This study describes a physics-based and data-driven nonlinear system identification approach for detecting early fatigue damage due to vibratory loads. The approach also allows for tracking the evolution of damage in real-time. Nonlinear parameters such as geometric stiffness, cubic damping and phase angle shift can be estimated as a function of fatigue cycles, which are demonstrated experimentally using flexible aluminum 7075-T6 structures exposed to vibration. Nonlinear system identification is utilized to create and update nonlinear frequency response functions, backbone curves and phase traces to visualize and estimate the structural health. Findings show that the dynamic phase is more sensitive to the evolution of early fatigue damage than nonlinear parameters such as the geometric stiffness and cubic damping parameters. A modifed Carrella-Ewins method is introduced to calculate the backbone from the nonlinear signal response, which is in good agreement with the numerical and harmonic balance results. The phase tracing method is presented, which appears to detect damage after approximately 40% of fatigue life, while the geometric stiffness and cubic damping parameters are capable of detecting fatigue damage after approximately 50% of the life-cycle.

A nature-inspired musculoskeletal system is designed and developed to examine the principle of nonlinear elastic energy storage–release for robotic applications. The musculoskeletal system architecture consists of elastically rigid segments and hyperelastic soft materials to emulate rigid–soft interactions in limbless vertebrates. The objectives are to (i) improve the energy efficiency of actuation beyond that of current pure soft actuators while (ii) producing a high range of motion similar to that of soft robots but with structural stability. This paper proposes a musculoskeletal design that takes advantage of structural segmentation to increase the system’s degrees of freedom, which enhances the range of motion. Our findings show that rigid–soft interactions provide a remarkable increase in energy storage and release and, thus, an increase in the undulation speed. The energy efficiency achieved is approximately 68% for bending the musculoskeletal system from the straight configuration, compared to 2.5–30% efficiency in purely soft actuators. The hybrid compliance of the musculoskeletal system under investigation shows promise for alleviating the need for actuators at each joint in a robot.