexible beams

Machines and other driving components like compressors or fans usually generate vibrations which frequently lead to acoustic noise. Flexible structures equipped with acoustic black holes minimise acoustic radiation by confining structural vibrations locally. One main restriction of its usage in the broad engineering field is its limited effectiveness at low frequencies. Recent investigations shifted the frequency range of attenuation successfully down to 1500 Hz. Moving the existing designs towards an even lower frequency demands a large structure. However, in general, sufficient space is often not available in machines and facilities. We propose a new design that enables a geometrically compact and simultaneously broadband vibration attenuation in the low-frequency below to 100 Hz: stacked wedges. The proposed design is calculated and optimised numerically by combining CAD and finite element calculations. The influence of geometrical parameters on the effectiveness of vibration attenuation is analysed with the help of transfer functions and dispersion curves. Successful designs of multi-stacked wedges at different lengths confirm their effectiveness at low frequency.Graphical abstract

Corotational isogeometric shear deformable geometrically exact spatial form beam element for general large deformation analysis of flexible thin-walled beam structures

In this paper, a new 3D generic order corotational geometrically exact beam element undergoing arbitrarily large deformations is presented. The novelty of the formulation lies in the use of the standard corotational framework, that is the decomposition into rigid body motion and pure deformation, to derive not only the objective, path-independent and singularity-free spatial exact strain measure but also the internal force and the consistent tangent stiffness matrix. The new formulation is derived by firstly conducting the consistent linearization of the weak formulation for the equilibrium equations of Reissner–Simo theory in the spatial form. By constructing a co-rotated frame that continuously rotates and translates with the element, the nodal strain-producing deformations can be extracted with the rigid-body translations and rotations removed from the element total motion. Subsequently, the corotational deformation variables are exploited to establish the distribution of deformation field within the beam element through B-spline basis functions, and derive the invariant and path independent exact strain measure in the spatial form by Lie derivative formalism. Through performing the variational operations of the compact transformation between corotational and global variables, the consistent tangent stiffness matrix are derived in closed form of the discrete variables for deformation field of any order. The proposed formulation is applicable to not only low-order two-node geometrically exact elements but also high-order multi-node straight or curved ones. The accuracy and robustness of the new formulation are demonstrated through the solutions of various benchmark problems.

Application of Composite Bars in Wooden, Full-Scale, Innovative Engineering Products-Experimental and Numerical Study.

The commercialization of modular timber products as cost-effective and lightweight components has resulted in innovative engineering products, e.g., glued laminated timber, laminated veneer lumber, I-beams, cross-laminated timber and solid timber joined with wedge joints. With the passage of time, timber structures can deteriorate, or new structural elements are required to increase the stiffness or load-bearing capacity in newly built structures, e.g., lintels over large-scale glazing or garages, or to reduce cross-sectional dimensions or save costly timber material while still achieving low weight. It is in such cases that repair or correct reinforcement is required. In this experimental and numerical study, the static performance of flexural timber beams reinforced with prestressed basalt BFRP, glass GFRP and hybrid glass-basalt fiber bars is shown. The experimental tests resulted in an increase in the load-carrying capacity of BFRP (44%), GFRP (33%) and hybrid bars (43%) and an increase in the stiffness of BFRP (28%), GFRP (24%) and hybrid bars (25%). In addition to this, glued laminated timber beams reinforced with prestressed basalt rods subjected to biological degradation, 7 years of weathering and prolonged exposure to various environmental conditions were examined, and an increase in the load-bearing capacity of 27% and an increase in stiffness of 28% were obtained. In addition, full-size laminated timber beams reinforced with prestressed basalt bars were investigated in the field as an exploratory test under fire conditions at elevated temperatures, and the effect of the physical-mechanical properties during the fire was examined via an analysis of these properties after the fire. In addition, a satisfactory correlation of the numerical simulations with the experimental studies was obtained. The differences were between 1.1% and 5.5%. The concordance was due to the fact that, in this study, the Young, Poisson and shear moduli were determined for all quality classes of sawn timber. Only a significant difference resulted in the numerical analysis for the beams exposed to fire under fire conditions. The experimental, theoretical and numerical analyses in this research were exploratory and will be expanded as directions for future research.

The collapse behavior of cold-formed steel composite beam structure

The innovation of cold-formed steel increases along with the development of sustainable development principles that prioritize eco-friendly, practical, and economical materials. This material, being recyclable, practical, lightweight, and durable, also has the disadvantage of a thin profile thickness, so that it is prone to buckling. In this study, an experimental study was conducted related to cold-formed steel composite beams with concrete material that also contained cavities to reduce the weight of the beams. The specimens are concrete and have a double canal profile of C80.30.9 with a profile thickness of 0.75mm. The connections are made using SDS 12x20 screw connections with a spacing of 150, 200, and 300 mm. The beam span is subjected to concentrated load until the structure collapses. From this research, it was found that collapse from the flexural beam is caused by cracks due to bending moments or bending collapse. The depth of the crack that occurs beyond the cold-formed steel inside the concrete.

