Amplitude Of Beam Research Articles

Dynamics of the Euler — Bernoully beam with distributed hysteresis properties

In this paper, we present a new mathematical approach to the analysis of a beam with distributed hysteresis properties. These hysteresis characteristics are described by two methods: phenomenological (Bouc — Wen model) and constructive (Prandtl — Ishlinskii model). The equations for beam are developed using the well-known Hamilton method. We investigate the dynamic response of a hysteresis beam under various external loads, including impulse, periodic and seismic loads. The results of numerical simulations show that the hysteresis beam exhibits differently to external influences as compared to the classical Euler-Bernoulli beam. In particular, under the same external loads, the vibration amplitude and energy characteristics of the hysteresis beam are lower than those of the classical one. These findings can be useful for buildings developers in the design of external load resistant buildings and structures

Modelling of cracking during beam oscillation laser welding of a creep-resistant nickel alloy

During high power laser welding of Inconel 740H, horizontal solidification cracks form at locations between approximately 70–80% of the weld depth. With the integration of circular beam oscillation, the laser energy density distribution and underlying thermo-mechanical conditions were altered. By coupling three-dimensional heat transfer, fluid flow, and stress modelling tools, the role that circular beam oscillation plays in the formation of the strain rates and stresses driving this cracking phenomenon was identified. While the addition of a circular oscillation pattern appeared to lower the stress levels along the solidification front, it did not eliminate the appearance of horizontal cracking. Only when the beam amplitudes reached 1.6 mm did solidification cracking disappear, but the weld depths were also significantly reduced.

Investigating the advantages of internal impact in high-performance lightweight ultra-low-frequency rotational energy harvesters

Piezoelectric energy harvesters are promising for collecting energy from ultra-low-frequency rotational machines due to their small-scale and lightweight characteristics. However, the power output for the reported rotational piezoelectric energy harvesters can hardly reach the milliwatt level, limiting their applications in sensor systems with high power consumption. To overcome this challenge, this Letter proposes an approach of using the internal impact mechanism to achieve high-performance lightweight ultra-low-frequency rotational energy harvesters. The internal impact is achieved by utilizing the velocity difference between a sliding mass and a tube on a piezoelectric beam. Through mathematical modeling and experimental validation, it is demonstrated that the velocity difference exists at ultra-low-rotational frequencies without a defined frequency lower limit, thus increasing the vibration amplitude of beam and enhancing the power output. The results show that the impact system achieves up to 136 times increase in power output compared to the non-impact system. With a maximum power output of 2.97 mW and a power density of 169.19 μW/g, the proposed energy harvester significantly outperforms the previously reported lightweight ultra-low-frequency rotational energy harvesters and shows great potential in self-powered sensing and monitoring of ultra-low-frequency rotational machines.

Analytical Solution for Dynamic Response of a Reinforced Concrete Beam with Viscoelastic Bearings Subjected to Moving Loads.

To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Mode matching with a phase camera for gravitational-wave detectors

Mode mismatch causes a large fraction of optical losses in gravitational-wave detectors. This effect will need to be considerably reduced in next generation detectors in order to fully exploit advanced techniques such as squeezing. Phase cameras are wavefront sensors capable of imaging the amplitude and phase of a laser beam. We simulate a measurement scheme with the phase camera and show that the two resulting error signals can be used to act on the two mismatch degrees of freedom in a closed loop.

