Three-dimensional free vibrations of a circular arch using the theory of a Cosserat point

Small deformation three-dimensional free vibrations of a circular arch with uniform rectangular cross-section have been investigated by using different theoretical approaches and by experimental verification. Special emphasis has been focused on a numerical formulation which models each element of the arch using the theory of a Cosserat point. Comparison has been made with accurate three-dimensional numerical modeling of the arch using the computer program ANSYS. Also, three-dimensional beam elements in the computer programs ANSYS and I-DEAS have been considered along with an exact solution of approximate model equations of the arch. The results indicate that appropriate modeling of rotary inertia is necessary to predict accurate frequencies associated with torsional out-of-plane modes. Moreover, in its general form the theory of a Cosserat point is a fully nonlinear theory that has already been tested for buckling of beams and arches. Therefore, the success of the Cosserat theory for the dynamic problem considered in this paper suggests that the theory of a Cosserat point can be used for more complicated nonlinear dynamic problems of thin rod-like structures.