General Beam Research Articles

Assessment of structural mechanical effects related to torsional deformations of propellers

AbstractLifting propellers are of increasing interest for Advanced Air Mobility. All propellers and rotors are initially twisted beams, showing significant extension–twist coupling and centrifugal twisting. Torsional deformations severely impact aerodynamic performance. This paper presents a novel approach to assess different reasons for torsional deformations. A reduced-order model runs large parameter sweeps with algebraic formulations and numerical solution procedures. Generic beams represent three different propeller types for General Aviation, Commercial Aviation, and Advanced Air Mobility. Simulations include solid and hollow cross-sections made of aluminum, steel, and carbon fiber-reinforced polymer. The investigation shows that centrifugal twisting moments depend on both the elastic and initial twist. The determination of the centrifugal twisting moment solely based on the initial twist suffers from errors exceeding 5% in some cases. The nonlinear parts of the torsional rigidity do not significantly impact the overall torsional rigidity for the investigated propeller types. The extension–twist coupling related to the initial and elastic twist in combination with tension forces significantly impacts the net cross-sectional torsional loads. While the increase in torsional stiffness due to initial twist contributes to the overall stiffness for General and Commercial Aviation propellers, its contribution to the lift propeller’s stiffness is limited. The paper closes with the presentation of approximations for each effect identified as significant. Numerical evaluations are necessary to determine each effect for inhomogeneous cross-sections made of anisotropic material.

Identification of multiple nonlinear lap joints using instantaneous power flow balance

PurposeThe purpose of this paper is to apply the novel instantaneous power flow balance (IPFB)-based identification strategy to a specific practical situation like nonlinear lap joints having single and double bolts. The paper also investigates the identification performance of the proposed power flow method over conventional acceleration-matching (AM) methods and other methods in the literature for nonlinear identification.Design/methodology/approachA parametric model of the joint assembly formulated using generic beam element is used for numerically simulating the experimental response under sinusoidal excitations. The proposed method uses the concept of substructure IPFB criteria, whereby the algebraic sum of power flow components within a substructure is equal to zero, for the formulation of an objective function. The joint parameter identification problem was treated as an inverse formulation by minimizing the objective function using the Particle Swarm Optimization (PSO) algorithm, with the unknown parameters as the optimization variables.FindingsThe errors associated with identified numerical results through the instantaneous power flow approach have been compared with the conventional AM method using the same model and are found to be more accurate. The outcome of the proposed method is also compared with other nonlinear time-domain structural identification (SI) methods from the literature to show the acceptability of the results.Originality/valueIn this paper, the concept of IPFB-based identification method was extended to a more specific practical application of nonlinear joints which is not reported in the literature. Identification studies were carried out for both single-bolted and double-bolted lap joints with noise-free and noise-contamination cases. In the current study, only the zone of interest (substructure) needs to be modelled, thus reducing computational complexity, and only interface sensors are required in this method. If the force application point is outside the substructure, there is no need to measure the forcing response also.

Design of an over-constraint based nearly-constant amplification ratio compliant mechanism

A constant displacement amplification ratio is less investigated in compliant mechanisms. This study addresses this need by presenting an over-constraint based nearly-constant amplification ratio compliant mechanism (OCARCM) that alleviates the change in displacement amplification ratio. The free-body diagram (FBD) combined with the generic beam constraint model (BCM) method is employed to obtain the closed-form solutions that accurately and insightfully elaborate the nonlinear kinetostatic characteristics of the OCARCM. Comparative analysis is provided between the proposed OCARCM and the widely-used bridge-type compliant amplifier in terms of the ability to remain a constant amplification ratio, with and without external payloads. The closed-form models are verified by the nonlinear finite element results (FEA) with a maximum difference of 1%. In our case studies, it shows that the amplification ratio of the OCARCM changes by 1% over the range, while that of the bridge-type amplifier changes by approximately 14% under the same conditions. The results also reveal that a higher amplification ratio results in a greater variation in the ratio. An experiment based on the CNC machined aluminium alloy prototype with distributed-compliance is conducted, and experimental results show a maximum error of 3.4% for the amplification ratio compared with the analytical or FEA results.

