Thin Rod Research Articles

Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion

In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ−1. Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ.

Novel radiation hard position sensitive detector using YAG:Ce fibers for ion beam instrumentation at FRIB

We are investigating the feasibility of a new detector concept for use in the beam line at the Facility for Rare Isotope Beams (FRIB). The detector is designed to withstand the high ion beam intensities and the high radiation environment while providing position, timing, and energy information. Based on the concept of a fiber detector, the device uses YAG:Ce crystals as sensing material, chosen for their extreme radiation tolerance to electromagnetic or hadronic exposure. The crystals are machined into long and thin rods which are laid out in orthogonal horizontal and vertical arrangements to obtain spatial sensitivity to impinging particles. The readout is performed at the extremities of the rods with strip Multi Pixel Photon Counters (MPPC) also referred to as Silicon Photomultipliers (SiPM) arrays model S13552 from Hamamatsu mounted on ribbon cables with connector ends.

A laser-based Ångstrom method for in-plane thermal characterization of isotropic and anisotropic materials using infrared imaging.

High heat fluxes generated in electronics and semiconductor packages require materials with high thermal conductivity to effectively diffuse the heat and avoid local hotspots. Engineered heat spreading materials typically exhibit anisotropic conduction behavior due to their composite construction. The design of thermal management solutions is often limited by the lack of fast and accurate characterization techniques for such anisotropic materials. A popular technique for measuring the thermal diffusivity of bulk materials is the Ångstrom method, where a thin strip or rod of material is heated periodically at one end, and the corresponding transient temperature profile is used to infer the thermal diffusivity. However, this method is generally limited to the characterization of one-dimensional samples and requires multiple measurements with multiple samples to characterize anisotropic materials. Here, we present a new measurement technique for characterizing the isotropic and anisotropic in-plane thermal properties of thin films and sheets as an extension of the one-dimensional Ångstrom method and other lock-in thermography techniques. The measurement leverages non-contact infrared temperature mapping to measure the thermal response from laser-based periodic heating at the center of a suspended thin film sample. Uniquely, our novel data extraction method does not require precise knowledge of the boundary conditions. To validate the accuracy of this technique, numerical models are developed to generate transient temperature profiles for hypothetical anisotropic materials with known properties. The resultant temperature profiles are processed through our fitting algorithm to extract the in-plane thermal conductivities without knowledge of the input properties of the model. Across a wide range of in-plane thermal conductivities, these results agree well with the input values. Experiments demonstrate the approach for a known isotropic reference material and an anisotropic heat spreading material. The limits of accuracy of this technique are identified based on the experimental and sample parameters. Further standardization of this measurement technique will enable the development and characterization of engineered heat spreading materials with desired anisotropic properties for various applications.

Dynamics of certain Euler-Bernoulli rods and rings from a minimal coupling quantum isomorphism.

In some parameter and solution regimes, a minimally coupled nonrelativistic quantum particle in one dimension is isomorphic to a much heavier, vibrating, very thin Euler-Bernoulli rod in three dimensions with ratio of bending modulus to linear density (ℏ/2m)^{2}. For m=m_{e}, this quantity is comparable to that of a microtubule. Axial forces and torques applied to the rod play the role of scalar and vector potentials, respectively, and rod inextensibility plays the role of normalization. We show how an uncertainty principle ΔxΔp_{x}≳ℏ governs transverse deformations propagating down the inextensible, force and torque-free rod, and how orbital angular momentum quantized in units of ℏ or ℏ/2 (depending on calculation method) emerges when the force and torque-free inextensible rod is formed into a ring. For torqued rings with large wave numbers, a "twist quantum" appears that is somewhat analogous to the magnetic flux quantum. These and other results are obtained from a purely classical treatment of the rod, i.e., without quantizing any classical fields.

The in-tissue molecular architecture of β-amyloid pathology in the mammalian brain

Amyloid plaques composed of Aβ fibrils are a hallmark of Alzheimer’s disease (AD). However, the molecular architecture of amyloid plaques in the context of fresh mammalian brain tissue is unknown. Here, using cryogenic correlated light and electron tomography we report the in situ molecular architecture of Aβ fibrils in the AppNL-G-F familial AD mouse model containing the Arctic mutation and an atomic model of ex vivo purified Arctic Aβ fibrils. We show that in-tissue Aβ fibrils are arranged in a lattice or parallel bundles, and are interdigitated by subcellular compartments, extracellular vesicles, extracellular droplets and extracellular multilamellar bodies. The Arctic Aβ fibril differs significantly from an earlier AppNL-F fibril structure, indicating a striking effect of the Arctic mutation. These structural data also revealed an ensemble of additional fibrillar species, including thin protofilament-like rods and branched fibrils. Together, these results provide a structural model for the dense network architecture that characterises β-amyloid plaque pathology.

Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.

Comparative Analysis of Movements of Curved Ultrasonic Instruments

The paper presents a theoretical analysis of vibrations of a curvilinear rod in the form of a loop of low rigidity formed from a quarter of a circle with a constant radius, limited by an angle π/2 < γ < π and two rectilinear rods. It is indicated that in the practice of ultrasonic technology, some types of structures are known in which elastic elements are used as resonators, waveguides, oscillation transformers and instruments for influencing the processed materials. Their use makes it possible to obtain an additional impulse of force in the working area by using the potential energy caused by the action of the elastic properties of such elements. However, insufficient attention has been paid to the theoretical justification of the use of elastic elements in ultrasonic systems. In this regard, the present work is devoted to the theoretical substantiation of the use of an elastic tool made of a thin rod having the shape of a loop. The diagram and calculation of displacements of the free end of a curved rod under the action of forces directed along the longitudinal axis are given in the paper. It is shown that elastic displacements are caused by a curved shape in the form of an arc of a circle of a curved rod. For comparison, calculation schemes of two types of curved rod with an attached rod are given. In the first case, the free ends of the rectilinear rods, directed vertically downwards, make elastic movements along two coordinates. In the second case, the ends of rectilinear rods directed at a certain angle to the vertical axis and converging at the bottom point due to the symmetry of their location, make vertical movements only along one coordinate. The considered shape of the curved rod can be successfully used as a tool for performing technological tasks in the ultrasonic method of processing holes in brittle materials, spot welding, etc. Such a scheme, in contrast to the traditional ultrasonic treatment scheme based on the use of rectilinear rods, makes it possible to increase the magnitude of the vibration amplitude of the instrument due to elastic displacements of the curved section of the rod of low rigidity. The proposed form will increase the intensity of tool vibrations and increase process productivity and processing accuracy. The resulting calculation formula shows that the amount of elastic displacements of curved rods is affected by the cross-sectional stiffness and the radius of curvature of the curved part, as well as the angle of inclination of the rectilinear rod. The theoretical calculation is supplemented by a comparative experimental study of the Chladni forms for both schemes obtained on the sheet surface using abrasive particles.

Numerical investigation of the stress-strain state of zirconium dioxide pin structures manufactured using CAD CAM technologies

Numerical studies were carried out to determine the stress-strain state of pin stump structures made of zirconium dioxide. The calculation models were part of the dentoalveolar segment in the form of a cylinder, composed of a single-rooted tooth, dentin, periodontal ligament, compact bone of the alveolus, gums, spongy bone and a monolithic structure consisting of a crown fixed on a stump insert and a rod-pin. Three cases of such pin design models were considered. A numerical study was carried out for three different thicknesses of the rod, which were modeled as follows: the volume of the 2nd and 3rd pins doubled compared to the previous one – case 1 (thin rod), case 2(medium) and case 3 (thick). The finite element method was used to study the field of displacements and stresses according to von Mises both in the structures themselves and in the tissues surrounding them. Two cases of the load on the chewing surface of the tooth crown were established for comparative analysis in all cases: a distributed vertical load of 100 N and the same load at an angle of 45°. As a result of numerical studies, pin structures case 2 and 3 showed an ad-vantage over the design with a thin rod (case 1) both in terms of displacements and stresses. Case2 (average rod thickness) is recommended for use in practice. Structures of this type can be used to restore the crown part of the tooth in case of its complete absence or significant destruction, as well as a support for a bridge prosthesis.

Capabilities of auxiliary techniques for low strain impact testing of piles foundations

Introduction. An increase in the complexity of tasks arising from the quality control of geotechnical structures ultimately increases the role of indirect methods as part of the survey set. Low strain impact testing of piles length and integrity is currently one of the most common non-destructive geophysical methods used in the state diagnostics of foundations. The capabilities and limitations of the method are associated with the peculiarities of its basic theoretical model describing the propagation of elastic waves in a thin rod. In this regard, specialists often have recourse to the auxiliary techniques of field research.Aim. To inform test engineers, designers and employees of supervisory organizations about the potential of auxiliary methods for the low strain impact quality control of pile foundations.Methods and materials. The features of the theoretical model of the low strain impact pile quality control, as well as the associated capabilities and limitations of the method are described. The auxiliary methods of data collection and analysis were used for the survey of pile foundations, including those in the composition of existing structures.Results. The results of the work are represented by additional information obtained about the foundations surveyed using the auxiliary methods of data collection and analysis. An alternative arrangement of sensors relative to the surveyed structure was used for determining the depth of piles in the composition of grade beam footings and existing structures. The common shot point profiling (ultra-seismic method) was used to assess the velocity of rod wave propagation in the body of the structure. The options of data presentation in the parallel seismic method were used to demonstrate its potential for the quality control of foundation concrete.Conclusion. The auxiliary methods of data collection and analysis used in the low strain impact survey of pile foundations can significantly increase the reliability of conclusions about the depth and integrity of a structural material.

