Impact attenuation of sphere on woodpile

The woodpile structure shows exceptional cushioning and vibration reduction under impact. The impact, such as the case of a sphere impacting on stacked beams (a beam chain), has been studied using the discrete element method (DEM) in the literature, which shows that the DEM approach is limited to low-frequency vibrations, mostly up to the third harmonic mode triggered by the impact. However, many impact contacts, similar to step loads, will induce high-order modal vibrations (excited eigenmodes beyond the fifth modes). Present work encompasses the higher vibrational modes under such impact. With Timoshenko beams considering shear effect, the dynamics of sphere-woodpile impact is studied by coupling the superposition method for higher modes and the Hertz law for nonlinear contact. Result reveals the high mode vibration greatly reduces the contact force on the stacked beam, thus slender beam can expedite the dissipation of impact energy. Also, the higher-order vibrations enhance the speed of wave propagating within the beam chain and amplify attenuation effects. These insights offer a guidance for the design of impact-resistant structures and advanced shock absorbers.