Numerical and Experimental Study on the Dynamic Interaction Between Highly Nonlinear Solitary Waves and Pressurized Balls

Abstract

This paper discusses the dynamic interaction between a monoatomic chain of solid particles and a thin-walled spherical pressure vessel. The objective is to find a relationship between the highly nonlinear solitary waves (HNSWs) propagating within the chain and the internal pressure of the vessel. The paper introduces first a general finite element model to predict the abovementioned interaction, and then a specific application to tennis balls. The scope is to demonstrate a new nondestructive testing (NDT) method to infer the internal pressure of the balls. The overarching idea is that a mechanically induced solitary pulse propagating within the chain interacts with the thin-walled ball to be probed. At the chain–ball interface, the acoustic pulse is partially reflected back to the chain and partially deforms the rubber giving rise to secondary pulses. The research hypothesis is that one or more features of the reflected waves are monotonically dependent on the internal pressure. Both numerical and experimental results demonstrate a monotonic relationship between the time of flight (TOF) of the solitary waves and the internal pressure of the tennis balls. In addition, the pressure inferred nondestructively with the HNSWs matches very well the pressure measured destructively with an ad hoc pressure gauge needle. In the future, the results presented in this study could be used to develop a portable device to infer anytime anywhere the internal pressure of deformable systems (including biological systems) for which conventional pressure gages cannot be used noninvasively.

Outlier analysis of nonlinear solitary waves for health monitoring applications

“…During the experiment, the primary reflected wave consisted either of a single hump (Figure 9(a)) or of twin peaks (Figure 9(b)). The mechanism that originates the twin peaks was observed in the past and explained in Nasrollahi et al 55 In brief, the dynamic force at each bead of the chain is the average of the dynamic force of the two adjacent spheres. When the body in contact with a transducer is much softer than the particles forming the chain or the pre-compression is small, the time delay between the two dynamic forces is relatively large, giving rise to the twin peaks.…”

Wireless Module for Nondestructive Testing/Structural Health Monitoring Applications Based on Solitary Waves

“…Another distinctive feature of the wireless platform is that it was able to detect a twin peak associated with the dynamic interaction of the waves with the foam. The origin of these twin-peaks, originally identified and detailed in [58] and elaborated further in [43], was found in several HNSW-based NDE related to soft materials including rubber [44]. For the sake of completeness, the dynamic interaction among the particles that induce the "twin-peaks" is discussed in Section 5.…”

“…The hardware generates the signal to open/close the electrical current to feed the solenoid, while the user interface allows for the selection of the repetition rate of the striker (by controlling the output signal), the number of measurements, the sampling frequency of the digitized waveforms, and the storage of the waveforms for post-processing analysis. The transducers used in this study were also successfully used elsewhere [19,[43][44][45]54] and were, therefore, the starting point to develop the proposed wireless platform. However, it is emphasized here that the proposed platform can be adopted and adapted to a chain of any size, length, and particle materials.…”

“…In the proposed wireless node, the DC current is provided by the PCB. Following the protocol implemented in the PXI in previous studies [19,[43][44][45]54], the solenoid is energized for 250 ms, an interval sufficiently long to lift the striker until it touches the electromagnet before falling freely onto the array. The energy necessary to deliver the current necessary to operate the electromagnet is significant with respect to the other electronic components and is directly proportional to the weight and the falling height of the striker.…”

“…A numerical study on the interaction of HNSWs with composite beams showed that solitary waves are helpful to evaluate the directional elastic parameters of the composites [40]. Others reported that the method is effective at detecting subsurface voids [38], assessing the quality of adhesive joints [22,30], composites [31,34,40,41], orthopedic and dental implants [32,42], and at measuring internal pressure [43][44][45][46] and axial stress [47,48].…”