Beam Displacement Research Articles

Nonlinear vibration and acoustic radiation of an internally resonant buckled beam

Although the nonlinear vibration of buckled beam has been thoroughly studied, its acoustic radiation does not get much attention. This paper deals with the nonlinear vibro-acoustic problem of an internally resonant buckled beam immersed in an infinite fluid. A finite element method based on an arbitrary Lagrangian-Eulerian framework is adopted to analyze the nonlinear interaction between the large-deformed buckled beam and the finite-amplitude acoustic waves in the fluid. The effects of acoustic pressure excitation, external harmonic excitation, and internal resonance on the vibro-acoustic responses of the buckled beam are discussed in the first and second primary resonances. It is found that the amplitude of the acoustic pressure can be comparable to the amplitude of the external harmonic force. This leads to an increase in the critical harmonic excitation amplitude for the occurrence of quasi-periodic responses and an increase in the second mode frequency component of quasi-periodic responses compared to the case neglecting the acoustic pressure excitation on the beam. Saturation phenomena are discovered in the second mode frequency components of beam displacement and acoustic pressure. Due to the 2:1 internal resonance, different time-frequency characteristics, quadrupole acoustic directivity patterns with low radiation efficiency, and dipole acoustic directivity patterns with high radiation efficiency can be observed at different harmonic excitation amplitudes and frequencies. Understanding these phenomena will help design loudspeakers and recognize sound sources.

Collaborative Methods of Resolving Road Graphic Conflicts Based on Cartographic Rules and Generalization Operations

The resolution of road graphic conflicts is a key aspect of map generalization, which involves both scale reduction and the symbolization of map features. This study proposes collaborative methods of road graphic conflict resolution considering different road characteristics. These methods consider both geometric and semantic characteristics, and they incorporate the bend characteristics of roads, the road symbol size, and road semantics. Constrained Delaunay triangulation skeleton lines are used to categorize road graphic conflicts, which are made up of four independent conflict types and four group conflict types. Based on their characteristics, three collaborative methods are designed to deal with the different types of road graphic conflicts: collaboration between deletion and the snake displacement model, collaboration between the snake displacement model and collinearity, and collaboration among simplification, smoothing, and the beam displacement model. Two types of independent conflicts can be processed using only one simple operation. This study summarizes the cartographic rules for resolving road graphic conflicts, and these are used along with geometric features to drive the collaborative methods or one simple operation presented here. The experimental results indicate that the method proposed in this study can effectively resolve road graphic conflicts.

A Machine Learning Model to Predict the Seismic Lifecycle Behavior of a Cross-Sea Cable-Stayed Bridge

Cross-sea cable-stayed bridges encounter challenges associated with cable corrosion and cable-force relaxation during their service life, which significantly affects their structural performance and seismic response. This study focuses on a cross-sea cable-stayed bridge located in Hainan Province. Utilizing an LSTM deep learning model, this study aims to fill in the gaps in short-term cable-monitoring data from the past year using the available cable-force-monitoring data from the same period. The authors of this study interpolated the cable-force data in the absence of sensors and employed a SARIMA machine learning time-series-prediction model to predict the future trends of all cable forces. A finite-element model was constructed, and a dynamic time-history analysis of the seismic response of the cross-sea cable-stayed bridge was conducted, considering the influence of cable-force relaxation and cable corrosion in the future. The findings indicate that the LSTM-SARIMA model predicted an average decrease of 11.81% in the cable force of the cable-stayed bridge after 20 years. During the lifecycle of the cables, cable corrosion exerts a significant impact on the variation in cable stress within the bridge structure during earthquakes, while cable-force relaxation has a more pronounced effect on the vertical displacement of the main beam of the bridge structure during seismic events. Compared to when using the traditional model that only considers cable corrosion, the maximum negative vertical displacement of the main beam increases by 29.7% when using the proposed model if the earthquake intensity is 0.35 g after 20 years, which indicates that the proposed machine learning model can exactly determine the seismic behavior of the lifecycle cross-sea cable-stayed bridge, considering the impacts of both cable-force relaxation and cable corrosion.