Crosswind impacts on comfort of straddle monorail vehicle running on flexible track beam

Crosswind impacts on comfort of straddle monorail vehicle running on flexible track beam

Frequency Selection in a MEMS Flexural Beam Resonator by Electrostatic Actuation

Frequency Selection in a MEMS Flexural Beam Resonator by Electrostatic Actuation

New optical quantum hyperbolic recursional ferromagnetic microscale

In this paper, we construct properties of quasi recursional normal electromagnetic flexible elastic quasi microscale beams in terms of quasi normalized operator. We give new characterizations for ferromagnetic electric normalized quasi optimistic density with quasi frame. Finally, we design optical applications for recursional electromagnetic flexible elastic quasi microscale beam with optical quasi resonator.

Heat Transfer Enhancement of a Mini Channel Heatsink by Utilizing Flexible Beams Placed Downstream of a Cylindrical Obstacle

Several studies have demonstrated that flexible vortex generators exhibit higher hydrothermal efficiency than their rigid counterparts. The present study focuses on the implementation of a cylindrical rigid obstacle located in the vicinity of the inlet of a mini channel. Downstream, several flexible beams are attached to the channel walls, oscillating due to the forces exerted by the Von-Karmann vortex street generated by the cylinder. The Reynolds number is sufficiently low to maintain a laminar regime throughout the mini channel. A parametric analysis is conducted to explore the performance of various configurations of flexible beams with differing numbers, heights, and inter-distances. The hydrodynamic, thermal, and hydrothermal performance of the mini channel is evaluated using the time average friction factor, Nusselt number, and thermal efficiency factor. Results indicate that the presence of flexible beams significantly enhances heat transfer. The best configuration increases the overall thermal efficiency by 45%, while elevating the heat transfer and mechanical loss by 3.05 and 8.52 times, respectively, in comparison with an empty mini channel.

Wideband directional-fed holographic metasurface with integrated monopole and parabolic reflector for far-/near-field beams manipulations

Holographic metasurface has been widely investigated, but suffers from the trade-off between bandwidth, gain, and integration. In this article, a wideband high-gain holographic metasurface with miniaturized integrated monopole is proposed. It employs the geometrical characteristics of parabolic reflector to realize directional-fed metasurface, and the footprint is reduced to only one-third of the conventional center-fed designs. By varying modulation index and paraboloid height, the bandwidth and gain are improved simultaneously. To validate the proposed idea, two prototypes are analyzed and fabricated to demonstrate flexible beam manipulation in respective far-field radiation and near-field propagation. Pencil beam pays more attention to the far-field and directionality of the beam, while Bessel beam focuses more on the near-field and non-diffractive of the beam. In both cases, the measured results are well-matched with the simulation. The proposed holographic metasurface for far-field applications features wide bandwidth, high gain, and planar integration simultaneously. Moreover, to the best of the authors’ knowledge, this is the first Bessel beam generator using directional-fed holographic metasurface with parabolic reflector.

Effects of carbon/glass nonwoven interleaving veils and their areal density on opening and shearing mode interlaminar fracture toughness of glass epoxy composites

The study explores the impact of Carbon and Glass nonwoven interleaving veils with varying areal density on delamination resistance in unidirectional (UD) Glass epoxy composites under Opening (Mode-I) and Shearing (Mode-II) mode loadings. Commercially available non-woven Carbon and Glass interleaves with areal densities of 15, 20, 25, and 30 g/m2 were used to manufacture the interleaved Glass epoxy laminates. Double Cantilever Beam (DCB) and End Notch Flexural (ENF) specimens were used to determine the mode-I and mode-II fracture energies. The results reveal that, during mode-I initiation, interleaved laminates exhibit a lower interlaminar fracture toughness (IFT) except for the Carbon fiber interleaved laminates of areal density 30 g/m2. However, during propagation, all veils interleaved laminates presented significant improvement in IFT ranging from 5 to 25 % accompanied by substantial fiber bridging. In case of mode-II test, the laminates with Carbon and Glass veils exhibit enhanced IFT (60–182 %) with increasing areal density compared with the non-interleaved Glass laminates. Optical and scanning electron micrographs (SEM) provide evidence of fracture mechanisms involved in the interleaved and non-interleaved composite laminates.

