Modal analysis of circular arches in rectangular coordinate system

This paper presents a modal solution method for circular arches in a right-angle coordinate system. Firstly, the flexibility matrix is solved using the Mohr integral, and the stiffness matrix is obtained by the inverse operation. Secondly, the structural mass matrix is obtained by quadratic staggered superposition of the half-mass matrix. Then, the eigenvalue method is used to obtain the circular arches modal. Furthermore, experimental tests are carried out on fixed round arches at both ends to obtain the natural frequencies of the arches. To illustrate the validity and accuracy of the presented methodology, the results are compared with laboratory and finite element results. It is found that there is a good agreement among the prediction of the proposed design equations, measured values and the finite element results.