Free vibration analysis and optimization of composite lattice truss core sandwich beams with interval parameters

The natural frequencies of composite sandwich beams with lattice truss core are investigated by combining the Bernoulli-Euler beam theory and Timoshenko beam theory. The governing partial differential equations of motion are derived using Hamilton's principle and the analytical formulations of the natural frequencies are determined. After validation of the present method by numerical techniques, the effect of geometric and material parameters on the natural frequencies is studied. Considering various uncertainties in composite sandwich beams, a novel interval analysis method is developed based on which uncertain analysis of the natural frequencies is accomplished subsequently. Finally, the interval optimization of sandwich beams w.r.t. the first order natural frequency is fulfilled by adopting an improved ranking method for interval numbers proposed in this paper. It is found that: (1) the natural frequencies of sandwich beams with lattice truss core by the present method agree well with those by FEM; and (2) the effect of uncertainties on the natural frequencies is significant and thus the design by the interval optimization method is more realistic than the conventional ones.