Papers by Keyword: Galerkin's Method

Abstract: Studying the diagrams of characteristics of complex subsystem of mechatronic one it has been determined that in case of approximate method the resonance frequencies cover with those which have been determined with exact method. However the values of the characteristic in other areas are different. Therefore there is the mistake of approximate method, which in case of studying the single systems does not have any influence because in resonance areas the characteristic values of the system approach to the infinity. However the difference in values of flexibility within two methods has the great influence on the result of complex systems. The main subject of deliberation was to determine the flexibility of the complex system with constant cross section using the exact and approximate that means Galerkin's method. The mechanical and/or mechatronic system composed from many mechanical subsystems having the same length and variable cross section, loaded by the focused moment was analysed. One case of attachment the complex system that means free torsional vibrating bar were examined. That why it was necessary to correct the results of approximate method. The problems presented in this paper, that means the analysis of subsystem of mechatronic and mechanical complex systems is however the introduction to the synthesis of torsional vibrating mechatronic systems with assumed frequency spectrum.

Abstract: The research of subsystems establishes the foundation to complex systems analysis with cascade structure. Analysing the diagrams of characteristics of confirmed system it has been determined that in case of approximate method the resonance frequencies cover with those which have been determined with exact method. However the values of the characteristic in other areas are different. The main aim of the paper is to study the dynamic characteristic of the discrete continuous mechatronic system determined by exact approximate, that means Galerkin's method for torsionally vibrating complex mechanical subsystems. The system composed from many subsystems having the same length and variable cross section, loaded by the focused moment was analysed. The main subject of deliberation was to determine the flexibility of the mechanic system with constant cross section using the exact and approximate Galerkin's method. Next the method comparison and the correction of approximate method where made. As far as the mechatronic system flexibility determinations concerned the Galerkin's method has been chosen. The analysis of subsystems of mechatronic and mechanic complex systems is however the introduction to the synthesis of torsionally vibrating mechatronic systems with assumed frequency spectrum.

Abstract: According to the deformation characteristics of global side torsion buckling for rectangle thin-walled aqueduct, the critical load of side torsion buckling for rectangle thin-walled aqueduct is deduced by Galerkin method. Influences of prestress and vertical deformation before buckling are considered. The variation rules of critical load are analyzed with four factors: span, flange width, ratio of height to width, thickness. The analysis results show that the aqueduct span is the biggest influence on the critical load of side torsion buckling for aqueduct; for rectangular thin-walled aqueduct, in conventional aqueduct section size and span, its critical stress of side torsion buckling is greater than concrete compressive strength design value , therefore side torsion buckling won't happen in usual aqueduct; if steel with high yield limit is used, stability check calculation must be carried out. Results and conclusions obtained can be referenced for the global stability design of thin-walled aqueduct.

Abstract: By mean of potential energy various principles,the governing differential equations of the steel and concrete composite girder in considering relative slips between steel girders and concrete slabs and shear lag effects of the flanges and the concrete slab are derived. The equations are solved by Galerkin method. It is shown from the calculating example that the proposed method not only is easy to calculate, but also has high convergent speed

Abstract: Platelet transpiration cooling is one of the key techniques for the developing reusable launch vehicle. The thinner of the platelet, the better effect plate transpiration will gain. Meanwhile, the platelet unit may get wrinkled if thermal stress is large enough. One-dimensional non-equilibrium model is adopted to analyze the heat transfer characteristics of platelet transpiration cooling. The assumption of rectangular plate with three-side simple supported and one-side free is taken and Galerkin method is applied for analyzing the stability of platelet unit. Analysis indicates that as the heat transfer intensity increases, the thermal soaking depth decreases, while more coolant is needed to keep the heated wall at design temperature. Also, the critical thickness for the platelet not to get wrinkled gets larger with the increasing thermal soaking depth.

Abstract: The transverse vibration equation of an axially moving cantilever beam with tip mass is given. The instant linearized equations are set up based on Galerkin’s method. The tip mass influences to the first three order modes of the beam are computed. The calculated responses using the modes with tip mass are compared with the results using the modes without tip mass. Modes without tip mass can replace the modes with tip mass while the tip mass is small. The heavier the tip mass is, the bigger the difference of using the replacement is. It is found that the experimental result is fit well with the theoretical result using the modes with tip mass.

Abstract: In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

Abstract: Under thermal stress, the formed platelet of Liquid Rocket Engine (LRE) transpiration cooling structure may result in wrinkling. The stability of rectangular sheet with three simple supported-sides and one free-side is simplified as the model of formed platelet. Applying the Galerkin method for analysis, the relationship of the critical thickness of formed platelet and the transpiration width is obtained. Also, the influence of different material properties on the critical thickness is presented. The theory and method proposed in this paper are applicable for more complicated temperature distribution and also can be used to choose material for transpiration cooling.

Abstract: Recently, with the development of mathematics itself and promotion of physics and other mechanics, the study of partial differential equation (equations) has become an important study subject. In this paper, we make research the initial-boundary value problem for a class of the thermoelastic beam equations. Namely, for the following coupled equations

Abstract: Based on a laminated composite structure, vibration and nonlinear stall aeroelastic stability of rotor blades modeled as anisotropic thin-walled closed-section beams are systematically addressed. The analysis is applied to a laminated construction of the circumferentially asymmetric stiffness (CAS) that produces bending-bending-twist coupling. The vibration characteristics of composite beam are determined by the Galerkin Method. The unsteady aerodynamic loads and centrifugal force are integrated with the nolinear aerodynamic model to deal with aeroelastic stability analysis. The influence of some related factors, pretwisted angle, ply-angle rotational speed, and wind speed, is investigated. The paper gives methods of eigenvalue analysis and aeroelastic response, which can determine the stability of the blade forced by the nolinear aerodynamics.