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Piecewise exact solution of nonlinear momentum conservation equation with unconditional stability for time increment
Get PDFExact solution is adopted for computation of the inviscid Burgers equation on finite difference grid. Initial condition and following computed values of the independent variable are assumed to be piecewisely linear between fixed grid points, and local exact solution is used to find the value at the next time step at each grid point. Comparisons of Piecewise Exact Solution Method (PESM), existing upwind scheme, and the analytic solution show that the present method is more accurate than the upwind scheme. The unconditional stability is a strong merit of this method and is shown with a test result
Numerical modelling and validation of light gauge steel top-seat flange-cleat connection
Get PDFThis paper presents the numerical investigation on the moment-rotation behaviour of cold-formed top-seat flange-cleat connection, a type of light gauge steel connection which structural connection has sparked a wide range of research interest. The cold-formed channel sections were assembled back-to-back to form I-shape beam and column members. Two components were used to connect the members, notably the 2 mm cold-formed bracket and the 6 mm hot-rolled angle. The results were collected from different beam depths, namely 150 mm, 200 mm and 250 mm. The rotational stiffness and strength obtained from the numerical modelling were then compared with design requirements from BS EN 1993-1-8 and experimental data. The comparison showed not more than 35 % difference in strength and about 50 % difference in rotational stiffness between numerical modelling and experimental data. However, there was a noticeable difference between finite element models and analytical calculation. The differences were from 18 % to 66 % for strength and between 1 % and 145 % for stiffness. Finite element models showed a better agreement with experimental data as compared to analytical study. Edge stiffener of numerical model and theoretical stiffness calculation had caused significant difference in comparison
Study of characteristic variations of high-speed spindles induced by centrifugal expansion deformations
Get PDFHigh-speed machining has continuously pushed the demand of spindles with higher speed and higher reliability. In order to design, analyze, and test spindles in a virtual environment, accurate modeling of the spindle dynamics during the running state is essential. This paper investigates the variations of interference fit and bearing preload condition induced by centrifugal expansion deformations at high speed. Firstly, the elastic expansion deformations of the rotating parts due to centrifugal force are calculated based on mechanics of elasticity. It is found that the centrifugal expansion deformation of the bearing inner ring is much larger than the deformation of the shaft when the rotational speed increases, and therefore the amount of the interference between the shaft and the bearing decreases with the speed. Then, with consideration of the centrifugal expansion deformation, a dynamic model of high-speed rolling ball bearings is presented with experimental validation. With the proposed bearing model, centrifugal effects on the bearing preload condition are studied in detail. It is shown that the bearing contact angle decreases, while the contact load increases with the centrifugal expansion deformation of the bearing inner ring. The radial bearing stiffness increases, whereas the axial bearing stiffness decreases a little, due to the resultant effects of the decreased contact angle and the increased contact load. The preload condition of the spindle bearing is strengthened by the centrifugal expansion effect of the bearing inner ring
Analytical model to determine fundamental frequency of free vibration of perforated plate by using unit step functions to express non-homogeneity
Get PDFIn the current study an analytical model to determine fundamental frequency of perforated plate is formulated. Non-homogeneity in Young’s modulus and density due to perforation is expressed by using unit step function in Rayleigh’s Quotient. In the present analysis the boundary condition considered is clamped at all edges. Perforated plate is considered as plate with uniformly distributed mass and holes are considered as nonhomogeneous patches. The deflected middle surface of the plate is approximated by a function which satisfies the boundary conditions. The proposed approach is validated by comparing results with finite element method modal analysis
Free flexural vibrations of a piezoelectric bimorph plate with periodic edge conditions
Get PDFThis work analyzes the vibrations of a fully-electroded annular piezoelectric bimorph plate with a free inner edge and an outer edge that is built-in with a periodicity. To this end, a variational formulation with the extensive use of Lagrange multipliers for a bimorph plate with polar orthorhombic symmetry is performed first. The mechanical displacement and the electric potential that must satisfy constraint conditions at the electrodes are expanded as the sums of powers in the thickness coordinate. The resulting piezoelectric bimorph plate equations are used along with the introduction of appropriate Lagrange multipliers to analyze the polar orthorhombic annular sectorial plates with free radial and inner circumferential edges, and an entirely built-in or free outer edge. The results are then combined to obtain the solutions for the mixed boundary value problem. The extended Hamilton’s principle with the method of Lagrange multipliers is employed, followed by a Frobenius-type series expansion for solution functions. The eigensolutions are calculated from the resulting transcendental equation and compared with those obtained from an FEA to ensure the validity of the procedure
Study on analysis method for deepwater TTR coupled vibration of parameter vibration and vortex-induced vibration
Get PDFConsidering the vertical vibration, caused by floating platform, of top tensioned riser (TTR), an analysis method for the coupled vibration of parameter excited vibration and vortex-induced vibration is presented in this paper. With the section rotation and shear deformation due to the bending large displacement of TTR, a coupled vibration model of parameter excited vibration and vortex-induced vibration is put forward. And the vortex-induced vibration (VIV) of a TTR for 1500 m water depth is analyzed based on the model. The results show that the vertical vibration caused by floating platform increases transverse vibration displacement of TTR
Research of dynamics of lifting equipment
Get PDFIn the recent years, girder bridge cranes are replaced by double-beam overhead cranes with beams of rectangular cross-section. In addition, new materials are used for their fabrication, characterized by different values of allowable loads and deformations. In the paper, two overhead cranes from JSC "Vilniaus kranai" are considered. A mathematical model is proposed that enables assessment of the impact of the hydraulic damper built in the cargo suspension system upon the dynamic features of the crane in the beginning of the lifting process. It was determined that in such a way the period of vibration damping is reduced. However, the impact of the damper upon the dynamics of the metal structure of the crane is limited because of high mobility of the rope as compared to the mobility of the total structure
Method of active synthesis of discrete fixed mechanical systems
Get PDFIn this work the method of active synthesis of mechanical systems in accordance with the desired frequency spectrum has been formulated and formalised. Active synthesis of a proportional regulation system has been performed in accordance with the method formulated and a verification of the correctness of the results has been carried out
Ultrasonic systems for liquid pulverizer
Get PDFAnalyzing known liquid pulverizers which are driven by piezoelectric transducers we obtain that almost all of them are using longitudinal vibrating mode. So we decide to create a dual-effect system which will act as a pump and sprayer. Using FEM analysis the proposed model was analyzed and it is natural longitudinal frequency was found. Modeling results (frequency, displacement) were compared with real parameters of working transducer and they were nearly the same. The main study object was to find how fluid moves through a capillary under ultrasonic vibrations. The experimental results are populated below
Comparison of the mechanical properties of flax and glass fiber composite materials
Get PDFIn this paper, the comparison of static and dynamic properties of flax and glass fiber composite materials is presented. For this comparison, dynamic and quasi-static experimental studies were carried out. As a dynamic test, vibration tests were fulfilled using the Oberst apparatus and the tensile test was fulfilled by a quasi-static test. The vibration tests were carried out under different temperatures by using temperature and climatic test cabinets. Flax and glass fibers were used as reinforcements, and polyester resin was used as a matrix to make up the composite specimens. According to the obtained results, the strength of flax fiber composite is lower than the glass fiber under tensile loading, but approximately the same under vibration excitation. On the other hand, damping characteristics of flax fiber composite is higher than glass fiber composite materials. These results demonstrated that natural fiber materials can be used instead of chemical materials for vibration absorption due to their high damping