Viscoelastic damping design – A novel approach for shape optimization of Constrained Layer Damping treatments at different ambient temperatures

Passive damping plays an important role in the vibration mitigation of aeronautic structures. In contrast to active systems, passive damping systems do not require any energy supply. Thus, their readiness is independent, which reduces the failure probability compared to active systems. Constrained Layer Damping (CLD) has become an established treatment for damping bending vibrations. Unlike other passive systems such as shock-mounts, CLD can be compactly integrated into an existing structure as an add-on solution. However, the design scope is limited by mass constraints and the optimal design for maximum damping must be found by optimization. For this purpose, a novel optimization approach is presented. The layer widths of the core and face layers of a CLD structure are treated as design parameters. Compared to the strategy of placing CLD patches on vibration antinodes, the proposed approach provides up to 52 % higher damping. The optimal design of a generic beam structure is determined considering different modes, viscoelastic material stiffnesses and ambient temperatures. Furthermore, the simulated damping is experimentally verified for a shape-optimized beam. The analyses show that the optimal design depends significantly on the viscoelastic material stiffness and is therefore temperature dependent. As a consequence, a generalized design guideline for CLD treatments cannot be derived.

Technical note: Consistency of IAEA's TRS‐483 and AAPM's extended TG‐51 protocols for clinical reference dosimetry of the CyberKnife M6 machine

While IAEA's TRS-483 code of practice is adapted for the calibration of CyberKnife machines, AAPM's TG-51 is still the protocol recommended by the manufacturer for their calibration. The differences between both protocols could lead to differences in absorbed dose to water during the calibrationprocess. The aims of this work are to evaluate the difference resulting from the application of TG-51 (including the manufacturer's adaptations) and TRS-483 in terms of absorbed dose to water for a CyberKnife M6, and to evaluate the consistency ofTRS-483. Measurements are performed on a CyberKnife M6 unit under machine-specific reference conditions using a calibrated Exradin A12 ionization chamber. Monte Carlo (MC) simulations are performed to estimate and using a fully modeled detector and an optimized CyberKnife M6 beam model. The latter is also estimated experimentally. Differences between the adapted TG-51 and TRS-483 protocols are identified and their impact isquantified. When using an in-house experimentally-evaluated volume averaging correction factor, a difference of 0.11% in terms of absorbed dose to water per monitor unit is observed when applying both protocols. This disparity is solely associated to the difference in beam quality correction factor. If a generic volume averaging correction factor is used during the application of TRS-483, the difference in calibration increases to 0.14%. In both cases, the disparity is not statistically significant according to TRS-483's reported uncertainties on their beam quality correction factor (i.e., 1%). MC results lead to and . Results illustrate that the generic beam quality correction factor provided in the TRS-483 might be overestimated by 0.36% compared to our specific model and that this overestimation could be due to the volume averagingcomponent. For clinical reference dosimetry of the CyberKnife M6, the application of TRS-483 is found to be consistent withTG-51.

Combination of Acoustic Black Holes with point masses

Passive acoustic measures are suitable for the targeted improvement of the vibration behaviour of technical products. In this context, Acoustic Black Holes (ABH) as innovative measures have shown great effect for an efficient damping of vibrations and a simultaneous mass reduction. The vibration reducing effect, however, is primarily apparent in the higher frequency range. The thickness reduction results in a mass reduction of the system, which could worsen the vibroacoustic behaviour in the lower frequency range. The idea of the approach here is to use the saved material in form of point masses to counteract this disadvantage at low frequencies by a targeted placement or direct consideration in the manufacturing process. The result is a mass-neutral acoustic design measure. In order to investigate the effectiveness of the ABH point mass combination, finite element models of generic beam and plate structures with ABH are used in this paper. In addition, the influence of point masses in terms of their position and number on the vibroacoustic behaviour is simulated. One focus is the assessment of the advantage by combining ABH with point masses. To validate the results, experimental investigations are carried out and compared with the numerical results.

