FREE IN-PLANE VIBRATION OF ARCHES WITH NONSYMMETRICAL AXIS

A semisnalyticsl method is developed to study the free in-plane vibration of arches with any shape. The fundamental dilfcrential equations are first translated into the integral equations. By applying the approximate solution of integral equation,semiunalytieal solutions of the origillal differential equations are obtained. The solutions have disc,'ete tYpe eXl'ressions concerned with the equally spaced points of the arch axis or the points On the arch axis corresponding to the equally sllaced points of the horizontal distance between the supports. The method is applied to analyze the free in-planc vibration of arches with nonsymme trical axis because of the unegual height of the supports. Numerical results for the cases of nonsymmetrical, 2-hinged and fixed arches with pal'abolical axis al'e compared with the solution of the symmetric arches