Out‐of‐Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

Abstract

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-ofplane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Elasti̇k Mesnetleri̇n Hafi̇fçe Eğri̇ Bi̇r Ki̇ri̇şi̇n Nonli̇neer Ti̇treşi̇mleri̇ne Etki̇leri̇

“…In simply supported case, the linear and nonlinear frequencies of the system were analyzed in detail. Ozyigit et al(2017) analyzed the free out-of-plane vibrations of the curved beams which are symmetrically and nonsymmetrically tapered. They also investigated the outof-plane free vibrations of the curved uniform and tapered beams with additional mass.…”