Rod Of Length Research Articles

Automation studies of thermo-stressed state of the core when exposed to local heat fluxes, heat transfer

Many load-bearing elements of power plants are influenced by local heat flows and convective heat exchangers. Because of this, a deformed thermostress state is formed in the bearing elements in the form of a rod of limited length. Therefore, it is important to develop special computational algorithms and corresponding programs for automated research of rods of limited length. At the same time, the developed system must take into account the physical-mechanical and geometric characteristics of the studied core and the simultaneous presence of local convective heat exchange.This work uses the fundamental laws of energy saving. The developed calculation algorithm is implemented in the form of an IBM PC Python program. The results are presented in tables.

One-dimensional thermal shock problem for a semi-infinite hygrothermoelastic rod

The present research article deals with the study of a boundary value problem of a one-dimensional semi-infinite hygro-thermoelastic rod of length l. The deformation of the rod is under consideration when the left boundary of the hygro-thermoelastic rod is subjected to a sudden heat source. The solutions of the considered variables are decomposed in terms of normal modes. Analytical expressions of displacement, moisture concentration, temperature field, and stresses are obtained and presented graphically for different periods. By studying the one-dimensional thermal shock problem for a semi-infinite hygrothermoelastic rod, the authors aim to gain insights into the fundamental behavior of materials subjected to rapid temperature changes and moisture effects.

First Frequency of Longitudinal Vibration of a Rod with Mass at one End and Partial Placement on Piecewise-Homogeneous Elastic Foundation

Statement of the problem. Despite the introduction of engineering practice of numerical methods for the calculation, in a case of engineering problems associated with extended structures, the well-known models «rod on an elastic foundation» and «beam on an elastic foundation» are widely used to describe the behavior of structures. Most of the known solutions were obtained in the conditions of an idealized setting and without differences in the properties of the foundation. This work is devoted to the study of the dynamics of a rod of finite length with a point mass at the end and partially placement on a piecewise-homogeneous elastic foundation, formed by two sections of different stiffness. The aim of this study is to obtain analytical dependences for the first frequency of the longitudinal vibrations of a rod with different boundary conditions at its ends: rigid support and free end. The available research results are obtained for special cases, which makes them difficult to apply in practice. To assess the influence of the inertial pro-perties of the foundation, the case with different linear masses of the rod in the pinched and cantilever sections is considered. Results. Using the Ritz method analytical dependences were obtained for the determination of the first frequency of the longitudinal vibrations of a fix and free rod with a point mass at the end and partially placement on a piecewise-homogeneous elastic foundation formed by two sections of different stiffness. Quantitative evaluation shows good agreement with those of other studies. The results for particular cases are obtained. Conclusions. It is shown that the first natural frequency of longitudinal oscillations is in a certain range and in the nonlinear ratios depending on the lengths of the sections various elastic. The inertial properties of the foundation leads to a decrease in the first frequency.

Impact of rigid body and viscous-plastic rod of finite length

The impact of a rigid body and a rod of finite length made of a viscoplastic incompressible material moving towards each other at constant velocity is studied in the article. One-dimensional motion is considered, i.e., velocity, stress, and other parameters are considered to be averaged over the rod section. According to the model of a viscous-plastic material, the rod is divided into two parts: the region of plastic strain and the region that moves as a solid body after impact. The boundary between these regions is unknown and needs to be determined. As a result, we arrive at a problem with a free boundary, a well-known example of which is the Stefan problem. However, the formulation of the problem under consideration differs significantly from the Stefan problem. In addition, the function to be determined that describes the unknown boundary, in contrast to the Stefan problem, is not explicitly present in the boundary conditions. There are various numerical methods for solving problems with an unknown moving boundary. However, as is known, implementing these methods is associated with significant difficulties. In this article, the method of integral relations is used - a modification of the Karman-Pohlhausen method known in the boundary layer theory. The problem is reduced to the Cauchy problem for a system of nonlinear ordinary differential equations proposed to be solved by successive approximations and the Runge-Kutta method. Numerical calculations were performed. The influence of changes in the mass and magnitude of the velocities of the rod and rigid body on the size of the plastic strain region and the change in stresses on the contact surface is revealed.