Bessel–Bessel–Gaussian vortex laser beams

Abstract We obtain and investigate Bessel–Bessel–Gaussian vortex beams (BBG beams) with the complex amplitude being equal to a product of the Gaussian function with two Bessel functions, whose arguments are expressed as complicated radicals including the cylindrical coordinates and a free parameter that defines the shape of the intensity distribution. If this parameter is small, the intensity has the shape of an inhomogeneous ring. For larger values of this parameter, the intensity has the shape of two arcs or ‘crescents’, oriented by their concave sides to each other. The complex amplitude of such beams is derived in explicit form for an arbitrary distance from the waist. We demonstrate that the BBG beams rotate upon propagation anomalously fast: at a distance much shorter than the Rayleigh length, the intensity distribution is already rotated by almost 45°, whereas typically, the rotation angle of vortex Gaussian beams is equal to the Gouy phase. It is also shown that the parameter of the BBG beam allows controlling its topological charge (TC): when the parameter value is positive and increases, the beam TC also increases stepwise by an even number. Besides, we study two other similar vortex BBG beams: either with four local intensity maxima, lying on the Cartesian coordinates axes, or with one intensity maximum with a crescent shape, whose center is on the horizontal axis. The derived three new families of asymmetric vortex laser beams, whose complex amplitude is described by explicit analytical expressions at an arbitrary distance from the waist, extend the variety of laser beams that can be used for manipulating and rotating microparticles, free space data transmission, and in quantum informatics.

Vibration Characteristics of Magnetostrictive Composite Cantilever Resonator with Nonlocal Effect.

Taking the nonlocal effect into account, the vibration governing differential equation and boundary conditions of a magnetostrictive composite cantilever resonator were established based on the Euler magnetoelastic beam theory. The frequency equation and vibration mode function of the composite cantilever were obtained by means of the separation of variables method and the analytic solution of ordinary differential equations. The lateral deflection, vibration governing equations, and boundary conditions were nondimensionalized. Furthermore, the natural frequency and modal function of the composite beam were quantitatively analyzed with different nonlocal parameters and transverse geometry dimensions using numerical examples. Compared with the results without considering the nonlocal effect, the influence of the nonlocal effect on the vibration characteristics was analyzed. The numerical results show that the frequency shift and frequency band narrowing of the magnetostrictive cantilever resonator are induced by nonlocal effects. In particular, the high-frequency vibration characteristics, such as vibration amplitude and modal node of the composite beam, are significantly affected. These analysis results can provide a reference for the functional design and optimization of magnetostrictive resonators.

Differential Signal-Amplitude-Modulated Multi-Beam Remote Optical Touch Based on Grating Antenna.

As screen sizes are becoming larger and larger, exceeding human physical limitations for direct interaction via touching, remote control is inevitable. However, among the current solutions, inertial gyroscopes are susceptible to positional inaccuracies, and gesture recognition is limited by cameras' focus depths and viewing angles. Provided that the issue of ghost points can be effectively addressed, grating antenna light-trapping technology is an ideal candidate for multipoint inputs. Therefore, we propose a differential amplitude modulation scheme for grating antenna-based multi-beam optical touch, which can recognize different incidence points. The amplitude of the incident beams was first coded with different pulse widths. Then, following the capture of incident beams by the grating antenna and their conversion into electrical currents by the aligned detector arrays, the incident points of the individual beams were recognized and differentiated. The scheme was successfully verified on an 18-inch screen, where two-point optical touch with a position accuracy error of under 3 mm and a response time of less than 7 ms under a modulation frequency of 10 kHz on both incident beams was achieved. This work demonstrates a practical method to achieve remote multi-point touch, which can make digital mice more accurately represent the users' pointing directions by obeying the natural three-point one-line aiming rule instantaneously.

Study of Resonance between Bogie Hunting and Carbody Mode via Field Measurements and Dynamic Simulation.

