Flexible Beam Research Articles

Analytical Analysis of Whole Loading Process of Ultra-High-Performance Fiber-Reinforced Concrete Beams in Flexure

Analytical Analysis of Whole Loading Process of Ultra-High-Performance Fiber-Reinforced Concrete Beams in Flexure

Investigation of flexural performance of concrete beams with nonwoven/polymer composites versus steel-rebar reinforcement

The research investigates the unique characteristics and benefits of using nonwoven fabrics and polymer I cross-section composites in concrete beams. These materials show improved strength, flexibility, and corrosion resistance compared to conventional steel-reinforced beams, offering promising solutions for various construction applications. This study constructed an I-beam structure using a nonwoven polyester fabric/polyester composite cast in a concrete beam. Other designs included woven carbon fabric or Kevlar nonwoven fabric applied to the bottom flange of the I-beam for reinforcement. The flexural behavior of an I-beam polyester nonwoven/polyester composite with Kevlar or carbon-reinforced concrete beams was examined. The comparison between the different samples indicates that: flexural strength: the carbon sheet-reinforced sample exhibits the highest flexural strength, followed by the steel rebar and Kevlar-reinforced samples. The ductility: The steel rebar-reinforced sample shows the highest ductility, indicating better deformation capacity before failure. Carbon sheet reinforcement also provides substantial ductility. Bending stiffness: The highest bending stiffness is observed in the Kevlar-reinforced sample, suggesting a stiffer and less flexible beam. These observations highlight the trade-offs between stiffness, strength, and ductility in reinforced concrete beams. The reinforcement material choice depends on the application-specific requirements, such as the need for higher bending strength, better flexibility, or greater stiffness.

Design and Sensing Theory for Flexible Multi-Layer Equal Strength Beam Force/Displacement Sensors With High Sensitivity

Design and Sensing Theory for Flexible Multi-Layer Equal Strength Beam Force/Displacement Sensors With High Sensitivity

Surrogate Modeling of a Lumped-Mass Multibody Structure Using Hamiltonian Neural Networks

The complexity of highly flexible structures restricts their use in real-time simulations. To address this challenge, we investigate the use of Hamiltonian neural networks (HNNs) as an alternative method for modeling a highly flexible cantilever beam. We derived the reference structural model using a lumped-mass rigid multibody method considering the Hamiltonian formalism and used it to generate a dataset consisting of generalized coordinates and momenta as inputs and their respective time derivatives as outputs. The trained neural networks are used as surrogate models to simulate the cantilever beam under free and forced conditions. Preliminary findings indicate that HNNs create accurate and efficient surrogate models whilst learning conservation laws. For forced-response simulations, our approach requires analytical calculation of external forces, offsetting the computational Efficiency gains of our surrogate models. The outcomes of this study give initial perspectives and limitations of the use of surrogate models based on HNNs as a means to efficient simulations of highly flexible structures.

Variational integrators for dynamics of a flexible beam undergoing large overall motion

Variational integrators for dynamics of a flexible beam undergoing large overall motion

Generating brick-like melt pools for Laser-Based Powder Bed Fusion using flexible beam shaping: a proof of concept on bead-on-plate single tracks

Despite the highest industrial maturity among additive manufacturing processes, laser-based powder bed fusion of metals (PBF-LB/M) lacks the productivity to further establish as an industrial manufacturing process. One approach for adjusting the melt pool shape to increase productivity in PBF-LB/M is spatial beam shaping. The freedom of beam shaping is almost unlimited, owing to modern optical concepts. The key is a beam shape optimized for a specific target. In this publication, the target is a brick-like melt pool cross-section. The publication demonstrates how the corresponding laser beam shape is designed using numerical optimization. The computed beam shape is reproduced using reflective spatial light phase modulators. The calculation is validated based on single-track experiments. Applying the optimized beam shape results in a melt pool shape similar to the optimization target. The width and depth of the melt track produced deviate by a maximum of 7 % from the specified target values.