Revisiting the Galactic Double Neutron Star merger and LIGO detection rates

ABSTRACT We revisit the merger rate for Galactic double neutron star (DNS) systems in light of recent observational insight into the longitudinal and latitudinal beam shape of the relativistic DNS PSR J1906 + 0746. Due to its young age and its relativistic orbit, the pulsar contributes significantly to the estimate of the joint Galactic merger rate. We follow previous analyses by modelling the underlying pulsar population of nine merging DNS systems and study the impact and resulting uncertainties when replacing simplifying assumptions made in the past with actual knowledge of the beam shape, its extent, and the viewing geometry. We find that the individual contribution of PSR J1906 + 0746 increases to $\mathcal {R} = 6^{+28}_{-5} \, \mathrm{Myr}^{-1}$ although the values are still consistent with previous estimates, given the uncertainties. We also compute contributions to the merger rates from the other DNS systems by applying a generic beam shape derived from that of PSR J1906 + 0746, evaluating the impact of previous assumptions. We derive a joint Galactic DNS merger rate of $\mathcal {R}^{\mathrm{gen}}_{\mathrm{MW}} = 32^{+19}_{-9}\, \mathrm{Myr}^{-1}$, leading to a LIGO detection rate of $\mathcal {R}^{\mathrm{gen}}_{\mathrm{LIGO}} = 3.5^{+2.1}_{-1.0}\, \mathrm{yr}^{-1}$ (90 per cent conf. limit), considering the upcoming O3 sensitivity of LIGO. As these values are in good agreement with previous estimates, we conclude that the method of estimating the DNS merger and LIGO detection rates via the study of the radio pulsar DNS population is less prone to systematic uncertainties than previously thought.

IAEA-AAPM TRS-483-based reference dosimetry of the new RefleXion biology-guided radiotherapy (BgRT) machine.

The purpose of this study is to provide data for the calibration of the recent biology-guided radiotherapy (BgRT) machine (Hayward, CA, USA) following the International Atomic Energy Agency (IAEA) and the American Association of Physicists in Medicine (AAPM) TRS-483 code of practice (COP) (Palmans etal. International Atomic Energy Agency, Vienna, 2017) and (Mirzakhanian etal. Med Phys, 2020). In RefleXion BgRT machine, reference dosimetry was performed using two methodologies described in TRS-483 and (Mirzakhanian etal. Med Phys, 2020) In the first approach (Approach 1), the generic beam quality correction factor was calculated using an accurate Monte Carlo (MC) model of the beam and of six ionization chamber types. The is a beam quality factor that corrects (absorbed dose to water calibration coefficient in a calibration beam quality ) for the differences between the response of the chamber in the conventional reference calibration field with beam quality at the standards laboratory and the response of the chamber in the user's A field with beam quality . Field A represents the reference calibration field that does not fulfill msr conditions. In the second approach (Approach 2), a square equivalent field size was determined for field A of and . Knowing the equivalent field size, the beam quality specifier for the hypothetical field size was derived. This was used to calculate the beam quality correction factor analytically for the six chamber types using the TRS-398. (Andreo et al. Int Atom Energy Agency 420, 2001) Here, TRS-398 was used instead of TRS-483 since the beam quality correction values for the chambers used in this study are not tabulated in TRS-483. The accuracy of Approach 2 is studied in comparison to Approach 1. Among the chambers, the PTW 31010 had the largest correction due to the volume averaging effect. The smallest-volume chamber (IBA CC01) had the smallest correction followed by the other microchambers Exradin-A14 and -A14SL. The equivalent square fields sizes were found to be 3.6cm and 4.8cm for the and field sizes, respectively. The beam quality correction factors calculated using the two approaches were within 0.27% for all chambers except IBA CC01. The latter chamber has an electrode made of steel and the differences between the correction calculated using the two approaches was the largest, that is, 0.5%. In this study, we provided the values as a function of the beam quality specifier at the RefleXion BgRT setup ( and ) for six chamber types. We suggest using the first approach for calibration of the RefleXion BgRT machine. However, if the MC correction is not available for a user's detector, the user can use the second approach for estimating the beam quality correction factor to sufficient accuracy (0.3%) provided the chamber electrode is not made of high Z material.

