Design optimisation of structures vibration behaviour using first order approximation and local modification

This paper presents an inverse formulation of eigenvalue problem for optimising the dynamics behaviour of structures. The formulation is applied to one- and two-dimensional finite elements which are commonly used in simulation of real structures. Based on this formulation an algorithm is developed for accurate and efficient modification of structures stiffness and mass characteristics to achieve the desired natural frequencies and interpretation of results in terms of physical design parameters. The proposed algorithm is tested by conducting four case studies and the results are validated against exact solutions.