Nonlinear primary resonances of lattice sandwich beams with pyramidal truss core and viscoelastic surfaces

In this paper, the nonlinear forced vibration properties of the lattice sandwich beam with pyramidal truss core and viscoelastic surfaces subjected to harmonic external excitation are investigated. The nonlinear dynamic model of the lattice sandwich beam is formulated based on the Kelvin-Voigt viscoelastic model and discretized into nonlinear ordinary equations with multiple degrees of freedom by using the assumed mode method. The nonlinear amplitude-frequency curves of the steady-state responses of the beam are obtained by an iterative algorithm. The effects of the external excitation amplitude, the inclination angle of the truss core, and the viscoelastic coefficient of the surface material on the nonlinear forced vibration behaviors of the beam are analyzed. From the research results, it can be seen that the lattice sandwich beam shows very rich and novel nonlinear dynamic behavior. The viscoelastic damping of the surfaces can decrease the resonance amplitudes of most modes of the beam. An acceptable optimal inclination angle considering the equivalent mass density of the pyramidal truss core and the resonance amplitude of the beam is obtained. The evolution rules of the lattice sandwich beam with the material and structural parameters obtained from the preset study are helpful for the engineering applications of this kind of lightweight sandwich structures.