By addressing the phenomenon of carbody abnormal vibrations in the field, the acceleration of the carbody and bogie was measured using accelerometers, and the diamond mode of the carbody was identified. The equivalent conicity of the wheelset and the acceleration at the frame end indicated that the shaking of the carbody was caused by bogie hunting. In the SIMPACK simulation, the acceleration frequency and amplitude at the frame end and midsection of the side beam were calculated. The lateral deformation amplitude of the side beam in the finite element model was extracted, and a modal shape function for the diamond-shaped mode was established. By utilizing the modal vibration equation, the modal generalized forces of the carbody were computed, revealing that, during carbody shaking, the yaw damper force contributed significantly among the forces of the secondary suspension, with the phase difference between the front and rear bogies approaching 180°. This insight offers a novel perspective for subsequent active control strategies. Subsequently, these modal generalized forces were applied as external excitation to a coupled vibration model encompassing both the carbody and transformer. Aiming to reduce the acceleration amplitude at the side beam, the transformer was treated as a dynamic vibration absorber, allowing for the optimization of its lateral suspension parameters. As a result, the lateral and vertical acceleration amplitudes at the side beam were concurrently reduced, with the maximum decrease reaching 58.5%, significantly enhancing the ride comfort.

Single-shot dual-wavelength telecentric in-line-and-off-axis hybrid digital holography with non-prior reconstruction

Dual-wavelength in-line-and-off-axis hybrid digital holography (iohDH) can achieve high-resolution holographic dynamic imaging. However, it requires the prediction of the diffraction distance and the complex amplitude of the reference beam, which is time consuming and results in complications and accuracy limitations. While telecentric imaging technique can obtain nondiffractive images without predicting the diffraction distance, it also can even eliminate spherical aberration and astigmatic aberration. Therefore, a dual-wavelength telecentric iohDH is proposed to realize non-prior high-resolution reconstruction in a single shot. Employing the dual-wavelength telecentric iohDH, our approach acquires the focused in-line-and-off-axis hologram using a color camera in a single shot. In this case, we perform wavelength conversion on the phase and low-frequency information about the off-axis hologram as constraints for in-line iteration. Then, the in-line amplitude constraints are performed in the spatial and frequency domains until the algorithm converges. Compared to the state-of-the-art dual-wavelength iohDH, our approach can streamline the reconstructed processes without demanding a priori information of the diffraction distance and the complex amplitude of the reference beam. More importantly, our approach enables higher quality and efficient reconstruction under the telecentric system. We verified our approach using simulations and experiments, and the results indicate that our approach can allow the amplitude and phase reconstruction with high resolution in a single shot.

Dynamic Analysis of Rigid–Flexible Structures with Piezoelectric Actuation and Control

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

Effect of Laser Beam Amplitude Profile on Second Harmonic Generation Efficiency

Effect of Laser Beam Amplitude Profile on Second Harmonic Generation Efficiency

Classical-quantum dual encoding for laser communications in space

In typical laser communications classical information is encoded by modulating the amplitude of the laser beam and measured via direct detection. We add a layer of security using quantum physics to this standard scheme, applicable to free-space channels. We consider a simultaneous classical-quantum communication scheme where the classical information is encoded in the usual way and the quantum information is encoded as fluctuations of a sub-Poissonian noise-floor. For secret key generation, we consider a continuous-variable quantum key distribution protocol (CVQKD) using a Gaussian ensemble of squeezed states and direct detection. Under the assumption of passive attacks secure key generation and classical communication can proceed simultaneously. Compared with standard CVQKD, which is secure against unrestricted attacks, our added layer of quantum security is simple to implement, robust and does not affect classical data rates. We perform detailed simulations of the performance of the protocol for a free-space atmospheric channel. We analyse security of the CVQKD protocol in the composable finite-size regime.

Realization of all two-dimensional Bravais lattices with metasurface-based interference lithography

Abstract Proximity-field nanopatterning (PnP) have been used recently as a rapid, cost-effective, and large-scale fabrication method utilizing volumetric interference patterns generated by conformal phase masks. Despite the effectiveness of PnP processes, their design diversity has not been thoroughly explored. Here, we demonstrate that the possibility of generating any two-dimensional lattice with diverse motifs. By controlling the amplitude, phase, and polarization of each diffraction beam, we can implement all two-dimensional Bravais lattices in three-dimensional space. The results may provide diverse applications that require three-dimensional nanostructures from optical materials and structural materials to energy storage or conversion materials.

