Laplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.
A system for precise angular laser beam deflection by using a plane mirror is presented. The mirror was fixed to two supports attached to its edges. This article details the theoretical basis of how this deflector works. The spring deflection of a flat circular metal plate under a uniform axial buckling was used and the mechanical stress was generated by a piezoelectric layer. The characteristics of the deformation of the plate versus the voltage control of the piezoelectrics were examined and the value of the change resolution possible to obtain was estimated. An experimental system is presented and an experiment performed to examine this system. As a result, a resolution of displacement of 10-8 rad and a range of 10-5 rad were obtained.
Assessment of the flexural buckling resistance of bisymmetrical I-section beam-columns using FEM is widely discussed in the paper with regard to their imperfect model. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode’s general method. Various imperfection profiles are considered. The global effect of imperfections on the real compression members behaviour is illustrated by the comparison of imperfect beam-columns resistance and the resistance of their perfect counterparts. Numerous FEM simulations with regard to the stability behaviour of laterally and torsionally restrained steel structural elements of hot-rolled wide flange HEB section subjected to both compression and bending about the major or minor principal axes were performed. Geometrically and materially nonlinear analyses, GMNA for perfect structural elements and GMNIA for imperfect ones, preceded by LBA for the initial curvature evaluation of imperfect member configuration prior to loading were carried out. Numerical modelling and simulations were conducted with use of ABAQUS/Standard program. FEM results are compared with those obtained using the Eurocode’s interaction criteria of Method 1 and 2. Concluding remarks with regard to a necessity of equivalent imperfection profiles inclusion in modelling of the in-plane resistance of compression members are presented.
The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defining the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.
This paper presents the beam tracing with refraction method, developed to examine the possibility of creating the beam tracing simulation of sound propagation in environments with piecewise non- homogenous media. The beam tracing with refraction method (BTR) is developed as an adaptive beam tracing method that simulates not only the reflection but also the refraction of sound. The scattering and the diffraction of sound are not simulated. The BTR employs 2D and 3D topology in order to efficiently simulate scenes containing non-convex media. After the beam tracing is done all beams are stored in a beam tree and kept in the computer memory. The level of sound intensity at the beginning of each beam is also memorized. This beam data structure enables fast recalculation of results for stationary source and geometry. The BTR was compared with two commercial ray tracing simulations, to check the speed of BTR algorithms. This comparison demonstrated that the BTR has a performance similar to state-of- the-art room-acoustics simulations. To check the ability to simulate refraction, the BTR was compared with a commercial Finite Elements Method (FEM) simulation. In this comparison the BTR simulated the focusing of the ultrasound with an acoustic lens, with good accuracy and excellent performance.
In this study, free and forced vibration responses of carbon nanotube reinforced uniform and tapered composite beams are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced uniform and tapered composite beams are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available in literature. Various parametric studies are also performed to investigate the effect of aspect ratio, percentage of CNT content, ply orientation, and boundary conditions on natural frequencies and mode shapes of a CNT reinforced composite beam. It was observed that the addition of carbon nanotube in fiber reinforced polymer composite (FRP) beam enhances the stiffness of the structure which consequently increases the natural frequencies and alters the mode shapes.
Image-guided High Intensity Focused Ultrasound (HIFU) technique is dynamically developing technology for treating solid tumors due to its non-invasive nature. Before a HIFU ablation system is ready for use, the exposure parameters of the HIFU beam capable of destroying the treated tissue without damaging the surrounding tissues should be selected to ensure the safety of therapy. The purpose of this work was to select the threshold acoustic power as well as the step and rate of movement of the HIFU beam, generated by a transducer intended to be used in the HIFU ablation system being developed, by using an array of thermocouples and numerical simulations. For experiments a bowl-shaped 64-mm, 1.05 MHz HIFU transducer with a 62.6 mm focal length (f-number 0.98) generated pulsed waves propagating in two-layer media: water/ex vivo pork loin tissue (50 mm/40 mm) was used. To determine a threshold power of the HIFU beam capable of creating the necrotic lesion in a small volume within the tested tissue during less than 3 s each tissue sample was sonicated by multiple parallel HIFU beams of different acoustic power focused at a depth of 12.6 mm below the tissue surface. Location of the maximum heating as well as the relaxation time of the tested tissue were determined from temperature variations recorded during and after sonication by five thermo-couples placed along the acoustic axis of each HIFU beam as well as from numerical simulations. The obtained results enabled to assess the location of each necrotic lesion as well as to determine the step and rate of the HIFU beam movement. The location and extent of the necrotic lesions created was verified using ultrasound images of tissue after sonication and visual inspection after cutting the samples. The threshold acoustic power of the HIFU beam capable of creating the local necrotic lesion in the tested tissue within 3 s without damaging of surrounding tissues was found to be 24 W, and the pause between sonications was found to be more than 40 s.