Enhancing low-orbit vibration energy harvesting by a tri-stable piezoelectric energy harvester with an innovative dynamic amplifier

Piezoelectric energy harvesting faces a primary challenge in effectively capturing low-orbit vibration energy across a broad frequency range. In this paper, we present a tri-stable piezoelectric energy harvester that incorporates a dynamic amplifier (TPEH + DM), specifically designed for efficient collection of low-orbit vibration energy. The TPEH + DM comprises a piezoelectric cantilever beam connected to an innovative dynamic amplifier at its restrained end, which enhances both the rotational and lateral displacement of the piezoelectric cantilever beam simultaneously. The governing coupled differential equations of motion for the system is derived based on the Lagrange equation, and analytical expressions for its steady-state response are obtained using the multi-scale method. The influence of factors such as the mass and the stiffness ratio of the dynamic amplifier on the steady-state dynamic output characteristics of the system is investigated using the theoretical analysis and numerical simulation. The results indicate that TPEH + DM exhibits significantly improved energy harvesting performance compared to TPEH under low-orbit external excitations. The bandwidth of inter-well motion and the TPEH + DM power output may be further increased by suitably modifying the relative stiffness between the cantilever beam and the dynamic amplifier. In addition, we analyze the time-domain behavior of the system’s output voltage using the ode45 solver under various external excitation frequencies and intensities. The results demonstrate that with appropriate adjustments to the mass of the tip magnet and the stiffness ratio of the dynamic amplifier, the proposed TPEH + DM system can harvest energy efficiently across a broad frequency range, even under low-orbit excitations.

Modeling and analysis of a macro-fiber piezoelectric bimorph energy harvester operating in d33-Mode using Timoshenko theory

Piezoelectric bimorph cantilevered beams are frequently employed in energy harvesting applications. The use of macro-fiber composites, which combine piezoelectric fibers with rectangular cross-sections and interdigitated electrodes, has significantly enhanced their performance by enabling operation in the 33-mode of piezoelectricity, thereby increasing conversion efficiency. In this article, the Timoshenko beam theory is applied to overcome the limitations of the Euler-Bernoulli theory in modeling transverse vibrations of harvesters with low slenderness ratios (length to thickness ratios). The mixture rule formulation is applied to determine the equivalent properties of the macro-fiber composite (MFC) structure. The electromechanical properties of a representative volume element (RVE) bounded by two successive interdigitated electrodes are coupled to the overall electro-elastic dynamic model of the structure using the Timoshenko theory. Frequency response functions for the power and tip vibration displacement of the MFC bimorph beam are determined from the model. Experimental data from the literature are used to validate the improved results predicted by the model developed in this article. A comparative analysis between the electromechanical responses predicted using a model based on Timoshenko and a model based on Euler-Bernoulli theory is conducted showing agreement, for harvesters with large slenderness ratios and discrepancies of up to 30% for low slenderness ratios. It has also been shown that the model based on Euler-Bernoulli theory overestimates both the mechanical and the electrical responses for low slenderness ratios as the shear and rotary inertia effects are not negligible in this case.

Optical shift spectroscopy in two-dimensional materials

Optical beam shifts, such as the Goos–Hänchen (GH) shift and the Imbert–Fedorov (IF) shift, are fundamental optical phenomena. However, because these shifts are so minute, direct measurement is challenging, and obtaining an optical shift spectrum is even more difficult. Here, we successfully obtained GH and IF shift spectra using a beam displacement amplification technique. The optical shift spectrum of graphene shows very good agreement with the predicted results. Meanwhile, we observed two distinct peaks in the optical shift spectrum of WS2, corresponding to the A- and B-exciton transitions at the K-point in the Brillouin zone. More importantly, when graphene is stacked on WS2 to form a van der Waals heterostructure, the A-exciton characteristic of WS2 increases by an order of magnitude, which is essentially different from absorption and fluorescence spectra. Furthermore, refractive index change can be precisely captured by GH shift spectroscopy, which proves the optical shift spectrum to be an ideal candidate for a highly sensitive biosensor. Optical shift spectroscopy could enable new applications for nanophotonic devices and provide a platform for the study of intrinsic properties of two-dimensional materials, especially for van der Waals heterostructure.

