In‐plane vibrations of shear deformable curved beams

Abstract

SUMMARYThis paper presents the exact dynamic sti ness matrix for a circular beam with a uniform cross-section. The sti ness matrix is frequency dependent, and the natural frequencies are those that cause the matrix to become singular. Using this matrix the exact natural frequencies of circular beams with various boundary conditions are calculated and compared with available results in the literature.

A displacement finite volume formulation for the static and dynamic analysis of shear deformable circular curved beams

“…It is observed that very close agreement exists between the present results and those published in Refs. [11,13,36]. The associated modal shapes are also presented in Fig. 14 where an excellent agreement is observed with the results given in Ref.…”

“…The associated modal shapes are also presented in Fig. 14 where an excellent agreement is observed with the results given in Ref. [11]. It should be noted that in figures depicting the modal shapes, the horizontal axis represents the non-dimensional length parameter s/l in which, s is the tangential curvilinear coordinate and l is the total length of the beam.…”

“…[11] has derived the finite element formulation using the shape functions which are the exact solutions of the differential equations of motion. Also, Ref.…”

“…Irie et al [10] calculated the natural frequencies of in-plane vibrations of circular curved beams with uniform cross-section where the effects of rotary inertia and shear deformation are considered. Eisenberger and Efraim [11] studied the uniform circular beams using the Timoshenko beam theory, which includes the effects of rotary inertia, shear deformation, and the couplings of the radial and tangential displacements. Friedman and Kosmatka [12] utilized the Ritz method based on the trigonometric functions and derived the exact static stiffness matrix for the uniform circular curved beams.…”

A mixed stress model for linear elastodynamics of arbitrarily curved beams

“…In these cases, it is necessary to introduce a representation of the centroidal axis. Many papers refer to the circular arch case (see for example, [8][9][10][11]), while the case of arbitrarily curved geometry was afforded earlier using simple straight beams and later using B-splines [12] or cubic Hermite functions. In this work, a modified Hermitian elementwise cubic parametric description is adopted.…”