VIBRATION ANALYSIS OF LINE CONTINUUM WITH NEW MATRICES OF ELASTIC AND INERTIA STIFFNESS

J.C Ezeh, O.M.Ibearugbulem, C.N. Okoli

Abstract: Vibration analysis of line continuum with new matrices of elastic and inertia stiffness is introduced in this research. The matrices were developed using Ritz method and assumed six term Taylor’s series shape function. Two deformable nodes were introduced at the centre and at the ends of line continuum which brings the number of deformable node to six. The six term Taylor’s series shape function assumed was substituted into strain energy equation and into inertia work (Kinetic energy) equation. Their resulting functional were minimized, resulting in 6 x 6 elastic stiffness matrix and 6 x 6 inertia stiffness matrix respectively, for vibration analysis. The two matrices were employed, as well as the traditional 4 x 4 matrices in classical free vibration analysis of four line continua with different boundary condition. The results from the new 6x6 matrices of elastic and inertia stiffness were very close to exact results, with average percentage difference of 0.212425421% from exact solution. Whereas those from the traditional 4 x 4 matrices and 5 x 5 matrices differed from exact results with average percentage difference of 14.72352281% and 0.275% respectively. Thus the newly developed 6 x 6 matrices of elastic and inertia stiffness are suitable for classical free vibration analysis of line continua

Keywords: 6x6 stiffness system; vibration; inertia; line continuum; variational principle; deformable node; shape function; classical; numerical; analysis; beam

DOI: https://doi.org/10.15623/ijret.2014.0304154