What is the limit of improvement the structure obtained directly from the liquid state, with possible heat treatment (supersaturation and aging)? This question was posed by casting engineers who put arbitrary requirements on reducing the DAS (Dendrite Arm Spacing) length to less than a dozen microns. The results of tests related to modification of the surface microstructure of AlSi7Mg alloy casting treated by laser beam and the rapid remelting and solidification of the superficial casting zone, were presented in the paper. The local properties of the surface treated with a laser beam concerns only a thickness ranging from a fraction to a single mm. These local properties should be considered in the aspect of application on surfaces of non-machined castings. Then the excellent surface layer properties can be used. The tests were carried out on the surface of the casting, the surface layer obtained in contact with the metal mould, after the initial machining (several mm), was treated by the laser beam. It turned out that the refinement of the microstructure measured with the DAS value is not available in a different way, i.e. directly by casting. The experimental-simulation validation using the Calcosoft CAFE (Cellular Automaton Finite Element) code was applied.
The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics. Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points. Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.
In the paper, the method of a numerical simulation concerning diagonal crack propagation in con-crete beams was presented. Two beams reinforced longitudinally but without shear reinforcement were considered during the Finite Element Method analysis. In particular, a nonlinear method was used to simulate the crack evaluation in the beams. The analysis was performed using the commercial program ANSYS. In the numerical simulation, the limit surface for concrete described by Willam and Warnke was applied to model the failure of concrete. To solve the FEM-system of equations, the Newton-Raphson method was used. As the results of FEM calculations, the trajectories of total stains and numerical images of smeared cracks were obtained for two analyzed beams: the slender beam S5 of leff = 1.8 m and the short beam S3k of leff = 1.1 m. The applied method allowed to generate both flexural vertical cracks and diagonal cracks in the shear regions. Some differences in the evaluation of crack patterns in the beams were observed. The greater number of flexural vertical cracks which penetrated deeper in the beam S5 caused the lower stiffness and the greater deformation in the beam S5 compared to the short beam S3k. Numerical results were compared with the experimental data from the early tests performed by Słowik . The numerical simulation yielded very similar results as the experiments and it confirmed that the character of failure process altered according to the effective length of the member. The proposed numerical procedure was successfully verified and it can be suitable for numerical analyses of diagonal crack propagation in concrete beams.
The paper presents a study of a possible application of structure embedded piezoelectric actuators to enhance the performance of a rotating composite beam exhibiting the coupled flexural-flexural vibrations. The discussed transversal and lateral bending modal coupling results from the directional properties of the beam's laminate and ply stacking distribution. The mathematical model of the beam is based on an assumption of cross-sectional non-deformability and it incorporates a number of non-classical effects. The final 1-D governing equations of an active composite beam include both orthotropic properties of the laminate and transversely isotropic properties of piezoelectric layers. The system's control capabilities resulting from embedded Macro Fiber Composite piezoelectric actuators are represented by the boundary bending moment. To enhance the dynamic properties of the composite specimen under consideration a combination of linear proportional control strategies has been used. Comparison studies have been performed, including the impact on modal coupling magnitude and cross-over frequency shift.
In this paper an alternative procedure to vibro-acoustics study of beam-type structures is presented. With this procedure, it is possible to determine the resonant modes, the bending wave propagation velocity through the study of the radiated acoustic field and their temporal evolution in the frequency range selected. As regards the purely experimental aspect, it is worth noting that the exciter device is an actuator similar to is the one employed in distributed modes loudspeakers; the test signal used is a pseudo random sequence, in particular, an MLS (Maximum Length Sequence), facilitates post processing. The study case was applied to two beam-type structures made of a sandstone material called Bateig. The experimental results of the modal response and the bending propagation velocity are compared with well-established analytical solution: Euler-Bernoulli and Timoshenko models, and numerical models: Finite Element Method – FEM, showing a good agreement.
This paper presents two methods for evaluation of the effective wavenumber of nearly-Gaussian beams in laser interferometers that can be used for determination of a so called diffraction correction in absolute gravimeters. The first method, that can be simply used in situ, is an empirical procedure based on the evaluation of the variability of g measurements against the amount of light limited by an iris diaphragm and transmitted to a photodetector. However, precision of this method depends on the beam quality similarly as in the case of the conventional method based on measurement of a beam width. The second method, that is more complex, is based on beam profiling in various distances and on calculation of the effective wavenumber using the second spatial derivative of a non-ideal beam field envelope. The measurement results achieved by both methods are presented on an example of two absolute gravimeters and the determined diffraction corrections are compared with the results obtained by measurements of beam width. Agreement of methods within about 1 mGal have been obtained with average diffraction corrections slightly exceeding +2 mGal for three FG5(X) gravimeter configurations.