Performance evaluation of cable-stayed bridge expansion joints based on Lasso dimensionality reduction and temperature-displacement-correlation model

Expansion joints play a crucial role in accommodating the longitudinal movement of the main beam, which is mainly caused by temperature variation. This paper establishes an accurate model that relates the temperature field of the main beam to the displacement of the expansion joint, enabling reliable performance prediction and early warning of the expansion joint. Firstly, three commonly used methods for characterizing the temperature field of the main beam are introduced, along with their advantages and disadvantages. Secondly, a novel method is proposed using the Lasso algorithm to calculate critical temperatures. The objective is to select temperature channels data that have significant impact on the longitudinal displacement of the main beam. The selected channels data is then linearly weighted based on feature importance to obtain critical temperature. Based on this, a precise relationship model between the main beam temperature and the expansion joint displacement is derived through regression. For the residual term in the model fitting, an expansion joint performance early warning procedure is developed based on the X-bar control chart. Finally, using one-year long-term monitoring data from a newly constructed cable-stayed bridge as an example, the proposed method demonstrates superior capability in predicting the predefined damage of the expansion joint compared to the other two commonly used methods.

Compact, remote optical waveguide magnetic field sensing using double-pass Faraday rotation-induced optical attenuation

Compact, magnetic field, B sensing is proposed and demonstrated by combining the two Faraday rotation elements and beam displacement crystals within a micro-optical fiber circulator with a fiber reflector and ferromagnets to allow high contrast attenuation in an optical fiber arm. Low optical noise sensing is measured at λ=1550nm as a change in attenuation, α, of optical light propagating through the optical noise sensing rotators and back. The circulator’s double-pass configuration, using a gold mirror as a reflector, achieves a magnetic field sensitivity s=Δα/ΔB=(0.26±0.02)dB/mT with a resolution of ΔB=0.01mT, over a detection range B=0−89mT. The circulator as a platform provides direct connectivity to the Internet, allowing remote sensing to occur. The method described here is amenable to multisensor combinations, including with other sensor technologies, particularly in future integrated waveguide Faraday optical circuits and devices, extending its utility beyond point magnetic field sensing applications.

Flexural behavior of concrete beams hybrid-reinforced with glass fiber-reinforced polymer, carbon fiber-reinforced polymer, and steel rebars

The utilization of fiber-reinforced polymer (FRP) reinforcements in structural design is increasing due to their non-corrosive nature. However, the anisotropic features and linear elastic behavior of FRP rebars have led researchers to explore the use of hybrid combinations of FRP and steel reinforcements. Current codes and guidelines predominantly focus on the design of glass FRP (GFRP) reinforced structural elements, leaving a gap in incorporating the hybrid use of FRP-steel combinations and different types of FRP materials, such as carbon FRP (CFRP). This study conducted experimental investigations on concrete beams reinforced with GFRP, CFRP, and hybrid (GFRP-steel and CFRP-steel in combination) rebars, comparing the results with theoretical models. Ten full-scale beams were tested under monotonic loading. Test results revealed that existing codes overestimate GFRP reinforced beam displacements while underestimating CFRP reinforced beam displacements. A reduction factor is proposed for the effective moment of inertia expression given by ACI 440.11-22 to predict the deflections of CFRP reinforced and hybrid reinforced beams. The experimental data for CFRP and hybrid reinforced concrete beams align well with the predictions calculated using the proposed equations.

Fires Following Earthquake Fragility Functions for Protected Steel Braced Frames

The paper describes the outcomes of the analysis of a steel braced frame protected with spray-applied fire resistive material and subjected to fires following earthquake (FFE). Nonlinear time-history analyses were performed in order to evaluate the seismic response. Then, the post-earthquake fire ignitions within selected compartments were considered based on the damage suffered by the structure, which was estimated according to the inter-storey drift ratio and floor acceleration. Natural fire curves were determined by means of zone models. Thus, compartmentation and opening characteristics were included in the analysis. Finally, thermomechanical analyses were completed and failure criteria based on the column and beam displacement and rate of displacement were investigated. The results of the probabilistic analyses were used to produce fragility functions to evaluate the probability of exceeding a limit state conditioned on an intensity measure in the context of FFE.

Radiated power and acoustic convergence zone properties of the vibration of the shaft-hull system in an ocean acoustic channel

To compute the vibroacoustic radiation of the shaft-hull system in an ocean acoustic channel, we apply the finite element method/boundary element method. For the convergence zone effect, we use the beam displacement ray normal mode to examine the profile of the speed of sound in seawater. To evaluate the radiation property of the system, we propose the concept of effective radiated acoustic power, where only reversing acoustic rays and seabed totally reflected rays are included. We reveal that the far-field radiation can be approximately inferred from the effective radiated acoustic power. Effective radiated acoustic power can be utilized to extract the main radiating modes, which dominate the far-field radiation. The axial force induces vibration, including breathing and bending modes, resulting in the highest peak of the radiated sound pressure level (SPL). The lateral and vertical excitation results in horizontal and vertical bending modes, respectively, and the SPL in convergence zones induced laterally are higher than those induced vertically.

