Finite Beam Research Articles

Evaluation of dose calculations with inhomogeneity correction in intensity-modulated radiation therapy for esophagus cancer.

Differences often exist in the dose calculation accuracy caused by using different dose calculation algorithms in non-uniform tissues. To evaluate the accuracy of dose calculation with inhomogeneity correction in intensity-modulated radiation therapy (IMRT) by comparing dose calculated in Monaco with measurements in lung-chest phantom for esophagus cancer treatments. Finite size pencil beam (FSPB) and X-ray voxel Monte Carlo (XVMC) were used respectively for IMRT dose recalculations. Ten IMRT plans were recalculated and measured in the chest-lung phantom. The dose measurements using the Gafchromic ® (EBT3) dosimetry films were validated with open fields in the interfaces of materials with various physical densities. The accuracy of dose calculations was then evaluated by both point dose comparison and Gamma analysis against the film measurements. For regular open fields, the discrepancies of the point doses were less than 3.0% and 2.0% between measurement and calculations by FSPB and XVMC, respectively. For 6 MV IMRT plans, the average passing rates based on 3% /3 mm Gamma criteria were 82.8±1.0% and 96.4±0.7% for FSPB and XVMC, respectively. The XVMC algorithms more accurate in IMRT dose calculations with inhomogeneity correction for esophagus cancer.

Authors’ Reply to Discussion on 1) “Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by ND Beskou and MV Muho [Soil Dyn. Earthq. Eng. 109(2018), 222-226] and 2) “Dynamic response of an infinite beam resting on a Winkler foundation to a load moving on its surface with

Authors’ Reply to Discussion on 1) “Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by ND Beskou and MV Muho [Soil Dyn. Earthq. Eng. 109(2018), 222-226] and 2) “Dynamic response of an infinite beam resting on a Winkler foundation to a load moving on its surface with

Discussion on 1) “Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by ND Beskou and MV Muho [Soil Dyn. Earthq. Eng. 109(2018), 222–226] and 2) “Dynamic response of an infinite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by

Discussion on 1) “Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by ND Beskou and MV Muho [Soil Dyn. Earthq. Eng. 109(2018), 222–226] and 2) “Dynamic response of an infinite beam resting on a Winkler foundation to a load moving on its surface with variable speed” by

Finite-element analysis of non-collinear mixing of two lowest-order antisymmetric Rayleigh-Lamb waves.

Recently, a perturbation approach was adopted for the non-collinear mixing of plate waves in an isotropic elastic plate with quadratic nonlinearity by Ishii, Biwa, and Adachi [J. Sound Vib. 419, 390-404 (2018)] and a resonance condition was derived theoretically, namely, that a significant scattered plate wave is generated when its frequency and wavevector coincide with the sum/difference of those of its primary waves. However, that analysis assumed monochromatic plane waves that interacted everywhere in the plate. To apply the non-collinear mixing of plate waves to nondestructive evaluation of plate-like structures, the influence of the spatial and temporal finiteness of the primary waves on the generation of the scattered wave must be elucidated. To that end, the present study conducts three-dimensional dynamic finite-element analyses on the mixing of lowest-order antisymmetric Rayleigh-Lamb waves that have finite beam widths and time durations. The generation of scattered lowest-order symmetric Rayleigh-Lamb and shear horizontal waves with sum frequencies is discussed for various beam widths, intersection angles, and primary frequencies. The resonance condition derived originally for monochromatic plane waves in the aforementioned study is found to be valid even when the wave interaction is allowed only within limited space and time.

Wave component solutions of free vibration and mode damping loss factor of finite length periodic beam structure with damping material

Free vibration and mode damping loss factor of the finite periodic beam structure with viscoelastic damping material are investigated in this paper based on wave component method. A simple iterative operation for the natural vibration modes of the beam structure is firstly proposed by considering that the mode shape can be formed through superposition of the wave shapes of the wave components of the beam structure at the corresponding natural frequency. And then, wave component solution of the mode damping loss factor of the beam structure is obtained and analyzed based on the modal stain energy method. It is found that the kinetic energy of the unit cell of propagative wave component is always the same with the strain energy, and for non-propagative wave component these two quantities will never be equal. In numerical examples, the proposed iterative operation is validated.