Influence of atmospheric turbulence on coherent detection performance of space coherent optical communication

Space coherent optical communication technology is considered to be an important way to overcome the bottleneck in current high-speed space communication. However, atmospheric turbulence seriously limits its realization. Based on the Huygens-Fresnel principle and the low-frequency compensation power spectrum inversion method, this work first investigates the random distribution characteristics of the amplitude and phase of a Gaussian beam after it has been transmitted through atmospheric turbulence. Then, using the coherent mixing efficiency and communication bit error rate model, the influence of atmospheric turbulence on the performance of spatial coherent optical communication systems is obtained. Finally, a laser heterodyne detection experimental system is built to quantitatively study the influence of atmospheric turbulence on the coherent detection performance of spatial coherent optical communication. The conclusions drawn from this study are as follows. 1) The spatial phase distortion caused by the weak turbulence channel is relatively small and will hardly affect the light intensity distribution characteristics of the Gaussian beam. In the case of weak turbulence, the influence of weak turbulence on the performance of coherent optical communication system is almost negligible. The communication bit error rate will decrease rapidly with the increase of the number of single bit data photons. The communication signal-to-noise ratio can be better than 10<sup>–5</sup> when the number of single-bit photons is greater than 10. 2) Moderate turbulence will change the intensity distribution characteristics of the Gaussian beam, but will not cause a serious shift in the center of the spot. Under moderate turbulence conditions, the coherent mixing efficiency decreases rapidly as the turbulence intensity continues to increase, but the communication bit error rate still decreases rapidly with the increase of the number of single bit data photons. At this time, increasing the number of single-bit photons can suppress the negative influence of moderate intensity turbulence on the performance of coherent optical communication systems. 3) Strong turbulence will cause severe spatial phase distortion of the beam, destroy the consistency of the light intensity distribution, and cause a serious shift in the center of the spot. Under strong turbulence conditions, the coherent mixing efficiency of coherent optical communication systems approaches zero, and increasing the number of single bit data photons cannot significantly reduce the bit error rate, seriously affecting the quality of coherent optical communication. Atmospheric turbulence is an important limiting factor for developing space coherent optical communication. This study can provide useful references for evaluating the performance of space coherent optical communication systems.

Elastic Lateral Torsional Buckling of Beams Under External Moments: A New Type of Nonconservative Problem

The important character of the applied moment with a fixed line of direction as implied in deriving the governing differential equations of LTB for elastic beams, however, is not represented in stating the boundary conditions based on conventional energy approaches. This paper sets out to consider the boundary conditions derived by conventional potentials in order to identify the ignored second-order moments that need to be added for maintaining the initial direction of the applied moment during LTB. By taking into account the non-zero work done by these ignored moments for modifying original potentials, the nonconservative nature of the elastic LTB of beam under external moments is clarified in two aspects — by discovering the path-dependent property of the non-zero work and by demonstrating that only trivial solution of LTB mode is expected from the analytical solution of the governing differential equations. Using the concept of dynamic instability, an analysis procedure combining the numerical solution of an eigen-value problem and the bisection method is proposed to identify the first appearance of imaginary or conjugate complex frequencies and to determine the value of the critical moment. Demonstrative examples are considered for illuminating the elastic LTB behavior using conventional energy methods and revised virtual work equation. It has been found that the critical moments given by conventional potentials are generally not consistent with each other unless the work done by the ignored second-order moments vanishes. However, consistent critical moment, under which the free vibrating amplitude of elastic beam is increased unboundedly with time, can be obtained by the kinetic approach based on any revised virtual work equation, indicating the necessity of considering the nonconservative nature of non-follower applied moment.

