In many applications, the dynamic behavior of large periodic structures must be modeled accurately, thus requiring the determination of a significant number of natural frequencies and mode shapes. In order to perform that task most efficiently, a continuum modeling approach can be adopted. The discrete structure is then replaced by a continuum model which can be analyzed more efficiently. Therefore, at the design stage many analyses can be performed while searching for the optimal solution.
Known structural models are usually used as continuum models, and several methods are available to determine the equivalent properties from the properties of the original structure. This task is usually cumbersome, and in addition, in certain cases, continuum models cannot represent all modes of deformation.
In this article, a simple approach to develop continuum models without explicit reference to an existing structural theory is presented. Very accurate results are obtained, and all vibration modes can now be handled easily.