Conversion of the hyperbolic-cosine Gaussian beam to a novel Finite Airy-related beam using an optical airy transform system

This work deals a novel expression of a Finite Airy-related beam generated by the conversion of the phase of a hyperbolic-cosine Gaussian (ChG) beam by means of an optical Airy transform system (OATS). The analytical expression of the Finite Airy-related beam generated from a fundamental Gaussian beam illuminating the tool of the OATS is deduced from our main study as a special case. Some numerical simulations are carried out in order to investigate the effects of the initial ChG beam parameters and those of the OATS on the change of the modules features of the generated Finite Airy-related beam. The study of results shows that we can adjust and control the distance between the modules of the created Finite Airy-related beams. Also, the positions and the orientations of these modules can be controllable and adjustable with the help of the manipulation of the optical system parameters.

Finite element steady periodic beam propagation analysis of mode instability in high power fiber amplifiers.

A finite element steady periodic scalar beam propagation method suited to treating mode instability in amplifiers incorporating fibers with complicated design features is presented and demonstrated on test cases. These incorporate large pitch photonic crystal fibers with confined and down-doped cores in co-pumped and counter-pumped configurations. Seed power fluctuations and slight launch misalignment are proposed and implemented as a noise source to seed the instability. Down doping the confined core by -7.0E-5 was found to increase the instability threshold by 25% in the co-pumped case and 9% in the counter-pumped case. The increase in threshold is correlated with the suppression of higher frequency components of intensity gratings associated with the instability.

Defect mode-induced unidirectional flexural wave transmission using prismatic beams with concentrated gradient masses

We study and realize unidirectional flexural wave transmission in finite phononic crystal beams based on the boundary defect modes. First, we show that by carrying a periodic array of concentrated masses, conventional prismatic beams become phononic crystal beams having multiple transmittance peaks in odd-order bandgaps. We point out that these bandgap transmittance peaks are induced by pass-band splitting and are essentially defect modes due to the existence of the imperfect boundary in finite beam structures. Significant asymmetric flexural wave propagation can be observed in these defect modes by gradually changing each concentrated mass. Using the spectral element method (SEM), the relationship between the concentrated gradient masses and the directivity at the defect modes is discussed. To realize concentrated gradient masses, we periodically attach near-point-contact steel balls with gradient diameters on a prismatic beam. The formation of the bandgaps and unidirectional displacement transmission are experimentally validated with a high-sensitive point-wise fiber Bragg grating displacement sensing system. Asymmetric one-way flexural wave propagation is further demonstrated in the time domain with a Hanning-windowed tone burst signal excited at the two ends of the phononic crystal beam. Agreements between the SEM and experimental results clearly indicate that the asymmetric one-way flexural wave propagation can be achieved in prismatic beams carrying a periodic array of concentrated gradient masses.

Complete semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation with non-homogeneous initial conditions

In this paper the new semi-analytical solution for the moving mass problem, published by the author of this paper, is extended to account for the non-homogeneous initial conditions. Derivations are presented for infinite homogeneous beams placed on a two-parameter visco-elastic foundation. Methods of integral transforms and contour integration are exploited to obtain the final closed-form solution, which is presented in form of a sum of the truly steady-state part, mass induced harmonic part, initial conditions induced harmonic part and transient vibration. Except for the transient part that is obtained by numerical integration, full evolution of the transversal vibrations can be quickly and accurately obtained by simple evaluation of the presented closed-form results.Newly derived formulas for infinite beams are validated by analysis of long finite beams, where the problem is solved by the eigenmode expansion method. Excellent agreement between the results is obtained validating the new formulas.

Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section

Abstract In this paper, results of numerical simulations and measurements are presented concerning the non-uniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linear-elastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results.

