A NUMERICAL METHOD FOR FREE VIBRATION ANALYSIS OF BEAMS

Authors

  • ALEKSANDAR PROKIć UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA
  • MIROSLAV BEÅ¡EVIć UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA.
  • DRAGAN LUKIć UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA.

Keywords:

NUMERICAL METHOD, INTEGRAL EQUATIONS, GREEN'S FUNCTION, VIBRA-TION, TIMOSHENKO BEAM.

Abstract

IN THIS PAPER, A NUMERICAL METHOD FOR SOLUTION OF THE FREE VIBRATION OF BEAMS GOVERNED BY A SET OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS OF VARIABLE COEFFICIENTS, WITH ARBITRARY BOUNDARY CONDITIONS, IS PRESENTED. THE METHOD IS BASED ON NUMERICAL INTEGRATION RATHER THAN THE NUMERICAL DIFFERENTIATION SINCE THE HIGHEST DERIVATIVES OF GOVERNING FUNCTIONS ARE CHOSEN AS THE BASIC UNKNOWN QUANTITIES. THE KERNELS OF INTEGRAL EQUATIONS TURN OUT TO BE GREEN'S FUNCTION OF CORRESPONDING EQUATION WITH HOMOGENEOUS BOUNDARY CONDITIONS. THE ACCURACY OF THE PROPOSED METHOD IS DEMONSTRATED BY COMPARING THE CALCULATED RESULTS WITH THOSE AVAILABLE IN THE LITERATURE. IT IS SHOWN THAT GOOD ACCURACY CAN BE OBTAINED EVEN WITH A RELATIVELY SMALL NUMBER OF NODES.

Author Biographies

ALEKSANDAR PROKIć, UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA

DEPARTMENT FOR CONSTRUCTIONS, PROF.

MIROSLAV BEšEVIć, UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA.

DEPARTMENT FOR CONSTRUCTIONS

DRAGAN LUKIć, UNIVERSITY OF NOVI SAD, FACULTY OF CIVIL ENGINEERING SUBOTICA, KOZARACKA 2A, SUBOTICA, SERBIA.

DEPARTMENT FOR CONSTRUCTIONS

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Published

2014-03-18

Issue

Vol. 11 No. 8 (2014)

Section

Articles

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