Analytic propagation variances and power spectral densities from a wave-optics perspective.

This work presents an approach for constructing equations describing the effects of atmospheric turbulence on propagating light based on equations and concepts that will be familiar to those with a background in paraxial wave-optics modeling. The approach is developed and demonstrated by working through three examples of increasing complexity: the variance and power spectral density of the aperture-averaged phase gradient (G tilt) on a point-source beacon, the variance of the Zernike tilt difference between two physically separated point-source beacons, and the irradiance-weighted average phase gradient (centroid tilt) and target-plane jitter variance for a generic beam. The first two results are shown to be consistent with the existing literature; the third is novel, and it is shown to agree with wave optics and to be consistent with the literature in the special case of a Gaussian beam.

Confinement Shear Effect in Fiber Composites

Composites have been playing an increasingly important role in various engineering applications. We examine the confinement shear effect arising in the neighborhood of the fiber-matrix interface in fiber-reinforced materials, which is a problem calling for further investigations. It is well known that the progressive failure process strongly depends on the interfacial transition zone (ITZ). Thus, we take the studied material as three-phased, i.e. fiber, matrix and interface in between. The generalized beam (GB) lattice model is adopted to simulate the compressive failure behavior of a representative volume element with one fiber included. Numerical results are provided to explain the confinement shear effect during the progressive failure process in specimens with various fiber-matrix properties, fiber orientations and distributions.

Simplified theoretical model for prediction of catenary action incorporating strength degradation in axially restrained beams

Catenary action is one of the structural mechanisms that could develop in a laterally restrained beam when subjected to large deformation, and it is a primary mechanism in the resistance to progressive collapse of frame structures in the typical scenario of a column removal. Analytical methods for the analysis of the catenary action exists for idealised beams with simple non-degrading yielding conditions. However, in a realistic beam assembly, especially under a column removal scenario, intermediate failure events such as failure of weld or a bolt component at the connection can occur; consequently, the strength of the beam in the plastic region degrades abruptly. This paper presents a simplified theoretical model taking into consideration the degradation of strength in the plastic regions. The basic model is formulated for a generic beam assembly axially restrained with a variable restraining stiffness (flexible axial support), and involves a middle connection. The strength degradation is represented by degraded yield functions. The model subsequently generates a realistic vertical load-deflection relationship, i.e. the resistance function. Comparison of load-deflection relationship so generated with corresponding finite element analysis shows good accuracy. Further comparison of the theoretical model with an existing laboratory experiment also exhibits good agreement. With the generated resistance functions, analysis of the actual dynamic response of beam assemblies in a progressive collapse scenario can be carried out using a standard procedure such as the energy method.

Evanescent morphing for tuning the dynamic behavior of composite lightweight structures: Theoretical assessment

