Axisymmetric deformation of a circular corrugated diaphragm is defined by the equations formulated in terms of projections of displacements on the axes of the principal plane equidistant from the tops of corrugations. The optimal design problem is considered basing on the homogenization of these equations. As a result, a diaphragm consisting of a flat central part and a corrugated part with variable amplitude is obtained.
BensoussanALionsJ-LPapanicolaouJ. Asymptotic analysis for periodic structures. Amsterdam: Elsevier, 1978.
2.
Sanchez-PalenciaE. Non-homogeneous media and vibration theory. (Lecture Notes in Physics). Berlin: Springer, 1980.
3.
ManevichLAndrianovIOshmyanV. Mechanics of periodically heterogeneous structures. Berlin: Springer, 2002.
4.
HerseyM. Diaphragms for aeronautic instruments. NACA Tech. Rep.165, 1924.
5.
GriffithA. The theory of pressure capsules. Technical report, British Aeronautical Research Committee 1, London, 1927.
6.
PanovD. On large deflection of circular membrane with weak corrugations. Prikl Mat Mekh1941; 5: 303–318 (in Russian).
7.
HaringxJ. The rigidity of corrugated diaphragms. Appl Sci Res1951; 2: 299–325.
8.
AndreevaL. Elastic elements of instruments. Jerusalem: Israel Program for Scientific Translations, 1966.
9.
BidermanV. Mechanics of thin-walled structures. Moscow: Mashinostroyenie, 1977 (in Russian).
10.
YuanHLiuR-h. Nonlinear bending of corrugated diaphragm with large boundary corrugation under compound load. Appl Math Mech2003; 24: 414–429.
11.
YechK-ySongW-pRimrottF. Nonlinear instability of corrugated diaphragms. AIAA J1992; 30: 2325–2331.
12.
LiewKPengLKitipornchaiS. Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Comput Meth Appl Mech Eng2007; 196: 2358–2376.
13.
GrigorenkoYBespalovaEUrusovaG. Dynamical stability of shells of revolution with corrugated generatrix. Rep Nat Ac Sci Ukraine2010; 10: 62–66 (in Russian).
14.
LiuRYuanH. Nonlinear bending of corrugated diaphragm with large boundary corrugation under compound load. Appl Math Mech2003; 24:414–420.
15.
Di GiovanniM. 1982. Flat and corrugated diaphragm design handbook. New York: M. Dekker.
16.
KeFMiaoJWangZ. Osmic series radio-frequency microelectromechanical system switch with corrugated diaphragm. J Micro/Nanolith MEMS MOEMS2009; 8: 211–223.
17.
DissanayakeDAl-SarawiSLuT-F. Finite element modeling of surface acoustic wave device based corrugated microdiaphragms. Smart Mater Struct2009; 1: 1–11.
18.
ZouQWangZLinR. A study on corrugated diaphragms for high-sensitivity structures. J Micromech Microeng1997; 7: 310–321.
19.
ArashiroECarresoM. Polymeric corrugated membranes of PMMA fabricated by micro-casting technique for MOEMS and optical applications. J Integr Circ Syst2006; 3: 42–55.
20.
GetmanIPKaryakinMIUstinovYA. Analysis of the non-linear behaviour of circular membranes with an arbitrary radial profile. J Appl Math Mech, 2010; 74: 654–662.
21.
SyerkoEDiskovskyAAndrianovI. Corrugated beams mechanical behavior modeling by the homogenization method. Int J Solids Struct2013; 50: 928–936.
22.
YeZBerdichevskyVLYuW. An equivalent classical plate model of corrugated structures. Int J Solids Struct2014; 51: 2073–2083.
23.
BartolozziCPieriniCDereniusU. An equivalent material formulation for sinusoidal corrugated cores of structural sandwich panels. Comp Struct2013; 100: 173–185.
WinklerM. Analysis of corrugated laminates. Doctor of Sciences dissertation. ETH, Zurich, 2012.
