Theoretical Analysis of Human Rhythmic Jumping on Oscillating Floors

Resumo

This study investigates the dynamic interaction between a human jumper and a concrete rectangular plate under cyclic vertical jumps. The plate is described using Von Kármans nonlinear relations, while the jumper is modeled as a spring-mass-damper (SMD) system with a harmonic force acting on the humans center of mass to represent the propulsion force during jumping. The mechanical system is described by a set of piecewise smoothtouch nonlinear differential equations, allowing the loss of contact between the jumper and the plate during jumps. The results show that the jumper exhibits complex dynamics, including periodic and chaotic responses, depending on the systems parameter combinations. Additionally, the SMD model can affect the mechanical behavior of the plate by coupling the jumpers vibration modes with the structures, creating new resonance frequencies and redistributing the vibrational energy.