Free vibration of microscale frameworks using modified couple stress and a combination of Rayleigh–Love and Timoshenko theories

Abstract

A model is proposed for investigating the size-dependent frequency response of arbitrarily oriented microscale frames used in the build-up of lattice structures with micro unit cells. The model employs the Rayleigh–Love, the Timoshenko and the modified couple stress theories to overcome the weaknesses of the conventional theories. Descriptions of the model and finite element implementation are presented. Predictions from the reduced forms of the model agree with published results. The frequency analyses of different microscale frames reveal the influence of material lengthscale, dead weight, lateral inertia and orientation angles. For small aspect ratios, neglecting the lateral inertia effect incurs a substantial error in predicting the frequencies of higher modes, but only marginally affects the lower modes. The resonant frequencies exhibit a sharp drop in the presence of dead weight, but it increases in the presence of material lengthscale.