Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams

Exact Shape Functions for Timoshenko Beam Element

“…The geometry and material data of the beam are given in the figure. Table 3, the results of the non-dimensional frequencies of the present formulation show lower convergence results under various boundary conditions compared to the results in [15]. In the free vibration problem, the beam element should be divided into sub-elements to accommodate the free degree of freedoms.…”

“…By using these shape functions, the analyses of beam elements require a significant number of element divisions to study the behavior of beam with non-uniformity and inhomogeneity problems accurately [1][2][3][4][5][6][7][8][9][10][11][12]. The latest accomplishment for developing the exact solutions of the shape functions makes use of the power series method [13][14], basic displacement function [15] and Taylor series expansion [16][17] approximations are reported.…”

Thermal Buckling Analysis of Functionally Graded Circular Plate Resting on the Pasternak Elastic Foundation via the Differential Transform Method

“…The literature review indicates that the present work is the first attempt to exploit DTM to evaluate the critical buckling temperature. A number of studies have been carried out by this method [18][19][20][21][22][23][24]. The results are presented in four categories based on linear and uniform thermal load and simply supported and clamped edge conditions in the proceeding sections.…”

Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation

“…Studies about dynamic analysis of the beams which were modeled as distributed parameter system also contribute to solution of the forced vibration equations of beams on elastic soil. In recent years, considerable amount of studies have been carried out by many researchers about dynamic response of uniform, prismatic or composite beams (Attarnejad et al 2010, Gunda et al 2011. Dadfarnia et al (2005) analyzed a Timoshenko beam by selecting different time function for displacement and angle of rotation using the Galerkin method.…”