Electron beam melting(EBM) is a useful technique to obtain high-purity metal ingots. It is also used for melting refractory metals such as tantalum, which require melting techniques employing a high-energy heat source. Drawing is a method which is used to convert the ingot into a wire shape. The required thickness of the wire is achieved by drawing the ingot from a drawing die with a hole of similar size. This process is used to achieve high purity tantalum springs, which are an essential component of lithography lamp in semiconductor manufacturing process. Moreover, high-purity tantalum is used in other applications such as sputtering targets for semiconductors. Studies related to recycling of tantalum from these components have not been carried out until now. The recycling of tantalum is vital for environmental and economic reasons. In order to obtain high-purity tantalum ingot, in this study impurities contained in the scrap were removed by electron beam melting after pre-treatment using aqua regia. The purity of the ingot was then analyzed to be more than 4N5 (99.995%). Subsequently, drawing was performed using the rod melted by electron beam melting. Owing to continuous drawing, the diameter of the tantalum wire decreased to 0.5 mm from 9 mm. The hardness and oxygen concentration of the tantalum ingot were 149 Hv and less than 300 ppm, respectively, whereas the hardness of the tantalum wire was 232.12 Hv. In conclusion, 4N5 grade tantalum wire was successfully fabricated from tantalum scrap by EBM and drawing techniques. Furthermore, procedure to successfully recycle Tantalum from scraps was established.
The first order variation of critical loads of thin-walled columns with bisymmetric open cross-sectiondue to some variations of the stiffness and location of bracing elements is derived. The con-siderations are based on the classical linear theory of thin-walled beams with non-deformablecross-section introduced by Vlasov . Both lateral braces and braces that restraint warping andtorsion of the cross-section have been taken into account. In the numerical examples dealing withI-column, the functions describing the influence of location of the braces with unit stiffness on thecritical load of torsional and flexural buckling are derived. The linear approximation of the exactrelation of the critical load due to the variation of the stiffness and location of braces is determined.
Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.
This paper is devoted to the application of ultrasonic wave propagation phenomena for the diagnostics of prestressed, concrete, bridge T-beams. A multi-point damage detection system is studied with use of numerically obtained data. The system is designed to detect the presence of the material discontinuities as well as their location.
For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently uses two forms of approximation function (moving least squares and kernel approximation functions) and two types of formulations, namely the weak form and collocation technique, respectively, to reproduce Element Free Galerkin (EFG) and Smooth Particle Hydrodynamics (SPH) meshless methods. The numerical implementation for beam problems of these two formulations is discussed and numerical tests are presented to illustrate the difference between the formulations.
This study aims to evaluate the efficiency of strengthening reinforced concrete beams using some valid strengthening materials and techniques. Using concrete layer, reinforced concrete layer and steel plates are investigated in this research. Experiments on strengthening beam samples of dimensions 100x150x1100 mm are performed. Samples are divided in to three groups. Group “A” is strengthened using 2 cm thickness concrete layer only (two types). Group “B” is strengthened using 2 cm thickness concrete layer reinforced with meshes (steel and plastic). Group “C” is strengthened using steel plates. The initial cracking load, ultimate load and crack pattern of tested beams are illustrated. The experimental results show that for group A and B, the ultimate strength, stiffness, ductility, and failure mode of RC beams, with the same thickness strengthening layer applied, will be affected by the mesh type, type of concrete layer. While for group C, these parameters affected by the fixation technique and adhesion type.
The paper describes an experimental behaviour of the basalt fibre reinforced polymer composite by external strengthening to the concrete beams. The BFRP composite is wrapped at the bottom face of R.C beam as one layer, two layers, three layers and four layers. The different characteristics – are studied in – first crack load, ultimate load, tensile and compressive strain, cracks propagation, crack spacing and number of cracks etc. To – investigate, total of five beams size 100×160×1700 mm were cast. One beam is taken as control and others are strengthened with BFRP composite with layers. From this investigation, the first crack load is increased depending on the increment in layers from 6.79% to 47.98%. Similarly, the ultimate load carrying – capacity is increased from 5.66% to 20%. The crack’s spacing is also reduced with an increase in the number of layers.