LONGITUDINAL TRANSIENT VIBRATIONS OF A FINITE MOMENT ELASTIC ROD

Non-stationary longitudinal vibrations of a moment elastic rod of finite length are investigated. To describe the motion of the rod, the system of equations of the general model of moment elastic thin bodies is used without additional hypotheses. The equations of this model take into account longitudinal movements, changes in the angle of independent microrotation, as well as transverse compression of the rod. The rod material is assumed to be homogeneous and isotropic. The system of equations of motion is supplemented by physical relations that describe the relationship of displacements, changes in angles and transverse compression with forces. In contrast to classical models, in addition to normal forces, additional force factors arise in a moment rod. They are: additional moments, moment cutting forces, moments of moment stresses. Accordingly, in addition to the elastic constants of the material, additional physical parameters of the medium are taken into account, which are necessary when taking into account moment effects in the material. The conditions of generalized hinged support are used as boundary conditions at the ends of the rod. The initial conditions are assumed to be zero. To construct the solution, expansions of the desired functions and the external load into trigonometric Fourier series are used. Substituting these expansions into the original relations leads to a system of equations for the coefficients of time-dependent series. To solve it, the integral Laplace transform a in time is used. As a result, expressions for the required coefficients of expansion series in the image space are found. Each of these expressions is the sum of three products. The factors in these products are the Laplace images of the coefficients of the Fourier expansions for the load and for the influence functions. Influence functions are fundamental solutions (Green's functions) of the problem under study. The original coefficients of the series for the influence functions are found analytically using residues. The final expressions for the coefficients of the expansion series of solutions have the form of convolutions in time. The cores of these integral representations are the original coefficients of the series for the influence functions. As an example, the response of a moment elastic rod to the action of a non-stationary axial load is considered. The results obtained are illustrated graphically. The practical convergence of expansion series is estimated.

Transverse vibrations of underground pipeline with pinched ends

The study of transverse oscillations of extended underground structures from the action of constant harmonic forces is of practical interest. Transverse vibrations of an underground cylindrical structure of finite length under the action of a system of concentrated forces that change according to a harmonic law are considered. The environment surrounding the structure is assumed to be elastic, while the interaction of the “environment-structure” system is studied. When considering the problem, the Fourier method and the results of solving the problem of vibrations of an unbounded cylindrical structure in an elastic medium from the action of concentrated harmonic forces were used. The problem of transverse vibrations of a cylindrical rod of finite length interacting with an elastic homogeneous medium is solved by the method of compensating loads. In this case, the structure is considered a source of waves radiated into space and satisfying the conditions of radiation to infinity. The resulting solution is approximate and reliable within the length of the rod. The analysis of the influence of soil conditions and geometric dimensions on the amplitude of oscillations of an underground structure was carried out according to the graphs of the amplitude-frequency characteristic of the object.

The Physical Pendulum: An Illustrative Teaching Laboratory Example Using a Long Rod

Here, a relatively simple laboratory experiment of a physical pendulum, suitable for students of science and engineering in the first courses of university physics, is presented to illustrate its dynamic behavior and to determine its inertia moment. To this end, a long wooden rod of length L = 99.8 cm and cross-section radius R = 1.73 cm was used as the physical pendulum. The period of oscillation was measured as a function of the distance from the rotation axis to the center of mass. It is shown that the oscillation period is a superposition of two contributions, namely, a linear and a hyperbolic function, which has a minimum at the distance hmin=I0/M, where I0 is the moment of inertia of the rod about the rotation axis at its center of mass, and M is its mass. It is further shown that this quantity is independent of mass for all bodies of constant density, and a numerical method is applied to obtain the moment of inertia of the rod. Results obtained from a laboratory experiment agree with the expected one within 4%.