Effects of crumb rubber particles on the dynamic response of reinforced concrete beams subjected to blast loads

Crumb rubber particles (RPs) can improve the impact resistance of concrete structures owing to their high toughness. In the current paper, the dynamic behaviours of RPs reinforced concrete beams under blast loads were investigated. The near-field explosion tests were first performed on the rubber-modified reinforced concrete (RRC) beams with different content of RPs (0%, 10%, 20%, 30%, and 50%). Numerical simulations based on the ConWep, Karagozian and Case concrete (KCC) models were then used to analysis the deformation/failure mechanisms of RRC beams. Finally, an improved single-degree-of-freedom (SDOF) method was proposed to predict the dynamic deflection of RRC beams. The experimental results indicated that the crack patterns of the RRC beams changed from bending cracks to shear–bending cracks as the scaled distance decreased. When the blast load had a small scaled distance (0.234 m/kg1/3), the number of cracks decreased with increased rubber content, particularly shear cracks. The numerical simulation revealed that due to the low damping ratio of RRC beams, the vibration amplitude of the RRC beams was lower than that of the beams without RPs. It is believed that the current study can provide valuable insights into the key factors for designing the blast resistance of RPs reinforced concrete structures.

Accuracy of Holographic Real-Time Mode Decomposition Methods Used for Multimode Fiber Laser Emission

Mode decomposition is a powerful tool for analyzing the modal content of optical multimode radiation. There are several basic principles on which this tool can be implemented, including near-field intensity analysis, machine learning, and spatial correlation filtering (SCF). The latter is meant to be applied to a spatial light modulator and allows one to obtain information on the mode amplitudes and phases of temporally stable beams by only analyzing experimental data. As a matter of fact, techniques based on SCF have already been successfully used in several studies, e.g., for investigating the Kerr beam self-cleaning effect and determining the modal content of Raman fiber lasers. Still, such techniques have a major drawback, i.e., they require acquisition times as long as several minutes, thus being unfit for the investigation of fast mode distribution dynamics. In this paper, we numerically study three types of digital holograms, which permits us to determine, at the same time, the parameters of a set of modes of multimode beams. Because all modes are simultaneously characterized, the processing speed of these real-time mode decomposition methods in experimental realizations will be limited only by the acquisition rate of imaging devices, e.g., state-of-the-art CCD camera performance may provide decomposing rates above 1 kHz. Here, we compare the accuracy of conjugate symmetric extension (CSE), double-phase holograms (DPH), and phase correlation filtering (PCF) methods in retrieving the mode amplitudes of optical beams composed of either three, six, or ten modes. In order to provide a statistical analysis of the outcomes of these three methods, we propose a novel algorithm for the effective enumeration of mode parameters, which covers all possible beam modal compositions. Our results show that the best accuracy is achieved when the amplitude-phase mode distribution associated with multiple frequency PCF techniques is encoded by Jacobi–Anger expansion.

Changing the Intensity on the Caustic of Autofocusing Chirp Beams Depending on the Incident Beam Amplitude

Changing the Intensity on the Caustic of Autofocusing Chirp Beams Depending on the Incident Beam Amplitude

Sensitivity Analysis of a Damage Detection Method Through High-Resolution Photos on Various Statically Deflected Beams

In this manuscript, the authors deeply investigate and test a modern technique that allows the analysis of a structure starting from a photo to identify and locate damage present on it, rapidly and non-destructively without any physical interaction with the analyzed structure. The technique suitability is tested on four statically deformed beams, on which notches represent the defects. The core of the proposed method is the correlation between the curvature that each beam presents under load conditions and its flexural stiffness. The proposed methodology consists in taking a photo of the inflected beam; subsequently, the acquired photo is manipulated with specifically designed image processing tools, and the second derivative of the beam axis is estimated using two distinct numerical differentiator filters (Lanczos filter and Gaussian wavelets) along with suitable processing to reduce border distortions. The tests conducted demonstrate that it is possible, with an opportune static deflection amplitude, to accurately detect the position of the notch with the proposed procedure; a sensitivity analysis is also conducted by testing the procedure with different beam thicknesses, notch positions, and amplitude of the static deflection. Although the authors realize that the technique can generally require sensibly large displacements, the results seem promising.