Singularly Loaded Semi‐circular Plate with Clamped Diameter and Free Circular Edge

Bassali, W. A.; Mahmood, S.; Refai, Mashhoor

doi:10.1002/zamm.19760560206

Cited by 1 publication

(2 citation statements)

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“…The initial-curvature term plays the role mathematically of a transverse distributed force. Continuing with Dickinson's sequential method [11] described in section 3.1, we consider (31) first.…”

Section: Static Analysis For Initially Curved Uniform Columnsmentioning

confidence: 99%

“…There were three types of uniform beamcolumn elements: (i) seven Au elements of various lengths over the portions of the beam arms without the Pt/C coating, elements having rectangular cross sections of width w = 3 μm, depth h Au = 0.5 μm, second area moment I i = wh 3 Au 12 and radius of gyration r i = h Au / √ 12; (ii) five Au elements, each 3 μm long, over the 15 μm diameter central disk, elements having rectangular cross sections of depth h Au ; and (iii) eight identical elements over the portions of the Au beam arms with Pt/C coating. The widths of the type-ii uniform beam-column elements were selected so that the bending deformation of this model closely resembled that of an edge-loaded circular plate, as determined by a closed-form plate-theory solution [31]. The photographs of figure 1 reveal some asymmetry, about midspan, of the Pt/C coating, and the lengths and locations of the elements accounted for that asymmetry.…”

Section: (X E ) = H T (X E )D = D T H(x E )mentioning

confidence: 99%

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On the mechanical behavior of slender, slightly curved, compressed microbridges

Hallauer¹,

Ma²

2011

J. Micromech. Microeng.

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We consider a clamped–clamped, slender beam–column that is slightly curved in its unloaded static equilibrium state. Perhaps the best practical example of this type of structure is a microbeam used in sensing and actuating devices. If the clamped ends are forced toward each other, or if stiff supports inhibit axial expansion that is fostered by fabrication processes and/or operational heating, then the column bends beyond its initial curvature. If the axial force approaches the buckling load, then the static flexural deflection can be relatively large, greater than the column's depth. We show that the dependence of moderately large static deflection upon compressive force is mathematically linear, and that nonlinearity arises only in the relationship of column shortening to transverse deflection. This leads to a linear finite-element method for static structural analysis of non-uniform columns, with which we simulate the behavior of a 62.5 µm long microbridge of 0.5 µm thin-film gold. This microbridge was observed experimentally to bend 4–5 µm under compression. We also examine previous studies of bending vibration about moderately large static deflection. Calculations and experimental measurements of the dependence of the fundamental natural frequency on axial compression and initial curvature indicate practical significance relative to design of microbridge resonators.

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Section: Static Analysis For Initially Curved Uniform Columnsmentioning

confidence: 99%

Section: (X E ) = H T (X E )D = D T H(x E )mentioning

confidence: 99%