TY - GEN
T1 - A static and nonlinear dynamic analysis of resonant microbeams
AU - Emam, Samir A.
AU - Khater, Mahmoud E.
AU - Gad, Emil H.
PY - 2008
Y1 - 2008
N2 - An investigation into the response of microbeams to DC and AC electric actuation is presented. The beam is modeled according to the Euler-Bernoulli beam theory and small strains and moderate rotation approximations are assumed. The governing equation is a nonlinear integral-partial-differential equation in space and time. The model accounts for mid-plane stretching, applied axial load, DC electrostatic forces, and AC harmonic forces. A reduced-order model based on the Galerkin discretization technique is introduced to simulate the behavior of microswitches and resonant sensors. The static behavior of the microbeam under electrostatic forces is studied and compared to the results available in the literature. The dynamic behavior of resonant microbeams under AC harmonic forces is investigated. An analytical solution for the vibration modes and natural frequencies of the microbeam around its statically deflected position is obtained. A shooting method is used to numerically integrate the nonlinear discretized equations and obtain periodic orbits of the response. The stability of these periodic orbits is investigated using Floquet theory. The sensitivity of the device to small-amplitude excitations is also investigated.
AB - An investigation into the response of microbeams to DC and AC electric actuation is presented. The beam is modeled according to the Euler-Bernoulli beam theory and small strains and moderate rotation approximations are assumed. The governing equation is a nonlinear integral-partial-differential equation in space and time. The model accounts for mid-plane stretching, applied axial load, DC electrostatic forces, and AC harmonic forces. A reduced-order model based on the Galerkin discretization technique is introduced to simulate the behavior of microswitches and resonant sensors. The static behavior of the microbeam under electrostatic forces is studied and compared to the results available in the literature. The dynamic behavior of resonant microbeams under AC harmonic forces is investigated. An analytical solution for the vibration modes and natural frequencies of the microbeam around its statically deflected position is obtained. A shooting method is used to numerically integrate the nonlinear discretized equations and obtain periodic orbits of the response. The stability of these periodic orbits is investigated using Floquet theory. The sensitivity of the device to small-amplitude excitations is also investigated.
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U2 - 10.1115/DETC2007-34376
DO - 10.1115/DETC2007-34376
M3 - Conference contribution
AN - SCOPUS:44849123432
SN - 0791848027
SN - 9780791848029
SN - 0791848027
SN - 9780791848029
T3 - 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
SP - 883
EP - 892
BT - 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
T2 - 21st Biennial Conference on Mechanical Vibration and Noise, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
Y2 - 4 September 2007 through 7 September 2007
ER -