The use and limitations of continuum modes for response calculations of cellular structures

In this paper, a method for the approximate calculations of response of cellular structures is presented. The method is based on the idea that for low-frequency modes, the cellular structures behave in a way similar as a continuum does. The range of validity of the method on the mode number scale is also examined. It is shown that the response is estimated very accurately from a reduced order model based on continuum modes for low-frequency vibration. The accuracy starts to deteriorate with the increase in the mode number. Beyond certain mode number, the improvement in accuracy due to the inclusion of additional continuum modes in the approximation shows a point of diminishing returns. Illustrative examples are given.