Weight-reduction focused design often leads to a problematic vibration susceptibility of the components. In order to reduce environmental and health risks, the vibrations have to be decreased preferably through lightweight-compatible solutions. The investigations presented in this manuscript aim at the establishment of a new method for almost weight-neutral adaptive tuning of the dynamic behavior. The proposed unique actuating principle is based on structural cavities generating forces and slight structural deformations (evanescent morphing) when supplied with fluid, air, or vacuum. The cavities encapsulate compressible, low-profile viscoelastic elements operating according to an extended principle of the constrained layer damping (CLD). The proposed active vibration mitigation consists of the damping capacity adaptation of the viscoelastic elements through their thickness variation using the evanescent morphing as an efficient actuating mechanism. To validate this mechanism, existing model of a beam with CLD was extended by the compression-driven change of the geometrical and material properties of the viscoelastic layer. The results of the preliminary studies on a generic beam are presented. A very significant reduction of the vibration amplitudes up to 33.5 dB could be observed at the first eigenfrequency, whereas in the whole analyzed frequency spectrum an averaged reduction of 9.2 dB was obtained.

Current status and desired precision of the isotopic production cross sections relevant to astrophysics of cosmic rays: Li, Be, B, C, and N.

The precision of the current generation of cosmic-ray (CR) experiments, such as AMS-02, PAMELA, CALET, and ISS-CREAM, is now reaching ≈1-3% in a wide range in energy per nucleon from GeV/nucleon to multi-TeV/nucleon. Their correct interpretation could potentially lead to discoveries of new physics and subtle effects that were unthinkable just a decade ago. However, a major obstacle in doing so is the current uncertainty in the isotopic production cross sections that can be as high as 20-50% or even larger in some cases. While there is a recently reached consensus in the astrophysics community that new measurements of cross sections are desirable, no attempt to evaluate the importance of particular reaction channels and their required precision has been made yet. It is, however, clear that it is a huge work that requires an incremental approach. The goal of this study is to provide the ranking of the isotopic cross sections contributing to the production of the most astrophysically important CR Li, Be, B, C, and N species. In this paper, we (i) rank the reaction channels by their importance for a production of a particular isotope, (ii) provide comparisons plots between the models and data used, and (iii) evaluate a generic beam time necessary to reach a 3% precision in the production cross sections pertinent to the AMS-02 experiment. This first road map may become a starting point in the planning of new measurement campaigns that could be carried out in several nuclear and/or particle physics facilities around the world. A comprehensive evaluation of other isotopes Z ⩽ 30 will be a subject of follow-up studies.

OA028] On the potential of direct MV calibration of ionization chambers by secondary standards laboratories

Purpose The IAEA protocol (TRS-398) for absorbed dose to water measurements in therapeutic MV photon beams, recommends that ionization chambers be calibrated directly in MV accelerator photon beams rather than in cobalt-60 combined with generic beam quality correction factors ( k Q ) tabulated in the protocol. The purpose of this work was to study the feasibility for secondary standards laboratories to provide direct MV calibrations for hospitals and to evaluate the benefit of such calibrations versus conventional cobalt calibrations. Methods A laboratory with the potential to provide direct MV calibrations was established. It includes both a cobalt irradiator and a linear accelerator with the following MV beams: 4, 6, 10, 15, and 18 MV with flattening filter and 6 and 10 MV without flattening filter. Procedures were designed for accurate positioning of ionization chambers, beam output monitoring and relevant ionization chamber correction factors. Over a two-month period, k Q -factors were measured in all beams for seven nominally identical chambers (IBA FC65G) covering a wide range of serial numbers. Traceability to primary standards were established using transfer chambers. The results were compared with published k Q -factors from TRS-398. Results The monitoring of beam output using an external monitor chamber was found to be essential for calibration purposes: The raw accelerator output changed systematically by 0.4% over the measurement period. However, with an external monitor chamber, the output variability was reduced to less than 0.05% (1 sd). For each beam quality, the relative standard deviation for the measured k Q factors for the seven ionization chambers was about 0.07%. Conclusions The study demonstrates the feasibility of highly reproducible MV calibrations at the level of a secondary standards laboratory, and the closeness of agreement (sd k Q -factors may be adequate for the tested ionization chamber model. Ongoing work focuses on characterization of additional ionization chambers models (PTW30013, PTW31021, and NE2571) and on an improved estimation of the uncertainty related to establishing traceability to primary standards. The latter work includes direct use of water calorimetry in the specific accelerator beams of the laboratory.

