Free In-Plane Vibration of Three-Hinged Arches with Nonsymmetrical Axis

A semianalytical method is developed to study the free in-plane vibration of arches with any shape. The fundamental differential equations are first transformed into the integral equations. By applying the approximate solution of integral equation, semianalytical solutions of the original differential equations are obtained. The method is applied to analyze the free in-plane vibration of arches with nonsymmetrical axis because of the unequal heigh of the supports. Numerical results for the cases of nonsymmetrical, 3-hinged arches with parabolical axis are compared with the solution of the symmetric arches