Effect of Crumb Rubber Modified Bitumen in Hot Mix Asphalt Concrete

Improving bituminous material using recycling waste (Crumb rubber) as modifier was emphasized in this paper. Crumb rubber (CR) waste was added by volume to the bitumen in 0, 5, and 7 %. The volumetric properties tests were conducted using the Marshall Test (ASTM D1559), others includes Characterization of Binder and Aggregate materials in HMA, (FTIR Analysis), Fundamental mechanical properties tests, also Rheological properties according with ASTM D7369-11, Dynamic Modulus Test, according with AASHTO R83-17, Rutting Test according with AASHTO T324-04, Fatigue Cracking Evaluation according with AASHTO TP124 and Flexural Beam Fatigue Beam Test according with AASHTO T 321-07. The result indicates that crumb rubber is very suitable as a modifier, with bitumen of 60/70 PEN grade. From the results, at the designed production temperature 135oC for unmodified 60/70 Bitumen, the modified admixed samples (0% and 5% CR) at the same binder content show a high void percentage for mixes (5% CR). This is an indication that the modified asphalt mixtures exhibited volumetric properties with higher voids and lower density due to change in viscosity caused by modification and requires compaction at higher temperature to be at par with regular unmodified bitumen grade. However, the air voids of mixtures fall within the specification range of 3% to 5%, and as such acceptable for use as a modifier in 60/70 PEN grade bitumen.

Concept design of a monolithic compliant series-elastic actuator with integrated position and two-level force sensing

Safe physical interaction is significant for the protection of the operated target during delicate micromanipulation tasks. This paper proposes the concept design of a series-elastic actuator mainly constructed by a fully compliant mechanism. It can reduce the transient contact force when the tip touches an object and monitor the interaction force in real time for safe handling. The rear end of the actuator is a flexible linear guide connected with a voice coil motor to offer a bidirectional displacement. The actuator’s front end features a stiffness-switchable mechanism based on folding flexure beams, which provides two-level force buffering and sensing to accommodate varying degrees of contact status. Three strain gauges are integrated into the flexible beam of the mechanism, one of which is used for displacement sensing and the others for monitoring interactive force. After the structural design of the actuator, an analytical model is developed to assess its kinematic performance, which is further verified by finite-element simulation and experimental testing. The experimental results agree with the model and simulation, confirming the effectiveness and reliability of the actuator. The compliant actuator can be applied to some micromanipulation scenarios requiring precision positioning, contact, and interaction at the operating end.

Vision based control strategy to suppress residual vibration of flexible beams for robotic assembly using wrist motion

Automated assembly tasks require industrial robots to improve the efficiency of the manufacturing process. Most rigid or flexible objects handled by robots vibrate due to motion and transient disturbance. This work proposes an active vision-based vibration suppression strategy for flexible beams by providing motion to the wrist of a robot during robotic assembly process, which reduces the time to suppress vibration. The proposed method uses a cheap monocular camera to identify objects through a virtual marker and measure their dimensions. Subsequently, finite element method based mathematical model of a flexible beam predicts the maximum error. The proposed second stage controller determines the controller input in terms of wrist motion based on the predicted maximum error. The performance of the controller is assessed through simulations and experiments on metallic beams with different material characteristics and dimensions. The controller suppresses vibration amplitude within a safe limit so that object is inserted into the slot. It was observed from experiments that the controller can reduce vibration amplitude by ~96% in less than 2 s and decrease suppression time up to ~97%. These improvements were achieved without disturbing the internal robot controller.

Modulus of recycled hot mix asphalt: Micromechanical modeling and experimental approaches

