Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method

A topology and shape optimization method is presented for structural eigenfrequency optimization problems using the concept of Optimal Material Distribution (OMD). First, a mean-eigenvalue corresponding to the multiple eigenfrequencies of a structure is defined. Three optimization problems are then considered for obtaining the desired eigenfrequencies using this mean-eigenvalue: maximization of the specified structural eigenfrequencies, maximization of the distances of the specified structural eigenfrequencies from a given frequency or frequencies, and optimization of the structure for obtaining prescribed eigenfrequencies. Several examples are presented to demonstrate the capability of this new technique which can be used to deal with a wide range of practical design problems for improving the dynamic nature of a structure.