Micromachined resonators are useful in making filteres and oscillators. a) Consider a doubly clamped beam with length L, width w and thickness h. Assume no residual stress. Use the variational function û = {c(1 + cos(27x/L)), where x = 0 is the center of the beam and cis the variational parameter. Show that the Rayleigh-Ritz method gives the resonant frequency 2 h wo = -72 3 L2 Ε р where E is the modulus of elasticity and p is the mass density of the material. = = c) Assume that the beam is made from a poly-Si layer of thickness 2 jm. Use a modulus of elasticity E= 160 GPa, Poisson ratio v =0.2 and mass density p= 2331 kg/m3. Find the beam length that gives a lowest resonant frequency fo = wo/27 = 10 MHz. d) Consider now a beam where width is changed to w=40 pm. Will this beam have the same lowest resonant frequency as the original thinner beam, or will it change? Give a reason for your answer.

Answer

over 3 years ago

Nakul