Structural Engineering and Mechanics Volume 4, Number 5, September 1996, pages 513527
DOI: http://dx.doi.org/10.12989/sem.1996.4.5.513  
General evolutionary path for fundamental natural frequencies of structural vibration problems: Towards optimum from below  
Zhao CB, Steven GP, Xie YM


Abstract [Full Text]  
In this paper, both an approximate expression and an exact expression for the contribution factor of an element to the natural frequency of the finite element discretized system of a structure in general and a membrane in particular have been derived from the energy conservation principle and the finite element formulation of structural eigenvalue problems. The approximate expression for the contribution factor of an element is used to predict and determine the elements to be removed in an iteration since it depends only on the quantities associated with the old system in the iteration. The exact expression for the contribution factor of an element makes it possible to check whether the element is correctly removed at the end of an iteration because it depends on both the old system and the new system in the iteration. Thus, the combined use of the approximate expression and the exact expression allows a considerable number of elements to be removed in a single iteration so that the efficiency of the evolutionary structural optimization method can be greatly improved for solving the natural frequency optimization problem of a structure. A square membrane with different boundary supports has been chosen to investigate the general evolutionary path for the fundamental natural frequency of the structure. The related results indicated that if the objective of a structural optimization is to raise the fundamental natural frequency of the structure to an optimal value, the general evolutionary path during its optimization is that the elements are gradually removed along the direction from the area surrounded by the contour of the highest value to that surrounded by the contour of the lowest value.  
Key Words  
evolutionary criterion, natural frequency optimization, membrane vibration, general evolutionary path  
Address  
UNIV SYDNEY,FINITE ELEMENT ANAL RES CTR,FAC ENGN,SYDNEY,NSW 2006,AUSTRALIA VICTORIA UNIV TECHNOL,DEPT CIVIL & BLDG ENGN,MELBOURNE,VIC 3000,AUSTRALIA  