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Research Papers

Electromagnetically-Induced Vibration in Particulate-Functionalized Materials

[+] Author and Article Information
T. I. Zohdi

Department of Mechanical Engineering,
6195 Etcheverry Hall,
University of California,
Berkeley, CA, 94720-1740

Such forces can arise from surrounding medium and the external electromagnetic fields.

The unit normal has been taken into account; thus the presence of a change in sign.

The superscript L is a time interval counter.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 21, 2012; final manuscript received October 26, 2012; published online March 28, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(3), 031007 (Mar 28, 2013) (8 pages) Paper No: VIB-12-1113; doi: 10.1115/1.4023251 History: Received April 21, 2012; Revised October 26, 2012

In many small-scale devices, the materials employed are functionalized (doped) with microscale and/or nanoscale particles, in order to deliver desired overall dielectric properties. In this work, we develop a reduced-order lumped-mass model to characterize the dynamic response of a material possessing a microstructure that is comprised of an electromagnetically-neutral binder with embedded electromagnetically-sensitive (charged) particles. In certain industrial applications, such materials may encounter external electrical loading that can be highly oscillatory. Therefore, it is possible for the forcing frequencies to activate the inherent resonant frequencies of these micro- and nanostructures. In order to extract qualitative information, this paper first analytically investigates the mechanical and electromagnetic (cyclotronic) contributions to the dynamic response for a single particle, and then quantitatively investigates the response of a model problem consisting of a coupled multiparticle periodic array, via numerical simulation, using an implicit temporally-adaptive trapezoidal time-stepping scheme. For the model problem, numerical studies are conducted to observe the cyclotronically-dominated resonant frequency and associated beat phenomena, which arises due to the presence of mechanical and electromagnetic harmonics in the material system.

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Grahic Jump Location
Fig. 2

The model problem for the numerical simulation. It is a periodic array of 7×7×7 charged particles embedded in a binding medium, due to external oscillatory loading. As for the isolated, single particle example, for each particle, vi(t = 0) = 0, Bext = B3exte3 and Eext=E1exte1, where E1ext=E0extsinΩt.

Grahic Jump Location
Fig. 1

A base, electromagnetically-neutral, solid that is doped with electromagnetically-sensitive particulates

Grahic Jump Location
Fig. 3

Various responses of the CG of the sample to the values of the forcing frequency, left to right and top to bottom: (a) Ω = 0.1ω, (b) Ω = 0.2ω, (c) Ω = 0.4ω, (d) Ω = 0.8ω, (e) Ω = 1.0ω (very near to resonance), (f) Ω = 1.2ω, (g) Ω = 1.4ω and (h) Ω = 1.8ω. Note that as for the isolated, single particle example, for each particle, vi(t = 0) = 0, Bext = B3exte3 and Eext = E1exte1, where E1ext = E0extsinΩt.

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