Refined Dynamic Stability Theory of Laminated Isotropic Circular Plates

Krizhevsky, G.; Stavsky, Y.

doi:10.1115/1.2789059

Cited by 4 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in radial coordinates ͑r , ͒ [23] where J ͑kr͒ is a Bessel function of the first kind of order with wave number k. Similar spatial dependencies have been seen in other systems [24,25]. Bessel functions of the second kind, Y ͑kr͒, were not chosen due to their unphysical divergence at r = 0.…”

Section: Modelingmentioning

confidence: 90%

Cylindrically symmetric electrohydrodynamic patterning

et al. 2004

View full text Add to dashboard Cite

Cylindrically symmetric structures such as concentric rings and rosettes arise out of thin polymeric films subjected to strong electric fields. Experiments that formed concentric rings and theory capable of explaining these and other cylindrical structures are presented. These rings represent an additional member of a class of structures, including pillars and holes, formed by electrohydrodynamic patterning of thin films, occasionally referred to as lithographically induced self-assembly. Fabrication of a set of concentric rings begins by spin coating a thin poly(methyl methacrylate) film onto a silicon wafer. A mask is superimposed parallel to the film leaving a similarly thin air gap. Electric fields, acting in opposition to surface tension, destabilize the free interface when raised above the glass transition temperature. Central pillars nucleate under small cylindrical protrusions patterned on the mask. Rings then emerge sequentially, with larger systems having as many as 10 fully formed rings. Ring-to-ring spacings and annular widths, typically on the order of a micron, are approximately constant within a concentric cluster. The formation rate is proportional to the viscosity and, consequently, has the expected Williams-Landel-Ferry dependence on temperature. In light of these developments we have undertaken a linear stability analysis in cylindrical coordinates to describe these rings and ringlike structures. The salient feature of this analysis is the use of perturbations that incorporate their radial dependence in terms of Bessel functions as opposed to the traditional sinusoids of Cartesian coordinates. The theory predicts approximately constant ring-to-ring spacings, constant annular widths, and growth rates that agree with experiment. A secondary instability is observed at higher temperatures, which causes the rings to segment into arcs or pillar arrays. The cylindrical theory may be generalized to describe hexagonal pillar/hole packing, gratings, and rosettes with the first being of particular importance given the ubiquitous observation of hexagonal packing. The perturbation analysis presented here is relevant to any system with cylindrical symmetry, for which the radial dependence can be described in terms of Bessel functions.

show abstract

Section: Modelingmentioning

confidence: 90%

Cylindrically symmetric electrohydrodynamic patterning

et al. 2004

View full text Add to dashboard Cite

show abstract

“…Beside the mechanical behavior known from homogeneous structural elements, additional complicating effects can appear in layered structures. The review article of Chia [4] compiles various geometrically nonlinear effects on the behavior of composite plates, and a refined dynamic stability theory of laminated plates is derived in [5]. Furthermore, in some widely used structures, such as in composite steel-concrete beams or in layered wood systems connected with nails, rigid bond between the layers cannot be achieved.…”

Section: Introductionmentioning

confidence: 99%