Effect of phosphate rock acid insoluble residue on hydration process and mechanical properties of α-hemihydrate gypsum

The application of α-hemihydrate gypsum (α-HH) is limited by several factors, such as a rapid hydration rate, short setting time, poor water resistance, and high cost. Especially because of the high production cost, although α-HH has excellent mechanical strength, it is rarely used in the field of building materials. In this study, based on the composition characteristics of new industrial solid waste (phosphate-rock acid-insoluble residue, PAIR) and to meet the needs of resource utilization, gypsum matrix composites were prepared by adding PAIR to α-HH to solve the problems of short setting time and poor water resistance of gypsum matrix composites and improve the comprehensive properties of α-HH products. The results show that when the different types of pores formed during the hydration of α-HH were filled with inert substances, such as silicon dioxide, insoluble phosphate, and calcium fluoride from PAIR, the proportion of mesopores in the composite products increased, whereas that of harmful macropores decreased. The compressive and flexural softening coefficients of the PAIR/α-HH system with 23% PAIR were the highest at 57.25 and 60.125%, respectively, and the water resistance of the system was improved; when the content of PAIR reaches 35%, the strength of the composite products decreased from 58.125 to 43.8MPa. The HPO42- in PAIR partially replaces the SO42- ion in the dihydrate gypsum (DH) lattice to form a Ca(SO4, HPO4)•2H2O double salt, leading to the production of eutectic phosphorus. Soluble F-, Al3+, Mg2+, and phosphorus-containing substances in PAIR form a variety of complex ions in PAIR/α-HH aqueous solution, which are adsorbed onto the surface of the new DH phase; the crystal morphology changed from thick, long columns to clusters, thin rods, and plates, inhibiting the nucleation and growth of DH and changing its crystal growth rate and crystallization behavior. Therefore, the setting time of gypsum is prolonged; when 35% PAIR was added, the induced nucleation period of the PAIR/α-HH system was prolonged from 40 to 265min, and the final setting time was from 12 to 360min. By mixing solid waste PAIR, while the setting time of α-HH is prolonged, its water resistance is improved, and its mechanical strength is not significantly reduced, reducing the cost. From the perspective of economy and environmental protection, this study is a way to α-HH is widely used in the field of building materials.

Relativistic theory of elastic bodies in the presence of gravitational waves

The equations of motion governing small elastic oscillations of materials, induced by gravitational waves, are derived from the general framework of Carter and Quintana. In transverse-traceless gauge, no bulk forces are present, and the gravitational wave is found to act as an effective surface traction. For thin rods, an equivalent description is given, in which there is no surface traction, but a bulk acceleration, which is related to the Riemann curvature of the gravitational wave. The resulting equations are compared to those of the Synge–Bennoun elasticity theory.

Determination of the critical velocity of a straight wing with a high aspect ratio

An aerodynamic problem on an air flow around a large aspect ratio rectangular wing is investigated in this study. According to the theory of Vlasov, the wing is considered to be a thin rod. External loads are assumed to be proportional to the airfoil angle of attack related to the dimensionless coefficient of the lift and the pitching moment coefficient. These coefficients depend on the airfoil parameters and the Mach number M and are determined by experimental measurements for subsonic and supersonic velocities. In this case, to define the unstable cases of the wing, one bases on the Lyapunov stability theory. Equations of bending and torsional free vibrations have resulted. Based on the analysis of natural frequencies (eigenfrequencies), it is possible to determine the changing positions of the real part and the imaginary part of the characteristic equation solution. These positions can cause instabilities for the wing such as torsional divergence and flutter.

Improving the Localization Accuracy of Dipole Sound Sources Using Planar Microphone Arrays

A method has been developed for tuning the microphone array for optimal visualization of acoustic dipoles. Acoustic dipoles were generated under experimental conditions in an anechoic chamber using a subsonic air flow around a thin metal rod and thin rectangular plate. To confirm the operability of this approach, we compared the visualization maps obtained using the approach with the results obtained with a similar array class tuned in the traditional monopole method. The developed approach, which adapts the array to the dipole radiation model and modifies the transfer functions that take into account the influence of the incidence pattern of sound waves, demonstrates an increase in the array’s dynamic range with optimal microphone placement.