Research on flexible beam-type nonlinear vibration isolators suitable for low frequencies

Ship vibration not only causes safety issues, but also easily generates noise pollution. Therefore, this paper introduces the quasi-zero stiffness (QZS) vibration isolator to solve the problem of low-frequency vibration. In terms of static analysis, this paper proposes a discretized beam constraint model (DBCM) to study the static properties of flexible beams with large deformation, and the finite element analysis (FEA) verifies the accuracy of DBCM. Regarding dynamic analysis, this paper combines the harmonic balance method (HBM) and the pseudo-arc length method (PALM) to analyze the dynamic response and explore the influence of excitation and damping ratio on the response stability. In addition, the performance of equivalent linear isolators is compared, revealing significant advantages of QZS isolator in terms of isolation bandwidth and peak transmissibility. The experimental data demonstrates that QZS isolator’s initial isolation frequency (2.14 Hz) is 68.5% lower than that of linear isolators (6.79 Hz), and the isolation efficiency at 5.35 Hz can reach 90%, making it suitable for low-frequency isolation. Furthermore, experimental data validate the accuracy of the theoretical model and FEA. The static and dynamic theoretical models can optimize the structural parameters of flexible beams and serve as valuable inspiration and reference for designing and improving isolator.

Synthesis and Networking of Spaceborne Deployable Prismatic Antenna Mechanisms Based on Graph Theory

Spaceborne deployable cylindrical antennas have broad application prospects in the fields of space earth observation and remote-sensing detection because of their significant advantages of ultralong aperture, high gain, and flexible beam scanning. As application requirements rapidly develop, a new type of spaceborne deployable cylindrical antenna mechanism with a large diameter and deployability is urgently needed. This paper presents an innovative design for a cylindrical deployable antenna mechanism based on 18R triangular prism elements based on graph theory. The correctness of the configuration is verified by developing a prototype. First, four kinds of nonoverconstrained 12-bar triangular prism-stabilized truss structure configurations and their corresponding topological diagrams are constructed. Second, based on graph theory, three types of 102 triangular prism-stabilized truss mechanism configurations that can be folded into linear mechanisms are derived. Third, the kinematic pair configuration is established to achieve a single-degree-of-freedom 7R2U9S triangular prism deployable unit. Fourth, combined with the geometric topology characteristics of the unit network, a triangular prism unit networking method is proposed, and a cylindrical network mechanism configuration based on 18R triangular prism units is obtained. A prototype was fabricated by 3D printing, and an expansion and retraction function test was conducted, which verified the correctness of the theoretical analysis in this paper. Finally, a new concept configuration for a parabolic cylindrical antenna is proposed. This paper provides a reference for the configuration of large-scale folding truss structures with unit expansion.

Inverse-designed flexural wave metamaterial beams with thermally induced tunability

Elastic metamaterials (EMMs) have been developed for more than two decades, but their practical applications have been scarcely reported due to their narrow bandgaps, relatively high working frequency ranges, poor load-bearing capabilities, and other implementation-related issues. As an attempt to solve some of these problems, in this work, a novel kind of tunable metamaterial beams is proposed to mitigate or isolate low-frequency and broadband flexural waves, where the integrated tunable elements made of a 3D-printed thermally sensitive material are inversely designed. The tunability is further achieved through the thermal-driving on the tunable elements. The optimized tunable elements are fabricated independently and have pretty good load-bearing capabilities under quasi-static uniaxial compression tests. They are directly glued on the host beams to form simple structured metamaterial beams without destruct the host beams. The experimentally measured transmission spectra under different thermal loadings demonstrate that the third pass-bands of the optimized three metamaterial beams at room temperature (RT) are changed to bandgaps or stop-bands as the temperature increases to about 60 °C, and vice versa. In addition, this temperature change induced bandgap is concatenated to the optimization obtained bandgap to form a wider bandgap. The good thermal reversibility is also validated by experimental tests under several thermal-loading cycles. Our present work suggests a dual-technique combined method to design low-frequency and broadband EMMs.

Vibration Training System Performance Test – Two Mass Absorber System Experiment

Two mass absorber is a vibration control system designed to enhance structural stability by strategically placing additional masses to effectively absorb and dampen vibrations. This technology mitigates resonance and harmful amplitude, reducing the risks of structural failure and operational inefficiencies in diverse engineering applications. Through this innovative approach, structures can withstand dynamic forces and operate efficiently in various fields. The TM 150 unit is used for conducting various experiments related to vibration phenomena. In this paper, experiments are carried out on a flexible beam that is oscillated using an unbalanced mass in the frequency range of 6 Hz to 18 Hz to see at which frequency the flexible beam will resonate. Another variation is to provide two mass absorbers under the flexible beam to see the difference. The experimental resonance graph was produced that was in accordance with the theoretical one, but with different amplitude units due to equipment limitations. The resulting graph shows before the absorber, the flexible beam resonates at its natural frequency. Afterward, small vibrations occur at that point, while resonance shifts. Furthermore, the performance of the vibration test unit is very good in showing the phenomena that occur in accordance with the theory.

Experimental and Analytical Investigation of FRP Reinforced Concrete Beams in Flexure

Experimental and Analytical Investigation of FRP Reinforced Concrete Beams in Flexure