Green hydrothermal synthesis of Ga doping derived 3D ZnO nanosatellites for high sensitive gas sensors

A green hydrothermal synthesis methodology is employed for the synthesis of Ga3+ doped ZnO 3D nanosatellite structures. XRD technique exposed the hexagonal wurtzite type crystal structure of the 3D Ga3+ doped ZnO nanostructures. Ga3+ induced 3D morphology evolution in accordance to Ga doping concentration is realized via. the FESEM images. The FESEM images indicated one sided capped rod like structures (50–250 nm) in pristine ZnO, whereas 3D satellite kind of morphology (>500 nm) was observed in 5% Ga3+ doped ZnO structures. TEM images revealed physical specifications of 3D nanosatellite structures exposing the central rod of 500 nm length & 250 nm in width and the branch rods grown vertical to the central rod of length 300 nm and width of 50 nm. Further, optical absorbance and photoluminescence spectra confirmed the electron rich state of ZnO with Ga3+ doping. The gas sensing performance has shown selectivity toward CO gas at a working temperature of 250 ⁰C. High CO sensing was recorded for 5% Ga3+ doped ZnO 3D nanosatellites with attractive sensing characteristics such as good response, fast response time & fast recovery time.

Light total velocity and speed: Aspects of special relativity through four centuries

Early descriptions of relative states of motion by Isaac Newton (1714) apply to modern diagrams depicting special relativity for light. True time is absolute and was distinguished from measured time, which is relative and subject to error. The time for light to pass a receding rod of length r is a single specific value regardless of the state of motion of an observer or detector and is not simply r/c as claimed in 1905 for an observer in motion. The assumption that the distance light actually travels unattached to physical objects is merely the length of the rod reflect errors of perception by the observer/detector unable to sense motion of the rod. The true time is absolute and would be properly computed and observed with respect to a position truly at rest in space. Light speed is fixed at c with respect to itself, or its own instantaneous position at any time, regardless of motion of source or observer. But relative velocity of moving objects with respect to light depend on the velocity of the object. Time dilation refers to the extent that a time measurement is in error due to motional effects of detectors, clocks, or observers, and does not mean that motion causes the time for a single event to be different than its true absolute magnitude. A single event requires a single amount of time, regardless of the amount claimed by observers in relative states of motion who do not control the event.

Application of the depth-averaged liquid film model to the annular flow regime in BWR fuel assemblies

The flow regime found in the downstream half of the BWR assembly can be described as an annular film flow with a central core of vapour with suspended droplets. This study presents the application of the fluid film model available in STAR-CCM+ to analyze the interplay between the vapour flow and the liquid film dynamics. The film model, based on depth-averaged equations, can be used to simulate film depth and velocity over complex geometries. Built on sound mathematical basis and applied to a wide variety of areas, the fluid film model, however, has not been widely used to study annular flow in nuclear fuel assemblies. Applying this model to a simplified geometry of a single rod with different gaps, the basic relationship between the vapour velocity, liquid film thickness and velocity distribution along the circumference of the rod is clarified. The minimum vapour velocity required to transport a liquid film along the surface of a fuel rod of a specific length against gravity was found using first-principles force balances. The model was then applied to a real, but simplified assembly geometry where the resulting flow pattern was primarily affected by the presence of part length rods. The minimum velocity required to transport a liquid film along the fuel rods in the assembly against gravity was found to be close to the range of velocities obtained using sub-channel codes. Strong circumferential variation in the wall shear across a short arc-length was observed for some fuel rods. The variation in wall shear also results in a corresponding variation in film velocity and film thickness and presumably has a strong impact on the local heat and mass-transfer characteristics. Cross flow from high resistance regions in the assembly towards lower resistance regions has a strong impact in terms of variations in the film thickness on the rods that are the furthest away from the low resistance paths.The modelling palette for the depth-averaged film model contains several features that can extend the validity of the modelling used in this study, such as the presence of droplets in the vapour core, deposition of droplets on to the film, heat transfer and boiling, and the influence of spacers in disrupting the liquid film. These features were not considered in this study and remain avenues for future work. The use of time-averaged turbulence modelling results in damping of unsteadiness of the vapour flow and perturbations in the film thickness. For better estimates of unsteady effects use of turbulence models such as the Large Eddy Simulation method is recommended. Current state-of-the-art in predicting dispersed annular flow using liquid film models is limited to single rods. The generalized depth-averaged film model can be applied to complex geometries including the effect of spacers.

Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan

We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact – namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of finite length wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the classic capstan problem to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan.

Investigation of dependence of solar-pumped laser power on laser medium length

The efficiency of solar-pumped lasers (SPLs) is limited when the length of the laser medium is unsuitable. This is because superfluous regions in the laser medium introduce losses and contribute slightly to the stimulation of radiation in the laser resonator. Before designing an SPL, an appropriate length of laser medium is critical. We present a method to calculate the optimal length of the gain medium in SPLs by exploring the relationship between the absorbed solar power and material loss for different laser medium lengths. Thus, the lengths of Nd:YAG crystals with diameters of 3 to 6 mm were optimized, and the output characteristics were calculated numerically. The maximum collection efficiency (CE) (40.1 W / m2) was obtained for the 5.5-mm diameter Nd:YAG crystal rod of length 21.1 mm, which was 1.7 W / m2 higher than the previous numerical record. The optimal length of the 6-mm diameter Nd:YAG crystal rod was found to be 21.9 mm. For a laser rod of this length, a CE of 36.3 W / m2 is expected. This value is 1.13 times greater than the existing experimental record for the Nd:YAG crystal of the same diameter, which highlights the importance of optimizing the length of the laser rod.

An approach for recovering initial temperature via a bounded linear time sampling

We have improved the results of DeVore and Zuazua's work in [6] and addressed some questions posed in their paper. By constructing a linearly growing finitely many future times in a bounded interval, we have improved their result of recovering initial temperature profile from known temperature measurements at a fixed location of a body and at finitely many later times. More explicitly, we have constructed a finitely many times with a linear growth in a bounded interval such that the temperature measurements taken at a fixed location of a thin uniform homogeneous rod of length π and at these finite time instances lead to a recovery of the initial temperature profile with a desired accuracy provided the initial temperature is in a suitable closed subset of L2[0,π].

Fractional Burgers wave equation on a finite domain

Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the displacement and stress of an arbitrary rod’s point as a convolution of the boundary forcing and solution kernel. Thermodynamically consistent Burgers models are adopted as the constitutive equations describing mechanical properties of the rod. Short-time asymptotics implies the finite wave propagation speed in the case of the second class models, contrary to the case of the first class models. Moreover, Burgers model of the first class yield quite classical shapes of displacement and stress time profiles resulting from the boundary forcing assumed as the Heaviside function, while model of the second class yield responses that resemble to the sequence of excitation and relaxation processes.

PUBIC SYMPHYSIS DIASTASIS TREATED WITH ANTERIOR SUBCUTANEOUS INTERNAL PELVIC FIXATOR A CASE REPORT

This is a new method of treatment for Pubic Symphysis diastasis with anterior subcutaneous pelvic internal fixation (later called as INFIX) using pedicle screws and a spinal rod. Pedicle screw and Spinal rod was used to address shortcomings of external fixation (EXFIX).Pedicle screws were passed into AIIS through small incision. Contoured Spinal rod of suitable length passed across the lower abdominal wall in subcutaneous plane, compression achieved manually and rod connected to screws and tightened. Patient is able to tolerate implants and is able to sit, stand and walk without difficulty. Complications include lateral femoral cutaneous nerve irritation, which resolved after 5weeks. Appearance of INFIX provides a new alternative treatment; INFIX is minimally invasive and time-saving for treatment of anterior pelvic ring injuries. The EXFIX is an effective tool for anterior ring fixation and has been widely used. However, it is associated with many complications such as pin-track infection, aseptic loosening and loss of reduction. INFIX is less disabling for treatment of Pubic Symphysis Diastasis.

On one problem, associated with lateral oscillations of elastic-viscous-relaxating rod

We obtain the solution of the problem about lateral oscillations of elastic-viscous-relaxating rod of finite length, variable profile, and variable momentum of rotation inertia of rod elements about the axis that is perpendicular to oscillation plane.

