2024/07/05 by Sunil Kumar Maurya, Anil Kumar, Prakash Kumar
Engineering · #Advanced Sensor and Energy Harvesting Materials #Artificial intelligence #Classical mechanics #Computer science #Control theory (sociology) #Mechanics #Nonlinear system #Physics #Quantum mechanics #Robotic Locomotion and Control #Sports Dynamics and Biomechanics
paper · doi:10.1142/s0219455425501780
openalex publication_date 2024/07/05 · crossref created 2024/07/05 · crossref issued 2024/07/31 · crossref published 2024/07/31 · crossref published-online 2024/07/31 · crossref deposited 2025/08/11 · crossref published-print 2025/09/15 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/05
This paper proposed a single-degree-of-freedom self-sustained nonlinear oscillator capable of precisely predicting the bouncing force induced by a person during bouncing activity on a flat and rigid surface. A bouncing person produces essential internal energy required to maintain its motion, so it can be modeled as a self-sustained oscillator that can generate (i) the stable limit cycle, (ii) the periodic bouncing force signal, and (iii) the self-sustained motion. A hybrid Van der Pol–Rayleigh oscillator added with two quadratic and one cubic nonlinear terms has been derived to yield desired softening and hardening effects as well as even and odd harmonics, as observed from the analysis of experimental bouncing force data. The force applied on the surface corresponds to its restoring force. The stability analysis of the oscillator has been performed using the energy balance and perturbation methods. The model parameters are extracted from the experimental bouncing force data resulting from a bouncing test on a group of seven subjects with shoe insoles at six different frequencies guided by a metronome. The bootstrapping method has been performed to examine the convergence of mean values of each model parameter by increasing the cardinality of the experimental set. The bouncing force signals produced by the proposed model and experimental results demonstrate an excellent agreement.