AN APPLICATION OF TRIGONOMETRIC SERIES FOR MODELLING OF THE ELASTIC LINE OF STRAIGHT TWO-SUPPORTED BEAM WITH ANGULAR ELASTIC CONNECTIONS
Hits: 34
- TITLE: AN APPLICATION OF TRIGONOMETRIC SERIES FOR MODELLING OF THE ELASTIC LINE OF STRAIGHT TWO-SUPPORTED BEAM WITH ANGULAR ELASTIC CONNECTIONS
- ABSTRACT: This article presents a method for modeling of the elastic curve of Euler-Bernoulli straight two-supported beam with angular elastic supports of the end cross-sections. These angular connections restrict the rotations of the end cross-sections when the beam is subjected to bending in principal inertia plane. The beam is statically undetermined. The method is based on an application of infinite trigonometric series. Each combination of simple circular functions, which corresponds to a serial number of the series, satisfies the generalized boundary conditions of the beam. The unknown coefficients in the model are found by means of the principle of virtual displacements for two cases – concentrated force and uniformly distributed load. The beam deflection and bending moments in the end and middle cross-sections are determined for the generalized boundary conditions through introducing dimensionless functions with general argument. The method has been applied for determination of the basic natural frequency of the beam with generalized boundary conditions.
- DOWNLOAD: AN APPLICATION OF TRIGONOMETRIC SERIES FOR MODELLING OF THE ELASTIC LINE OF STRAIGHT TWO-SUPPORTED BEAM WITH ANGULAR ELASTIC CONNECTIONS