Sensitivity analysis of a smart soft composite robotic finger design using geometrically nonlinear laminated composite finite beam elements

Soft robotics is an emerging research field that uses deformable materials to build compliant and adaptable systems, using simple integrated mechanisms, enabling biomimetic behavior. This paper presents a sensitivity analysis of a shape memory alloy (SMA)-driven smart soft composite (SSC) bending actuator that is used as an artificial finger in robots or prosthetics. This SSC structure is made of a flexible material, such as polydimethylsiloxane (PDMS), reinforced with some layers of glass fiber sheets, and actuated via SMA wires embedded in the flexible material. The SMA wires shrink when thermally activated, resulting in bending the three flexible hinges of the finger. Designing such smart soft structures involves optimizing large number of design parameters such as the flexible hinge length and thickness, the number of composite layers and their orientation, the number of SMA wires and their diameters. Hence an accurate and efficient computational tool is required to perform sensitivity analysis, and facilitate and accelerate the design process. The mathematical model should also account for geometric nonlinearity due to the large deformation and rotation of the structure in hand. A recently-developed accurate and efficient novel geometrically-nonlinear laminated composite beam finite element model is used in this work for analyzing the SSC robotic finger. The sensitivity analysis revealed that the effect of the flexible hinge thickness in the studied design is much more significant than the hinge length, and that the relationship between the fingertip rotation and the hinge thickness is nonlinear for the case of one glass fiber sheet and approaches linearity as the number of sheets increases to three.

Vibro-acoustic properties of sandwich structures

The vibro-acoustic properties of three-layered sandwich elements depend on the bending stiffness of the structure. It is found that the apparent bending stiffness of a sandwich beam depends on frequency, its length and boundary conditions. A beam with free ends appears stiffer than the same beam clamped at both ends. The apparent bending stiffness of a sandwich beam with clamped ends decreases as the length of the beam is reduced. The opposite is the case for a beam with free ends. A method for estimating the material parameters of a sandwich beam is described. The frequency and space averages of the point mobility of a finite sandwich beam is found to be equal to the point mobility of an infinite sandwich beam of the same type. Coupling loss factors between sandwich beam elements for some simple types of junctions are given.

Drive-by damage detection with a TSD and time-shifted curvature

‘Drive-by’ damage detection is the concept of using sensors on a passing vehicle to detect damage in a bridge. The newly developed traffic speed deflectometer (TSD) is a device used for pavement velocity/deflection measurements and is investigated here in numerical simulations as a means of bridge damage detection. A TSD vehicle model containing five displacement sensors is simulated crossing a simply supported finite element beam containing damage simulated as a loss in stiffness of one of the elements. Time-shifted curvature is derived from the displacements and is proposed as a novel damage indicator, which removes the influence of the road profile and all vehicle motions except for pitch. Results show that the time-shifted curvature can be reliably used as a damage indicator in the presence of noise and changes in transverse position of the vehicle on the bridge.

Conditions for the onset of the current filamentation instability in the laboratory

The current filamentation instability (CFI) is capable of generating strong magnetic fields relevant to the explanation of radiation processes in astrophysical objects and leads to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral$e^{-}~e^{+}$beams to explore the CFI with realistic parameters, by performing two-dimensional particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI growth rate and as long as the role of the competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma-based accelerated electron–positron fireball beams, plays a minor role in the growth of CFI in these scenarios.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Ultralight cellular composite materials with architected geometrical structure

A novel computational approach is presented to predict the overall hyperelastic properties of ultralight cuboct cellular lattices made of brittle carbon fiber-reinforced polymer composites, such as the ones recently fabricated at the MIT Media Lab-Center for Bits and Atoms. The repetitive unit cell (RUC) approach is employed to model the fabricated cellular micro-lattices. Each member of the cellular structure is modeled using only one finite beam element with 12 degrees of freedom, and the nonlinear coupling of axial, bidirectional-bending, and torsional deformations is studied for each 3D spatial beam element. Since the cellular composite material is fabricated via the assemblage of building blocks by mechanical interlocking connections, we utilize the standardized Ramberg-Osgood function for the moment-rotation relation at the ends of adjacent members to enable tuning the appropriate flexibility for connections between two extreme limits of pin-jointed or rigid-jointed connections. The mixed variational functional in the updated Lagrangian co-rotational reference frame is obtained to derive explicitly the stiffness matrix. Then, we use newly proposed homotopy methods to solve the algebraic equations.

