Rozwiązanie Ogólne Płyty O Kształcie Trójkąta Prostokątnego

The solution is found for a plate whose form is that of right-angled triangle (3.2) by means of eigen-transforms (see [1]). The solution obtained may be used for the investigation of concrete cases if the form of the eigen- function is known. This is, as yet, the case of 30°-60°-90° and 45°-45°-90° triangles, the first being considered in the Ref. [1], the other in [2], by Z. KACZKOWSKI. The method used in [2], enabled the solution of some of the possible problems, for homogeneous and continuous supports. The. solutions (4.11) and (4.14) following from (3.2) and further solutions enable also the solution of the remaining cases. Of the ten examples solved in the present paper let us mention the plate with the entire periphery clamped, (4.28), and the plate supported on the corners (all the edges being free), (4.58).
All the solutions reduce of course to infinite homogeneous systems or non-homogeneous linear algebraic equations with infinite number of unknowns and concern the problems of: steady state vibration, stability and combined compression and bending of a plate resting on an elastic foundation