To improve the availability of reclaimed asphalt pavement (RAP) in recycled hot mix asphalt (HMA), this study is focused on the mechanical performance of recycled HMA, which is beneficial for environmental conservation and consistent with the concept of sustainability. To alleviate the heterogeneity of the material composition of recycled HMA and enhance the usability and applicability of research means, micromechanical modeling is used to examine the modulus of recycled HMA, which is a critical parameter for asphalt pavement analysis. In this investigation, a four-layer built-in micromechanical model was constructed and derived to characterize recycled HMA. The micromechanical model indicated that the modulus of recycled asphalt was the main factor influencing the modulus of recycled HMA. Thus, the following study took the modulus of recycled asphalt as the main study subject. The frequency sweep test and three-point flexure beam test for recycled asphalt were designed and conducted to clarify the change trend of influence factors and further verify the reasonability and feasibility of the micromechanical model. Considering the diffusion behavior of the rejuvenator, the change trends of the factors are explored. The curing time apparently influences the modulus of recycled asphalt, followed by the curing temperature and the rejuvenator proportion. Finally, analytical results from micromechanical model matched well with the experimental results. The results of this study may be valuable for predicting the dynamic moduli of recycled HMA.

Dynamic analysis of novel bionic piezoelectric vibration energy harvester for power transformer

Inspired by the morphological transformation of spiders during motion, a novel bionic spider-type piezoelectric vibration energy harvester is proposed. By observing the movement of spiders in nature, we simulated their skeleton structure and constructed a model collection structure using three pairs of symmetrical flexible beams with rods corresponding to the pinholes. The displacement of the middle mass at the free end causes the substrate beam to bend and deform, thereby driving the piezoelectric element to generate voltage. The detailed descriptions of the design steps and principles is provided. We also developed a concentrated mass-spring model for theoretical analysis, which is verified through numerical simulation. We investigated the dynamics of the bionic piezoelectric energy harvester under swept frequency and harmonic excitation. The results demonstrated that the harvester experiences localized vibrations, including broadband high-frequency oscillations. We evaluated the energy harvesting performance of the harvester under different excitations in the frequency range of 108–115 Hz. At a frequency of 111 Hz and an acceleration of 1 g (=9.81 m/s2), the average power output is 0.63 mW. The maximum power output of 5.66 mW can be achieved at an excitation acceleration of 3 g and an operating condition of 111.5 Hz.

Improved interlayer performance of short carbon fiber reinforced composites with bio-inspired structured interfaces

The weak layer interfaces of 3D-printed short carbon fiber (SCF) reinforced polymer composites have remained an issue due to planar layer printing by traditional 3D printers. Recently, multi-axis 3D printing technology which can realize non-planar layer printing has been developed. This study’s aim was to evaluate and compare the bonding performance of non-planar interfaces produced by multi-axis 3D printing with that of planar interfaces. The tested non-planar interfaces were designed as bio-inspired structured interfaces (BISIs) based on microstructural interfacial elements in biological materials. The standard specimens with the 0°/90° and 0° infill line directions were printed by a robotic arm multi-axis 3D printer. Double cantilever beam (DCB) and end-notched flexure (ENF) tests were conducted to obtain Mode Ⅰ and Mode Ⅱ interlaminar toughness of SCF-reinforced composites. Test results showed that the critical energy release rates of the integrally formed BISI were significantly improved compared with the planar interface (PLAI) for both Mode I and Mode II delamination. In particular, the BISI with 0° infill line direction exhibited the greatest increase in critical energy release rate, and the damaged areas were spatially swept through the curved interfaces of the BISI with different infill line directions by scanning electron microscopy (SEM) and computed tomography (CT), which showed that the higher critical energy release rate was always accompanied with a larger damaged area. In addition, the tensile and flexural properties of 0°-infilled PLAI and BISI specimens were also measured. This work provides an in-depth investigation of the PLAI and BISI properties of SCF-reinforced composites, demonstrating the potential benefits of integrally formed BISI by multi-axis 3D printing and fostering new perspectives to enhance layer interfaces of 3D printed composites.

Dynamic Modeling of the Ball-on-Flexible Beam Using Euler–Lagrangian Formulation

Abstract Nonprehensile manipulation involves moving objects without physical grasping using methods such as rolling, sliding, pushing, and throwing. In the context of rolling manipulation, a novel nonconventional type manipulator, referred to as the ball-on-flexible beam system, is presented in this paper. A flexible beam with multiple linear actuating rods attached to the underside of it can be controlled to move an overlying ball using rolling manipulation. Since the absence of physical grasping in nonprehensile manipulation often requires taking into account the dynamics of the system, we focus on the derivation of the dynamic model of the ball-on-flexible beam in this paper. The dynamic model is derived using the Euler–Lagrangian formulation. In the calculation of the kinetic and potential energies of the beam and the ball, the deflection of the flexible beam is taken into account based on the Euler–Bernoulli beam theory. The accuracy of the derived model is verified through a finite element analysis (FEA) case study.

