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A note on the Burger’s method

Abstract The existence and uniqueness of the solutions to an infinite system of nonlinear equations arising in the  dynamic analysis of large deflection of a plate are discussed. Under the assumption that the rim of the plate is prevented from inplane motions, explicit equation for the coupling parameter is given. Keywords: Existence, uniqueness, Berger’s method.1991 Mathematics Subject Classification. 46(Functional analysis),73(Mechanics of solids) Introduction In the analysis of classical mechanics problems, there are cases where linear mathematical model can not fully describe the phenomena. If the deflection of the plate is of order of magnitude of its thickness, the differential equations for the deflection and displacements can be written in terms of nonlinear equations. These nonlinear equations are usually difficult to obtain the solution. Thus several attempts have been tried to obviate the difficulties. Among these attempts, it was Berger’s met

Existence and Uniqueness of the solution of large deflection of circular plate by the Burger’s method

Introduction In the analysis of classical mechanics problems, there are cases where linear mathematical model can not fully describe the phenomena. If the deflection of the plate is of order of magnitude of its thickness, the differential equations for the deflection and displacements can be written in terms of nonlinear equations. These nonlinear equations are usually difficult to obtain the solution. Thus, several attempts have been tried to obviate the difficulties. Among these attempts, it was Berger’s method which drew much attention. Berger[1] derived as implified nonlinear equations for a plate with large deflections by assuming that the strain energy due to the second invariants of the middle surface strains can be neglected when deriving the differential equations by energy method. Berger restricted his analysis to static and isotropic cases. Later, his procedure was generalized to dynamics of isotropic plates by Nash and Modeer [2] and to dynamic phenomena in anisotr

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Theoretical Feasibility Research on 3D Printing Technology Applied to Statics Model Experiment

  Abstract 3D printing is effective to manufacture experimental models widely used in analogous statics tests before practical engineering applications. Whereas, traditional statics model experiments with strict dimensionless function are hardly to be established through 3D printing items according to similarity theory. To find a solution, this paper theoretically simplifies the statics system based on reducing constrains of weight and Poisson’s ratio. This simplification is the core of a new method of additional weight and correction to identify the simplified and the original statics systems. Operation procedures are displayed through case studies using the new method. 3D printed materials for specific statics experiments are validated as well through coefficient corrections. The results will finally contribute to 3D printing technology applied to analogic static research, for not only academic but also industrial purposes.   Read more about this article : https://lup

Computational modelling of plate-fin and tube heat exchanger for heat transfer and pressure drop analysis

  Introduction The plate-fin and tube heat exchanger are a cross-flow type heat exchanger, which uses plates as fins as indicated in (Figure 1); therefore, the flow external to the tubes is unmixed. Often, it is categorized as a compact heat exchanger to emphasize its relatively high heat transfer surface area to volume ratio. The plate fin and tube heat exchanger is widely used in many industries, including the aerospace industry, for its compactness and low weight. Different types of fin patterns, in addition to the plate, exist, such as louver, convex-louver, and wavy; however, in general, the plate fin tends to be the best in terms of performance and of constructional effectiveness. The tube geometry used in plate fin and tube heat exchangers is either circular or elliptical. The majority of the studies dealing with plate fin and tube heat exchangers have been conducted resorting to experiments. Shepherd [1] analyzed early experimental data for heat transfer of plate fi

Corrosion Protection of Aluminium in Sulphur dioxide Environment by the use of Nanocoating and Electrospray Techniques

  Abstract Aluminium is a very useful metal. It is easily converted into suitable forms so it fits for in various appliances like households, industries, aerospace, electronic, transport and other processes. It is produced corroding affect in sulphur dioxide environment. Al interacts with sulphur dioxide in presence of humidity to produce corrosive medium for its. It creates acidic environment for Al metal and forms corrosion cell on its surface. The electrode potential difference occur between Al|Al3+ anode and cathode H+|H2 thus corrosion reaction takes place on the surface of base metal and produces different forms corrosion like galvanic, pitting, stress, crevice, intergrannular etc. The organic compound terahydro-dibenzo[a,d][7]annulene-5,11-dioxime and zinc oxide electrospray were used for corrosion protection of Al in sulphur dioxide environment. The terahydro-dibenzo[a,d] [7]annulene-5,11-dioxime and ZnO electrospray formed composite barrier on aluminium metal

Potential Opportunities for Development of Mechanical Engineering with The Context of Historical Evolution of This Engineering Branch

Short Communication Mechanical engineering is not only one of the oldest engineering disciplines but also the broadest one, i.e., with the wide-scope as well as a large number of its branches. This engineering discipline requires a clear understanding of the principles of engineering physics, engineering mathematics, and materials science to design, analyze, manufacture, and maintain mechanical systems such as mechanisms, devices, and machines. With a view to machines’ development, the progress of mechanical engineering advancement is often directly related to the course of civilization history. Therefore, it can be studied from many perspectives. Our attention often directs to significant particular forms or stages of civilization, which arisen throughout human history. One cannot forget about ancient cultures, both Greco-Roman (in Europe) and Chinese (in Asia), which adopted to a great extent and, then, developed often anonymous technical achievements of the fi