A multi-modal energy harvesting device for low-frequency vibrations

This paper presents an innovative design of a low-frequency multi-modal system vibration-based energy harvester (VEH) for powering wireless autonomous monitoring systems wind turbines of 30 kW. The main objective is to design an energy harvesting device capable to operate in a very low-frequency bandwidth (3 to 10 Hz) increasing as much as possible the operational bandwidth by enhancing the amplitude of the second mode of vibration. The electrical power performance is evaluated for four different energy harvesting designs, which are mainly composed of multi-beams cantilevers with tip masses. For the harvesting system with two multiple-beams trident, a rigid beam is selected to join them. This versatile geometric configuration offers the possibility to modify the vibration characteristics of the harvester in several alternative ways, not only by increasing the tip mass which may be not favorable from a structural viewpoint. The resonant frequencies values, the time voltage signals and the electric power are obtained through a finite element beam formulation early proposed by the authors, capable to modeling three dimensional systems. The numerical results are validated through experimental tests. Regarding the output power, the most promising design with two multiple-beams trident with a tip mass delivers 36.48 μW and 96.04 μW in the proposed range of operation (first two resonance frequencies 4.76 and 7.91 Hz, respectively) excited by 0.1 g of base acceleration. This clearly indicates that the device is a very good candidate for the proposed application of autonomous wireless monitoring, since the output power is larger than the minimum of 20 μW required.

High near-infrared transmittance and waveguide structures in polycrystalline ZnSe by carbon and proton implantation combined with photolithography

We report on near-infrared (NIR) waveguide structures in polycrystalline ZnSe using the carbon ion implantation technique combined with standard lithography. High NIR transmittance is observed by the absorption spectra before and after carbon and proton implantation at room temperature. Two half-Gaussian curves are used to reconstruct the refractive index profile of the waveguides at a wavelength of 1539 nm. The results show that the numerically simulated mode by the finite difference beam propagation method (FD-BPM) is in good agreement with the experimental data by end-facet setup, which exhibits a high potential for designable NIR waveguide devices in polycrystalline ZnSe by carbon ion implantation.

Scour influence on the fatigue life of operational monopile‐supported offshore wind turbines

AbstractOffshore wind turbines supported on monopiles are an important source for renewable energy. Their fatigue life is governed by the environmental loads and in the dynamic behavior, depending on the support stiffness and thus soil‐structure interaction. The effects of scour on the short‐term and long‐term responses of the NREL 5‐MW wind turbine under operational conditions have been analyzed by using a finite element beam model with Winkler springs to model soil‐structure interaction. It was found that due to scour, the modal properties of the wind turbine do not change significantly. However, the maximum bending moment in the monopile increases, leading to a significant reduction in fatigue life. Backfilling the scour hole can recover the fatigue life, depending mostly on the depth after backfilling. An approximate fatigue analysis method is proposed, based on the full time‐domain analysis for 1 scour depth, predicting with good accuracy the fatigue life for different scour depths from the quasi‐static changes in the bending moment.

Fracture analysis of finite length angle-ply composite double cantilever beam specimens

The double cantilever beam specimen is assumed as two finite length beams, connected together, except at the initial delamination length. The energy release rate ( GI) is evaluated analytically by considering a Timoshenko beam on Winkler and Pasternak elastic foundations. The current data reduction methods have a blind spot in calculating GI when crack approaches the end of the ligament, which is considered in this study and, therefore, the simplifying assumption of infinite ligament length is not assumed here. GI will be strongly dependent on the ligament length if it is less than twice the thickness. Furthermore, the R-curves of different layups including their first points (fracture toughness) are drawn using Ρ–δ curves reported in the literature and they are compared to the experimental results. These comparisons show that Timoshenko beam on Winkler foundation gives the best results in comparison with experimental results for unidirectional and angle-ply laminates.