Research Papers

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

[+] Author and Article Information
Amir Nasrollahi

Laboratory for Nondestructive Evaluation
and Structural Health Monitoring Studies,
Department of Civil and Environmental
University of Pittsburgh,
Pittsburgh, PA 15261

Piervincenzo Rizzo

Laboratory for Nondestructive Evaluation and
Structural Health Monitoring Studies,
Department of Civil and Environmental
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: pir3@pitt.edu

Mehmet Sefa Orak

Laboratory for Nondestructive Evaluation and
Structural Health Monitoring Studies,
Department of Civil and Environmental
University of Pittsburgh,
Pittsburgh, PA 15261;
Department of Civil Engineering,
Istanbul Technical University (ITU),
Maslak, Istanbul 34469, Turkey

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 3, 2017; final manuscript received January 3, 2018; published online January 24, 2018. Assoc. Editor: Walter Lacarbonara.

J. Appl. Mech 85(3), 031007 (Jan 24, 2018) (11 pages) Paper No: JAM-17-1553; doi: 10.1115/1.4038990 History: Received October 03, 2017; Revised January 03, 2018

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.

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Fig. 1

Thin-walled spherical pressure vessel in contact with a metamaterial

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Fig. 2

Scheme of four-node quadrilateral isoparametric element

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Fig. 3

Stretched shell due to internal pressure equal to: (a) −80 MPa, (b) 40 MPa, (c) 60 MPa, and (d) 80 MPa. To ease visibility, the deformations have been magnified 500 times.

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Fig. 4

Schematic of the FEA model of a tennis ball model in contact with a HNSW transducer

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Fig. 5

Ogden model used as Hertzian stiffness to describe the particle-to-ball interaction

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Fig. 6

Numerical simulation: Time waveform of the HNSW chains in contact with the ball with internal pressure of (a) 0, (b) 60 kPa, and (f) 100 kPa

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Fig. 7

Dynamic forces exerted on the Nth particle of the chain in presence of: (a) strong precompression or hard interface material and (b) weak precompression or soft material in contact with the metamaterial

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Fig. 8

Numerical Simulation. Effect of the internal pressure on some selected features: (a) Amplitude of the incident wave, (b) amplitude of the primary reflected wave to the amplitude of the incident wave, (c) amplitude of thesecondary reflected wave to the amplitude of the incident wave, (d) TOF of the PSW, (e) TOF of the SSW, and (f)normalized TOF.

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Fig. 9

(a) The time waveform of the fifth particle of a 20 particle chain for internal pressure of 100 kPa and (b) the ISW versus the internal pressure of the fifth particle of the 20 particle chain for internal pressure of 100 kPa

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Fig. 10

(a) Scheme of the HNSW transducer and (b) photo of the transducer above one of the test specimens

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Fig. 11

Time waveform relative to sample PED #2 under pristine and deflated conditions

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Fig. 12

Experimental results. Amplitude ratio of the (a) primary reflected wave and (b) secondary reflected wave to the amplitude of the incident wave. Time of flight of the (c) primary reflected wave and (d) secondary reflected wave.

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Fig. 13

Error bars of TOF of PSW for different ball types in pristine and deflated states

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Fig. 14

A cut of each ball type shows that they are made of different materials

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Fig. 15

Internal pressure versus TOF of PSW and the fitted curve

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Fig. 16

The results of internal pressure estimation of the pressurized balls



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