Exact Solution of in-Plane Vibrations of Circular Arches With Account Taken of Axial Extension, Transverse Shear and Rotatory Inertia Effects

A mixed stress model for linear elastodynamics of arbitrarily curved beams

“…The analysis is carried out with 2, 4, 8 and 16 elements. Again, the comparison is made with the analytical solution found in [21] and the approximated method proposed by Heppler [18]. The values in Table III evidence very good agreement between the solution with the present approach and the analytical solution reported in [21] and a better performance with respect to [18].…”

“…Table I shows very good agreement of the solution between the present approach and the analytical solution reported in [21] and the better performance with respect to another approximated method like that developed in [18]. Table II shows the competitive performance of the present model, in terms of the first natural frequency, with respect to the other approximated methods available in literature.…”

“…The reference solution is the analytical solution found in [21] and reported in Table III. Figure 9 collects the first three frequencies of the circular arch and shows how both the elements proposed successfully converge.…”

“…The first test is the vibration of a circular arch in the case of constant or variable cross section [18][19][20]. In the case of constant cross section, an analytical solution to compare with is available in the literature [21]. In the same framework the comparison is made with other approximated methods [18,19].…”

In-Plane Vibrations of Circular Curved Beams with a Transverse Open Crack

“…Natural frequencies were calculated for classical boundary conditions including shear stress and rotary inertia [13]. Exact solutions of free in plane vibrations including extension, shear and rotary inertia were obtained by Tüfekçi and Arpacı [14]. Inextensional vibrations were investigated by using another version of DQM [15].…”