Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

The use of bounding scenarios is a common practice which greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems, and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree of freedom mass-spring system with an elastic-plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

shorts: An R Package for Modeling Short Sprints

Short sprint performance is one of the most distinguishable and admired physical trait in sports. Short sprints have been modeled using the mono-exponential equation that involves two parameters: (1) maximum sprinting speed (MSS) and (2) relative acceleration (TAU). The most common methods to assess short sprint performance are with a radar gun or timing gates. In this paper, we: 1) provide the {shorts} package that can model sprint timing data from these two sources; 2) discuss potential issues with assessing sprint time (synchronization and flying start, respectively); and 3) provide model definitions within the {shorts} package to help alleviate errors within the subsequent parameter outcomes.

Averaging analysis on a semi-active inerter–based suspension system with relative-acceleration–relative-velocity control

The semi-active inerter–based suspension system with a semi-active inerter is proposed in this article to improve the dynamic performance of the passive one. The fluid inerter is used to implement the semi-active inerter and has two adjustable inertances: the maximum and minimum inertances. Based on the relative acceleration and relative velocity between the unsprung mass and sprung mass of the suspension system, and combined with the mechanical property of the semi-active inerter, the relative-acceleration–relative-velocity control strategy is proposed and has two different types: relative-acceleration–relative-velocity+− and relative-acceleration–relative-velocity−+ control strategies, respectively. The relative-acceleration–relative-velocity+− control strategy means adjusting the inertance of the semi-active inerter to the maximum one when the signs of relative acceleration and relative velocity are the same, and to the minimum one when the signs are the opposite, and the meaning of relative-acceleration–relative-velocity−+ control strategy does the reverse. The dynamic response of the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity control strategy is obtained using the averaging method, and its dynamic performance is evaluated using three performance indices: vehicle body acceleration, dynamic tire load, and suspension system stroke. The results show that the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity+− control strategy can have a better dynamic performance for the dynamic tire load and suspension system stroke in which the low-frequency and high-frequency resonance peaks can be smaller, but is poor for the vehicle body acceleration in which the high-frequency resonance peak can be significantly larger; whereas the relative-acceleration–relative-velocity−+ control strategy does the reverse. For smaller maximum and minimum inertances, the relative-acceleration–relative-velocity+− and relative-acceleration–relative-velocity−+ control strategies can achieve the corresponding better performance indices, with a small degeneration for the other performance indices.

Paradoxical Chaos-Like Chattering in the Bouncing Ball System

This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behaviour) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.

Transport Estimates

This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, with the goal of choosing the lifespan parameter τ‎ sufficiently small so that all the phase functions which appear in the analysis can be guaranteed to remain nonstationary in the time interval, and so that the Stress equation can be solved. In order for these requirements to be met, τ‎ small enough is chosen so that the gradients of the phase functions do not depart significantly from their initial configurations. The chapter presents a proposition that bounds the separation of the phase gradients from their initial values in terms of b (b is less than or equal to 1, a form related to τ‎). Finally, it gathers estimates for relative velocity and relative acceleration.