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. 2021 Aug 2;21(15):5237. doi: 10.3390/s21155237
Ω bounded circular smooth domain
d distance between the two parallel disks
r radial coordinate
R radius of the device
u(r) profile of the membrane
V external electrical voltage
T radial mechanical tension of the membrane at rest
λ2 parameter depending on V and T
δ parameter that weighs the fringing field effect
E electrostatic field
|E| amplitude of the electrostatic field
K(r,u(r)) mean curvature
d critical security distance
θ factor of proportionality
ϵ0 permittivity of the free space
fel electrostatic force
pel electrostatic pressure
p mechanical pressure
u0 displacement in the center of the membrane
Cel electrostatic capacitance
ρ density
h thickness
Y Young modulus
ν Poisson ratio
D stiffness coefficient
μ(r,u(r),λ) function of proportionality
u1(r), u2(r) auxiliary functions
k constant of proportionality between p and pel
H supr(0,1]|u(r)|
FEM Finite Element Method
tol tolerance for Brent procedure
TOL tolerance for Keller–Box Scheme
RK Runge–Kutta Methods
G(r,s) Green function