Design, numerical analysis and experiments of different types auxetic beams for vibration based energy harvester

In this study, different types of auxetic beams were designed and their vibration characteristics were investigated experimentally and numerically for to improve output electrical power in energy harvesting applications. In order to analyze the energy harvesting performance of all designed beams, different frequency conditions were investigated. To see the vibration-based energy harvesting potential of all auxetic beams, the displacement responses under vibration were analyzed using different methods. Firstly experimental modal analysis of non-traditional beams were made and compare with the FEM methods numerically. The displacement of beam were obtained under forced vibration by numerical harmonic analysis to evaluate beams in terms of energy harvesting performance. Then, sinusoidal vibration experiments in the electro-mechanical shaker were carried out in order to verify numerical modal analyses results for non-classical beams. Finally, galloping geometry was attached to the ends of all auxetic samples produced and exposed to wind load. The effect of air flow on beam vibrations and energy harvesting performance was investigated experimentally.

A 1D model for the dynamic instability of magnetized beams in leakage flow energy harvesters

This paper presents a one-dimensional fluid–structure interaction model for investigating the dynamic stability of elastic mounted beams under the influence of magnetic forces in a leakage flow energy harvesting environment. The interaction between the beam and external magnetic fields is represented by a nonlinear long range force distribution that is non linearly dependent on the beam displacement. The formulation results in a two way coupled fluid–structure interaction system that is one way coupled with the electromagnetic system. A perturbation technique is utilized to linearize the second order equilibrium equations of the coupled system, which are then transformed into a set of first-order ordinary differential equations in the state space. The effect of the linearized magnetic force coefficient on the eigenvalues and dynamic stability of the system is analyzed through a parametric study. The results indicate the onset of oscillatory dynamics in the coupled magneto-fluid-structural system is a non monotonic function of the magnetic force.

A novel fiber-optic beam monitor

A novel beam monitor based on Ce-doped silica optical fibers is being presented. Four fibers are mounted on the outside of a beam transport pipe, at the location of a beam stop at a proton cyclotron. The secondary radiation caused by the proton beam interaction with the beam stop is measured by the optical fibers via Radiation-Induced Emission (RIE). The light signal in the individual fibers is correlated to the proton flux closest to the fiber and can therefore be used as a detector to monitor the position of the proton beam in the beam stop. Initial testing shows that monitoring of a 150 nA beam of 18 MeV protons into a beam dump is possible. The monitor can measure relative beam current and beam displacement in X and Y as a function of magnetic steering.

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.

Impact response analysis and prediction of FRP-RC beams with varying flexural stiffness: Numerical simulation and modified two-DOF calculation

The damage behavior and simplified calculation of fiber-reinforced polymer reinforced concrete (FRP-RC) beams subjected to impact loading have attracted substantial attention. In this study, a finite element model incorporating strain rate was employed. Based on the model, the progressive damage behavior and nonlinear impact response of FRP-RC beams with varying stiffness under hammer-to-beam mass ratios were examined. The results indicate that in the investigated conditions, the damage mode of FRP-RC beams does not vary with the changes in the tension reinforcement ratio, but is affected by the hammer-to-beam mass ratio. Due to the absence of a yielding stage for FRP bars, a nonlinear alteration occurred in the rebound of the FRP bars’ strain and the beam’s displacement with a redistribution of stress. When the reinforcement ratio varies from 0.32% to 3.37%, the peak displacements, reaction and impact forces vary by 25%-49%, 53%-78%, and 0.1%-1% under different mass ratios, respectively. The reinforcement ratio does not change the relationship between the mass ratio and the curve shape of the impact force time history. Additionally, an improved two-degree-of-freedom model considering the FRP’s elastic brittleness effect and modified contact stiffness scaling factor was developed, their accuracy was verified. However, there are still many inconveniences to applying the two-DOF model in engineering. Consequently, based on the above two-DOF model, explicit formulas considering contact stiffness, bending stiffness, impactor velocity and mass for displacement and impact force response of impacted FRP reinforcement concrete beams were proposed, which greatly facilitates engineering calculations.