Analysis of the process of deployment of a lunar tether system taking into account the Earth's gravity

The development of space transport systems for the delivery of payloads and the study of the lunar surface is an important scientific and technical challenge. The article considers a near-lunar space tether system consisting of a station and a microsatellite. The station is considered as a rigid body having a cylindrical shape, and the microsatellite is considered as a spherical rigid body. The tether is considered as a weightless inextensible rod of variable length. The station moves in a near-lunar orbit, which is influenced by the Earth's gravity. The process of deployment of a radially directed near-lunar tether system is considered. The equations of motion of the space tether system are obtained using Newton's second law and the theorem on the change in the angular momentum. To release the tether and bring the orbital tether system to a working state, the article proposes to use the control program of tethers tension force, which ensures the deployment of the tether system to a position close to the vertical. A comparison of the motion of the tether system along the unperturbed lunar orbit and along the perturbed one, taking into account the gravitational influence of the Earth, is made. To substantiate the theoretical results, a numerical simulation was carried out, based on the results of which a conclusion was made about the influence of the Earth's gravity on the amplitude of oscillations of the microsatellite relative to the local vertical.

A New Frame for Orienting Infants With Cleft Lip and Palate During 3-Dimensional Facial Scanning.

Nonradiographic 3-D assessment of soft tissue facial structures is an ideal tool to measure 3-D facial change and smartphone apps like Bellus 3D have brought these technologies to our doorsteps. Although this app works well for adults, it doesn't do so well with infants as their stabilization is difficult thus proper alignment becomes problematic often leading to distortion. This seriously hampers the repeatability and reliability of the whole process. A stainless steel rod of 150-cm length is curved into a semicircle of a radius of 42.5 cm. Bases are fabricated at both the ends to firmly hold the stand on the table. A Teflon ring of one inch is made for adjusting the diameter of the camera holder. A camera holder is then attached to the Teflon ring. The mobile holder mounted is free to move within the arc. A 3-D facial scan of a single patient was carried out with the camera mounted on the frame and once without the frame. The same was compared using side-by-side comparison and superimposition of the .STL files from the frontal, profile, and worm's eye view. It was found that considerable distortion was noted around the nasal and paranasal areas when the scan was performed without the frame as compared to the one that was taken with the frame. This technique avoided distortion and the difficulty in turning the baby's head to record the lateral portion of the face.

Analytical Solution vs. Numerical Solution of Heat Equation Flow Through Rod of Length 8 Units in One Dimension

The paper presented the basic treatment of the solution of heat equation in one dimension. Heat is a form of energy in transaction and it flows from one system to another if there is a temperature difference between the systems. Heat flow is the main concern of sciences which seeks to predict the energy transfer which may take place between material bodies as result of temperature difference. Thus, there are three modes of heat transfer, i.e., conduction, radiation and convection. Conduction can be steady state heat conduction, or unsteady state heat conduction. If the system is in steady state, temperature doesn’t vary with time, but if the system in unsteady state temperature may varies with time. However, if the temperature of material is changing with time or if there are heat sources or sinks within the material the situation is more complex. So, rather than to escape all problem, we are targeted to solve one problem of heat equation in one dimension. The treatment was from both the analytical and the numerical view point, so that the reader is afforded the insight that is gained from analytical solution as well as the numerical solution that must often be used in practice. Analytical we used the techniques of separation of variables. It is worthwhile to mention here that, analytical solution is not always possible to obtain; indeed, in many instants they are very cumber some and difficult to use. In that case a numerical technique is more appropriate. Among numerical techniques finite difference schema is used. In both approach we found a solution which agrees up to one decimal place.

Motion equations of a pendulum gear system

This work presents a dynamic system that is composed of gears which have an angular velocity . Each of the gears was added a rod of known length and mass which can move freely. This system can move in such a way that the rods oscillate as the gears rotate. With the Lagrangiana formulation, the motion equations that govern the system were built, differential equations were solved with standardized numerical methods and graphs were obtained in different phase spaces.