On the Time-Optimal Control Problem Associated with the Heating Process of a Thin Rod

On the Time-Optimal Control Problem Associated with the Heating Process of a Thin Rod

Stress-based topology optimization of thermoelastic structures considering self-support constraints

A thermoelastic topology optimization method considering stress and manufacturing constraints is developed for engineering structures under thermo-mechanical coupled field in this paper. A design dependent non-uniform temperature field is considered for the heat conduction and the thermoelastic analysis during the topology optimization. Based on the solid isotropic material with penalization (SIMP), a topology optimization model is formulated to minimize the structural compliance under stress and overhang angle constraints. The overhang angle constraint to achieve the self-support property in additive manufacturing is established by connecting the elemental density values between the printing element and the corresponding support elements in the lower layer. The stress aggregation function is built to approximate the maximum stress value and an improved adaptive normalization scheme is applied to deal with the highly nonlinearity of the optimization. The sensitivity of the objective function and constraints with respect to the design variables are derived by the adjoint method, and the design variables are updated by the gradient-based optimization method. Moreover, a robustness scheme is proposed for the thermoelastic topology optimization to eliminate possible manufacturing issues such as “single node connection” and “thin rod” phenomena. Several typical numerical examples are provided to demonstrate the effectiveness of the proposed method in stress value reduction and overhang angle control. Meanwhile, the topology optimization with robustness scheme is also proved to result in more robust designs for manufacturing.

Experimentally probing the stability of thin-shell structures under pure bending.

This paper studies the stability of space structures consisting of longitudinal, open-section thin-shells transversely connected by thin rods subjected to a pure bending moment. Localization of deformation, which plays a paramount role in the nonlinear post-buckling regime of these structures and is extremely sensitive to imperfections, is investigated through probing experiments. As the structures are bent, a probe locally displaces the edge of the thin shells, creating local dimple imperfections. The range of moments for which the early buckling of the structures can be triggered by this perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by a stability landscape, and probing is extended to the entire structure to reveal alternate buckling modes disconnected from the structure's fundamental path. These results can be used to formulate efficient buckling criteria and pave the way to operating these structures close to their buckling limits, and even in their post-buckling regime, therefore significantly reducing their mass. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Large times existence for thin vibrating rods

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for arbitrarily large times, if the diameter of the cross section is chosen sufficiently small. The scaling regime is such that the limiting equations are linear.

Occult pediatric skull fracture and implications for delay in diagnosis: illustrative case.

After being struck in the left side of the head by a thin metal rod, a 10-year-old, previously healthy male presented to an urgent care clinic with a subcentimeter scalp laceration in the midline parietal area and a normal neurological exam. Evaluation included skull radiographs, which did not demonstrate a definitive fracture. Following laceration repair, the patient was discharged to home. Subsequently, progressive neurological symptoms prompted his family to bring him back for evaluation 2 days later, and computed tomography (CT) and magnetic resonance imaging (MRI) revealed an open, depressed skull fracture. Surgical intervention was performed with debridement and closure. The patient was placed on a course of intravenous antibiotics and had no subsequent evidence of infection. In cases involving potential cranial perforation by a thin projectile, use of CT imaging or MRI, rather than plain radiographs, may prevent a delay in diagnosis and subsequent complications.

Tracking the histories of individual fuel particles in packed bed combustion

This paper introduces a simple technique for sampling individual fuel particles at various stages in overfeed packed bed combustion. A particle is secured to the end of a thin stainless steel rod, which is then used to track the motion of the particle and to remove it from the bed for sampling at the desired time. The particles so tracked provide a record of changes in mass, volume, density, and individual dimensions as combustion proceeds in the bed. Results of a number of experiments of this sort on the packed bed combustion of parallelepipedal wood particles are presented, which among other things show that particle shrinkage during pyrolysis is generally – but not always – largest along the direction of the wood grain and less in the cross-grain directions. The “tracker rod” technique has the advantage over single particle experiments in a furnace that the particles are exposed to the varying and non-uniform conditions in the actual packed bed of fuel; it is, however, only suited to fixed beds, not fluidized or moving beds.

Suppression of Leidenfrost instability using multiple rods and rectangular mesh elements

Large Leidenfrost drops may be unstable when their diameters exceed a critical value. Through theoretical and experimental investigations, this study explored the feasibility of suppressing Leidenfrost instability in a large container, by meshing the container or its central portion into rectangular elements. Thin rods were used to construct these rectangular elements. Leidenfrost instability was considered in four rectangular configurations. They were also the rectangular mesh elements that might be used. There were two findings. First, the diameter of the largest inscribed cylinder in a rectangular configuration was the critical dimension for determining Leidenfrost instability. Second, the threshold value of this diameter in a rectangular configuration with rod(s) was 8.9λ ± 0.7λ, where λ is the capillary length of water. It was larger than its counterparts in both a rectangular container (without the presence of a rod) and a circular container (with or without the presence of a rod), due to the strong effect of the rod in a rectangular configuration. Based on these two findings, a large rectangular container was meshed into rectangular elements using thin rods, with the diameter of the largest inscribed cylinder in each element below the threshold value. This mesh method suppressed the Leidenfrost instability in the large container.