Beam displacement tolerances on a segmented mirror for higher-order Hermite–Gauss modes

Odd-indexed higher-order Hermite–Gauss (HG) modes are compatible with four-quadrant segmented mirrors due to their intensity nulls along the principal axes, which guarantees minimum beam intensity illuminating the bond lines between the segments thus leading to low power loss. However, a misplaced HG beam can cause extra power loss due to the bright intensity spots probing the bond lines. This paper analytically and numerically studies the beam displacement tolerances on a segmented mirror for the mode. We conclude that for ‘effective’ bond lines with 6 µm width, and the beam size chosen to guarantee 1 ppm clipping loss when centered, the beam can be rotated by roughly 1∘ or laterally displaced by 4% of its beam size while keeping the total power on the bond lines under 1 ppm. We also demonstrate that the constrained beam displacement parameter region that guarantees a given power loss limit, or the beam displacement tolerance, is inversely proportional to the bond line thickness.

Theoretical Analysis on Thermo-Mechanical Bending Behavior of Timber–Concrete Composite Beams

In this study, an analytical approach is introduced for predicting the bending behavior of a timber–concrete composite (TCC) beam subjected to a mechanical load and a non-uniform temperature field, in which the orthotropy of timber as well as interfacial slip are taken into consideration. The analytical model addresses the non-uniform temperature field using Fourier series expansion based on the heat transport theory. The stresses and displacements of the TCC beam under the thermo-mechanical condition are governed by the thermo-elasticity theory, and the corresponding solution is derived analytically by solving a group of non-homogeneous partial differential equations. The proposed solution is in good agreement with the finite element solution and exhibits higher accuracy compared to the Euler–Bernoulli beam solution that relies on the assumption of transverse shear deformation and isotropy. An extensive investigation is carried out to analyze how the bending behavior of TCC beams is influenced by variations in interfacial shear stiffness and temperature field.

Floor slab composite action effects on hysteresis behaviors of steel-framed-tube structures with shear links

The utilization of spandrel beams with a low span-to-depth ratio in a Steel-Framed Tube (SFT) structure can potentially diminish its ductility and energy dissipation characteristics. Conversely, integrating an SFT with end-plate-connected, replaceable low-yield-point steel shear links (SFT-RLYPSL) may significantly enhance its seismic response. This study introduces a prototype SFT-RLYPSL configuration designed to mitigate the premature separation of a reinforced concrete (RC) slab from the spandrel beams, a phenomenon observed in prior research. A series of finite element (FE) models were established, utilizing the prototype structure as a basis, to systematically investigate the impact of various parameters, including the presence and thickness of the RC slab, concrete strength, shear link length, and initial spandrel beam stiffness, on the cyclic behavior of an SFT-RLYPSL substructure module. Additionally, the failure mechanisms of the substructure module were assessed. The findings of this study reveal that the utilization of T-shaped connectors can effectively delay the pull-out of studs from the RC slab, especially under substantial vertical displacement of the spandrel beam. The initial elastic stiffness and load-carrying capacity of the substructure module can be significantly enhanced through the promotion of RC slab composite action. An optimal shear link length ratio falls within the range of 0.95 to 1.25, and given the assumption of LYP225 steel shear links with length ratios of 0.95 to 1.25 in the SFT-RLYPSL, the recommended minimum thickness and concrete grade for the RC slab, based on numerical simulation results, are 120 mm and C30, respectively. It is further recommended to employ C30 concrete for an RC slab with a thickness of 120 mm. Finally, a restoring force model is proposed, accurately reflecting the observed mechanical behaviors of the SFT-RLYPSL substructure module.

Seismic performance of improved multistorey X-braced steel frames

During an earthquake, the brace of a multistorey X-braced steel frame experiences out-of-plane instability. After the brace becomes unstable, the middle span of the brace-intersected beam exhibits a large imbalance force. This force causes a significant vertical displacement in the middle of the brace-intersected beam. To address this issue, an improved multistorey X-braced steel frame is proposed. Adding an arc energy-dissipation structure to the original structure adjusts the bearing capacity of the brace and ensures that the brace does not lose stability. The deformation of the arc energy-dissipation structure reduces the vertical displacement of the brace-intersected beam. A finite element model of the improved multistorey X-braced steel frame is established, and the seismic performance of the structure is analysed. The analysis shows that the brace of the improved multistorey X-braced steel frame does not experience instability, and the lateral bearing capacity is increased by 20%. The vertical displacement in the middle of the brace-intersected beam is small. The improved multistorey X-braced steel frame exhibits good seismic performance.