28.
TalbiNRezakAGuoY. An analytical homogenization model for finite element modeling of corrugated cardboard. Comp Struct2009; 88: 280-289.
29.
XiaYFriswellMSaavedra FloresE. Equivalent models of corrugated panels. Int J Solids Struct2012; 49: 1453–1462.
30.
AndrianovIDiskovskyAKholodE. Homogenization method in the theory of corrugated plates. Techn Mech1998; 18:123–133.
31.
ChenJLiuL-TLiZ. Design, simulation, and evaluation of novel corrugated diaphragms based on backside sacrificial layer etching technique. In: proceedings of SPIE 4601, micromach. microfabr. process techn. devices, 2001, pp. 79–83.
32.
Van MullemCGabrielKFujitaH. Large deflection performance of surface micro machined corrugated diaphragms. In: solid-state sensors and actuators, digest of technical papers(TRANSDUCERS ’91), 1991, pp.1014–1017.
33.
ScheeperPOlthuisWBergveldP. The design, fabrication, and testing of corrugated silicon nitride diaphragms. J MEMS1994; 3: 36–43.
34.
WangWLinRRenY. Performance of a novel non-planer diaphragm for high sensitivity structures. Microelectr J2003; 34: 791–796.
35.
KanH-CYangP-HWangY-T. Modeling of corrugated diaphragms for condenser microphones. In: microsystems, packaging, assembly and circuits technology, 2007, pp.161–164.
36.
DissanayakeDAl-SarawiSLuT-F. Design and characterization of micro-diaphragm for low power drug delivery applications. In: Proc SPIE2008; 6928: 69282P–2.
37.
VarvakPMedvedevNPerelmuterA. Optimization of the geometrical form of the axisymmetric corrugated diaphragm, nonlinear problems of the structural mechanics. Optimization of Structures. Civil Engineering Institute, Kiev, 1978 (in Russian).
38.
DzjubaABulakajevP. Weight’s optimization of the shells based on Pontryagin’s maximum principle. In: abstracts of annual scientific conference(GAMM 2001), Swiss Federal Institute of Technology, Zurich, 2001.
39.
RossI. A primer on Pontryagin’s principle in optimal control. San Francisco, CA: Collegiate Publishers, 2009.
40.
AndrianovIAwrejcewiczJDiskovskyA. Asymptotic investigation of corrugated elements with quasi-periodic structures. In: 10th conference on dynamical systems – theory and applications, Lodz, Poland, 2009, pp.523–532.
41.
LiuTDengZLuT. Design optimization of truss-cored sandwiches with homogenization. Int J Solids Struct2006; 43: 7891–7918.
42.
KohnRVogeliusM. Thin plates with varying thickness, and their relation to structural optimization. Homogenization and effective moduli of materials and media. Vol. 1. New York: Springer, 1986, pp.126–149.
43.
LiptonRStuebnerM. Optimal design of composite structures for strength and stiffness: an inverse homogenization approach. Struct Multidiscipl Optimiz2007; 33: 351–362.
44.
AllaireG. Shape optimization by the homogenization method. New York: Springer, 2002.
45.
LiptonRStuebnerM. Optimization of composite structures subject to local stress constraints. Comput Meth Appl Mech Eng2006; 196: 66–75.
46.
ZavodaJ. Ultra-sensitive diaphragm with dual stress-relief structures. Patent F16J 302, USA, 1983.
47.
BertrandP. Corrugated diaphragm for a pressure sensor. Patent 4809589, USA, 1989.
48.
TimoshenkoSWoinowsky-KriegerS. Theory of plates and shells. New-York: McGraw-Hill, 1959.
49.
MasurEMrozZ. Singular solutions in structural optimization problems. Variation methods in the mechanics of solids. Oxford: Pergamum Press, 1980.
50.
BanichukN. Introduction to Optimization of Structures. New York: Springer, 1990.