Thesis Defense Presentation

Numerical Modeling: After “Pull-in”sLδdδmaxc(x)h 0yxsFleftLFrightδp(x)Model after pull-in•Numerical solutions•Eliminate varying B.C by adding parameterCantilever Beam Deflection profiles when the tip isconstrained at zero displacement(different voltages)ε bU0•Beam equation: EIy ''''( x) = p( x)=−2 s ≤ x ≤ L[ yx− cx+h ε ]2 ( ) ( )0/r2λ = 1− s / L15Analytical Modeling: After Pull-in•Approximation equation:654321F1/42E b εε0 rUhright~ ⎜d h0•Comparisons between analytical approximations and numerical results:Force (mN)7Device I, Numerical resultsDevice I, Analytical ResultsDevice II, Numerical ResultsDevice II, Analytical results⎛⎝⎞⎟⎠3/40100 120 140 160 180 200 220 240 260Voltage (V)168