Nonlinear normal modes of highly flexible beam structures modelled under the SE(3) Lie group framework

This work presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled under the special Euclidean (SE) Lie group formulation. The formulation is combined with a pseudo-arclength continuation method, while special adaptations are made to ensure compatibility with the SE framework. Nonlinear normal modes (NNMs) of various two-dimensional structures including a doubly clamped beam, a shallow arch, and a cantilever beam are computed. Results are compared with a reference displacement-based FE model with von Kármán strains. Significant difference is observed in the dynamic response of the two models in test cases involving large degrees of beam displacements and rotation. Differences in the contribution of higher-order modes substantially affect the frequency-energy dependence and the nonlinear modal interactions observed between the models. It is shown that the SE model, owing to its exact representation of the beam kinematics, is better suited at adequately capturing complex nonlinear dynamics compared to the von Kármán model.

Vibration Suppression of a Flexible Beam Structure Coupled with Liquid Sloshing via ADP Control Based on FBG Strain Measurement

In this study, an adaptive dynamic programming (ADP) control strategy based on the strain measurement of a fiber Bragg grating (FGB) sensor array is proposed for the vibration suppression of a complicated flexible-sloshing coupled system, which usually exists in aerospace engineering, such as launch vehicles with a large amount of liquid propellant as well as a flexible beam structure. To simplify the flexible-sloshing coupled dynamics model, the equivalent spring-mass-damper (SMD) model of liquid sloshing is employed, and a finite-element method (FEM) dynamic model for the beam structure coupled with the liquid sloshing is mathematically established. Then, a strain-based vibration dynamic model is derived by employing a transformation matrix based on the relationship between displacement and strain of the beam structure. To facilitate the design of a strain-based control, a tracking differentiator is designed to provide the strains’ derivative signals as partial states’ estimations. Feeding the system with the strain measurements and their derivatives’ estimations, an ADP controller with an action-dependent heuristic dynamic programming structure is proposed to suppress the vibration of the flexible-sloshing coupled system, and the corresponding Lyapunov stability of the closed-loop system is theoretically guaranteed. Numerical results show the proposed method can effectively suppress coupled vibration depending on limited strain measurements irrespective of external disturbances.

Behavior of Smart Beams Reinforced with Superelastic Shape Memory Alloy Rebar (SMA)Subjected to Repeated Loading

A reinforced concrete beam with shape memory alloy rebar (SMA) is a novel form of smart beam used in smart seismic structural systems to reduce the effects of earthquakes while keeping nearly the same load-carrying capability as conventional concrete beams. The experimental research investigation is carried out to study beams' flexural behavior by replacing some steel rebars with shape memory alloy rebars (SMAs) in the longitudinal reinforcement zone. The experimental program included testing three beams to investigate the effects of the replacement of longitudinal steel rebar by shape memory alloy rebar on the flexure behaviour of beams. The beams were tested by the repeated load. The study was focused on determining ultimate load, maximum deflection, and load-deflection behaviour. Experimentally, the flexure behaviour beams are significantly affected by changing the number of reinforcing bars with shape memory alloys (SMA) longitudinal direction. However, for using one rebar of shape memory alloy as a longitudinal reinforcement, the replacement of one bar and two bars of shape memory alloy SMA beams have less yield load than the control beam by about (12.5%) and (37.5%) respectively. The replacement of one bar and two bars of shape memory alloy SMA beams having less ultimate load compared with reference beam by about (9.82%) and (21.94%) respectively. Because of its superelasticity quality, the introduction of superelastic SMA bars to the beam shows excellent recentering ability.

