Rectangular, thin plates are common structural elements employed in many engineering applications and are subject to a wide variety of excitations, including acoustic excitations. This article analyses the deflection of an isotropic rectangular clamped thin plate. An exact solution of the governing equation of the problem is given in the form of a double series expansion in terms of a set of orthogonal functions. Furthermore, a simple and efficient finite element for thin-plate bending applications is also used. Numerical solutions for rectangular plates with various side ratios are presented and compared to the previous results and the finite-element analysis.
Based on gear geometry and generating mechanism with gear-type shapers, this paper studies the computerized tooth profile generation of involute gears. Generating and generated surfaces are obtained by using vector analysis, differential geometry, matrix transformation, and meshing equation. Trochoidal envelope traced by the cutter during generating process is also investigated. This study also develops a computer program for generation of external and internal tooth profiles. Simulated motion path of the cutter during generation process is also illustrated. Using the given method, designers can create and observe geometry simulation. The effect of tool settings on the generated profile can easily be investigated before manufacturing.
This paper studies the equations of rack cutters for generating involute gears with asymmetric teeth. The asymmetry means that different pressure angles are applied for the driving and coast sides. By applying the equations of the designed profile of the rack cutter, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of involute helical gear are given. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Furthermore, a computer simulation program is developed to generate the tooth profile of asymmetric involute gears and to illustrate the effect of tool geometry on the generated surfaces. A CAD/FEM procedure for finite element modeling of asymmetric gear teeth is presented. This simulation should be helpful in the design and manufacture of asymmetric gears.
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