By the method of modern physical material science (optic microscopy scanning and transmission electron microscopy) the analysis of structural phase states, the morphology of the second phase inclusions and defect substructure of Al-Si alloy (silumin) of hypoeutectic composition, subjected to electron beam processing was done with the following parameters: energy density 25-35 J/cm2, beam length 150 μs, pulse number – 3, pulse repetition rate – 0.3 Hz, pressure of residual gas (argon) 0.02 Pa. The surface irradiation results in the melting of the surface layer, the dissolution of boundary inclusions, the stricture formation of high speed cellular crystallization of submicron sizes, the repeated precipitation of the second phase nanodimentional particles. With the increased distance from the irradiation surface the layer containing the second phase inclusions of quasi-equilibrium shape along with the crystallization cells was revealed. It is indicative of the processes of Al-Si alloy structure globalization on electron beam processing.
The results of bearing capacity, deformability and fracture toughness of reinforced concrete beams with the external reinforcement in the form of steel cut and stretchy sheet, obtained due to the conducting of the experiment and mathematical simulation which were made of concrete of C40/50 class are given in the article. Mathematical simulation of beam structures is done on the basis of the deformation model which allows to conduct calculations of the unified methodological positions of different elements with diverse configuration of cross section and reinforcement as well as take into consideration elastic and plastic properties of concrete and reinforcement, assessing the actual stress-strain state of sections of reinforced concrete elements at different loading levels, including ultimate one. The deformation model is based on the actual diagrams use of concrete and reinforcement materials deformation and conditions of efforts balance in the normal section and hypothesis of flat sections. The theoretical value of bearing capacity and deformability, obtained as a result of the mathematical simulation was compared to the experimental data. The satisfactory coincidence of the mathematical calculation of bearing capacity, deformability, fracture toughness and experimental data gives an opportunity to use the algorithm not only for beam structures with bar reinforcement but also for beam structures with the external reinforcement in the form of steel cut and stretchy sheet.
This paper presents experimental observation of nonlinear vibrations in the response of a flexible cantilever beam to transverse harmonic base excitations around its flexural mode frequencies. In the experimental setup, instead of manual control of the signal excitation frequency and amplitude, a closed-loop vibration system is used to keep the excitation amplitude constant during the frequency sweep and to increase confidence in the experimental results. The experimental results show the presence of the third mode in the response when varying the excitation frequency around the fourth mode. The frequency-response curves, response spectrum and Poincaré plots were used for characterization of nonlinear dynamic behaviour of the beam.
An active beam-pointing stabilization system has been developed for a high-power KrF laser system to eliminate the long-term drift of the directional change of the beam in order to have a stable focusing to a high intensity. The control of the beam direction was achieved by a motor-driven mirror activated by an electric signal obtained by monitoring the position of the focus of the output beam. Instead of large sized UV-sensitive position sensitive detectors a simple arrangement with scatter plates and photodiodes are used to measure the directionality of the beam. After the beam stabilization the long-term residual deviation of the laser shots is ~14 μrad, which is comparable to the shot-to-shot variation of the beam (~12 μrad). This deviation is small enough to keep the focal spot size in a micrometer range when tightly focusing the beam using off-axis parabolic mirrors.
The double barrier separate confinement heterostructure (DBSCH) design aimed at reduction of vertical beam divergence and increase of catastrophic optical damage (COD) level for high power laser diodes (LDs) operation is presented. Insertion of thin, wide-gap barrier layers at the interfaces between waveguide and cladding layers of SCH gives an additional degree of freedom in design making possible more precise shaping of the optical field distribution in the laser cavity. By comparison with the large optical cavity (LOC) heterostructure design it has been shown that the low beam divergence emission of DBSCH LDs can be attributed to the soft-profiled field distribution inside the cavity. This soft mode profile seems to determine narrow laser beam emission rather than the field distribution width itself. The potential problem with the soft-profiled but relatively narrow (at half-maximum) mode distribution is a lower COD level. Widening of the mode profile by the heterostructure design corrections can increase it, but care must be taken to avoid excessive decrease of confinement factor (Γ). As a result it is shown that DBSCH design is possible, where the low beam divergence and high COD level is achieved simultaneously. Wide stripe gain-guided LDs based on GaAsP/AlGaAs DBSCH SQW structures have been manufactured according to the design above. Gaussian-shaped narrow directional characteristics are in relatively good agreement with modelling predictions. Vertical beam divergences are 1315o and 1718o FWHM for design versions experimentally investigated. Threshold current densities of the order of 350270 Acm-2 and slope efficiencies of 0.95 and 1.15 W/A have been recorded for these two versions, respectively. Optical power at the level of 1 W has been achieved. The version with lower beam divergence proves to be more durable. Higher optical power levels are to be obtained after heterostructure doping optimisation.