EFFECTIVE COUPLE-STRESS DYNAMIC BEAM MODEL OF A TYPICAL CELLULAR SOLID

The e ective continuum beam model can be used to study the dynamic behavior of the one-dimensional cellular solid structure. However, this e ective model will bring the size e ect when the cell size is close to the height dimension of the beam-like structure. The classical continuum model, which has no length scale, cannot describe this size dependent feature. By contrast, the generalized continuum model is pertinent to the description of the size e ect. The purpose of this paper is to develop an e ective Timoshenko continuum beam model for the transverse natural vibration analysis of a periodic cellular solid beam-like structure whose unit cell has a circular void, based on the couple-stress theory. The properties of the e ective couple-stress continuum are generated under the criterion of the equivalent strain energy and the geometrical average by the analysis of a unit cell. These properties are then employed in the Timoshenko beam theory to obtain the dynamics di erential equations. Comparison is made with the prediction of a finite element analysis of the complete cellular structure, which is taken as the benchmark for accuracy. Good agreements both on the frequencies and mode shapes are found by a variety of examples where the method of modal assurance criterion (MAC) is employed for the comparison of the mode shapes. The emphasis is put on the influence of the relative size of the void diameter, the size ratio of the beam height to the cell size, and the aspect ratio of the beam-like structure on the accuracy of the e ective beam model. A series of methods on the natural vibration analysis of a cellular solid beam-like structure is recommended conservatively based on these analyses.