Coupled Dynamics of Droplet Impact on a Flexible, Hydrophilic Cantilever Beam.

We experimentally study the droplet impact on a flexible, hydrophilic cantilever beam. Droplets of water, water-glycerol (1:1 v/v), and glycerol were considered on a copper beam. Side visualization of the droplet impact on the cantilever was carried out by using a high-speed camera. We systematically vary cantilever stiffness to obtain a characteristic time scale of the beam dynamics, that is, shorter on the same order and longer than the characteristic time scale of droplet dynamics. Water droplet spreading reduces with an increase in the beam's flexibility, due to the "springboard effect". Results reveal that a threshold cantilever length exists beyond which the droplet vibration mode "locks-in" to the cantilever vibration mode. During lock-in, the bending energy of the beam increases with an increasing length or decreasing stiffness. The time-varying cantilever deflection exhibits an oscillatory, exponentially decaying response. However, in the case where both time scales are almost the same, we found a two-stage damping in the measurements: a fast, initial damping followed by a slower, damped response. We explain this damped response by the interplay of droplet and cantilever early dynamics. As expected, increasing the droplet viscosity dampens the magnitude of droplet spreading and displacement of the cantilever's tip due to a larger dissipation of kinetic energy in the bulk of the droplet. The decay is exponential in all cases, and the time taken to reduce the spreading and displacement is shorter with a larger viscosity. The damping coefficient is found to inversely scale with the cantilever length or mass. We corroborated the measurements with available analytical models, confirming the hypotheses used to explain the results. Overall, the present study provides fundamental insights into controlling the coupled dynamics of droplet and flexible substrates, with potential applications such as the design of efficient agricultural sprays and wings of microaerial vehicles.

Development of a Frequency-Adapted Virtual Fields Method as an alternative to the Corrected Force Analysis Technique for dynamic forces and structural parameter identification

In vibroacoustics, inverse methods use the vibratory response of a structure to identify either a load or a structural parameter. The Force Analysis Technique (FAT) and the Virtual Fields Method (VFM), are two inverse methods that have been used in the past to identify loads or structural parameters of flexural beams or plates. The Corrected Force Analysis Technique (CFAT) is another inverse method that corrects the singularity of FAT, making this approach more accurate at higher frequencies. In this study, this principle is applied to the VFM, using polynomial interpolation of the displacement field, in order to adapt the method so that at each frequency, the accuracy of the method is improved. The accuracy of the Frequency-Adapted VFM is demonstrated using numerical simulations. A formal comparison between FAT, CFAT and the VFM is also proposed.

Fault tolerant vibration control of constrained flexible beam systems with uncertain parameters and actuator failures

This work presents an adaptive fault-tolerant boundary control algorithm for a flexible beam system with actuator failures, external disturbances, and uncertain system parameters. Firstly, partial differential equations with boundary conditions are employed to model the system, and an adaptive compensation method is introduced to solve the issue that the overall number of faults can be infinite, encompassing complete and partial faults. By constructing the barrier Lyapunov function, a fault-tolerant boundary controller is designed to dampen beam vibrations and ensure that all states of flexible beam systems remain within the constraint domain. Simultaneously, the uniformly bounded stability of the flexible beam system is proved by Lyapunov's direct approach. Lastly, the validity of the presented algorithm is demonstrated through simulation results.

Boundary event-triggered FTC of uncertain Euler–Bernoulli beam systems with actuator failures

This work presents an event-triggered fault-tolerant boundary control approach for Euler–Bernoulli beam systems with actuator failures, uncertain system parameters, and external disturbances. Firstly, partial differential equations with boundary conditions are employed to model the system, and an adaptive compensation method is introduced to solve the issue of infinite times actuator faults, encompassing complete and partial faults. By using the relative threshold strategy, the event-triggered fault-tolerant boundary controller is developed to dampen vibration and reduce communication load between actuators and controllers. Simultaneously, the uniformly bounded stability and well-posedness of flexible beam systems are proved by Lyapunov's direct approach and semigroup theory, respectively. Lastly, the validity of the presented algorithm is demonstrated through simulation results.