Free Vibration and Hardening Behavior of Truss Core Sandwich Beam

Abstract

The dynamic characteristics of simply supported pyramidal truss core sandwich beam are investigated. The nonlinear governing equation of motion for the beam is obtained by using a Zig-Zag theory. The averaged equations of the beam with primary, subharmonic, and superharmonic resonances are derived by using the method of multiple scales and then the corresponding frequency response equations are obtained. The influences of strut radius and core height on the linear natural frequencies and hardening behaviors of the beam are studied. It is illustrated that the first-order natural frequency decreases continuously and the second-order and third-order natural frequencies initially increase and then decrease with the increase of strut radius, and the first three natural frequencies all increase with the rise of the core height. Furthermore, the results indicate that the hardening behaviors of the beam become weaker with the increase of the rise of strut radius and core height. The mechanisms of variations in hardening behavior of the sandwich beam with the three types of resonances are detailed and discussed.