On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests.

This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based—and hence high-order—discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters. In developing the dynamic equations of motion, an Euler angle parametrization is selected as it is found to yield fast computational performance. The resulting dynamic formulation is closed using an example shape function set satisfying the single generic kinematic constraint. The formulation is demonstrated via its application to the modelling of a series of static and dynamic test cases of both simple and non-prismatic structures; the simulated results are verified using MSC Nastran and an element-based intrinsic beam formulation. Through these examples, it is shown that the nonlinear beam shapes approach is able to accurately capture the beam behaviour with a very minimal number of system states.

Practical algorithm for custom-made caustic beams.

We present a practical algorithm for designing an aperture field (source) that propagates along a predefined generic beam trajectory that consists of both convex and concave sections. We employ here the mechanism that forms the well-known Airy beam in which the beam trajectory follows a smooth convex caustic of the geometric optics rays and generalize it for a class of beams that are referred to as "caustic beams" (CBs). The implementation is based on "back-tracing" rays from the predefined beam trajectory to the source's aperture to form its phase distribution. The amplitude is set in order to form a uniform smooth amplitude of the CBs along their trajectories. Several numerical examples are included.

Symplectic modeling of beam loading in electromagnetic cavities

Simulating beam loading in radiofrequency accelerating structures is critical for understanding higher-order mode effects on beam dynamics, such as beam break-up instability in energy recovery linacs. Full wave simulations of beam loading in radiofrequency structures are computationally expensive, while reduced models can ignore essential physics and can be difficult to generalize. We present a self-consistent algorithm derived from the least-action principle which can model an arbitrary number of cavity eigenmodes and with a generic beam distribution.

Experimental method for measuring classical negativity of generic beam shapes

Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the experimental quantification of the level of classical entanglement can be carried out in more general instances. Our approach enables the extension to arbitrarily shaped transverse modes and hence delivering a suitable quantification tool to describe concisely the modal structure.

Role of beam waist in Laguerre-Gauss expansion of vortex beams.

Laguerre-Gauss (LG) modes represent an orthonormal basis set of solutions of the paraxial wave equation. LG modes are characterized by two integer parameters n and ℓ that are related to the radial and azimuthal profile of the beam. The physical dimension of the mode is instead determined by the beam waist parameter w0: only LG modes with the same w0 satisfy the orthogonality relation. Here, we derive the scalar product between two LG modes with different beam waists and show how this result can be exploited to derive different expansions of a generic beam in terms of LG modes. In particular, we apply our results to the recently introduced circular beams by deriving a previously unknown expansion. We finally show how the waist parameter must be chosen in order to optimize such expansion.

From the Euler–Bernoulli beam to the Timoshenko one through a sequence of Reddy-type shear deformable beam models of increasing order

Abstract A sequence of elastic Reddy-type shear deformable beams of increasing (odd) order is envisioned, which starts with the Euler–Bernoulli beam (first order) and terminates with the Timoshenko beam (infinite order). The kinematics of the generic beam, including the warping mode of the cross sections, is specified in terms of three deformation variables (two curvatures, one shear angle), work-conjugate of as many stress resultants (two bending moments, one shear force). The principle of virtual power is used to determine the (static) equilibrium equations and the boundary conditions. The equations relating the bending moments and shear force to the curvatures and shear angle are also reported. Two governing differential equations (equivalent to a deflection differential equation of the sixth order) are provided, along with their general solution to within six unknown constants; the solutions for the Euler–Bernoulli and Timoshenko beams are recovered for first and infinite orders, respectively. A principle of minimum total potential energy is shown to hold for the generic beam. Extended forms of the classical Navier formula for the computation of the (axial) normal stress, and of the Jourawski formula for the computation of the “equilibrium” shear stress, are provided. A simple cantilever beam is used for an illustrative application.