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. 2021 Oct 12;14(20):5992. doi: 10.3390/ma14205992
a Radius of the circular membrane
h Thickness of the circular membrane
E Young’s modulus of elasticity
ν Poisson’s ratio
H Height of the liquid in the storage container
ρ Density of the liquid in the storage container
g Acceleration of gravity
r Radial coordinate of the cylindrical coordinate system (r, φ, w)
φ Circumferential angle coordinate of (r, φ, w)
w Axial coordinate of (r, φ, w) as well as transverse displacement
u Radial displacement of the deflected circular membrane
w m Maximum deflection of the deflected circular membrane
q(r) Transverse loads that varies continuously with the radial coordinate r
F(r) External force produced by q(r) within radius r
σ r Radial stress
σ t Circumferential stress
e r Radial strain
e t Circumferential strain
θ Rotation angle of the deflected circular membrane
π Pi (ratio of circumference to diameter)
W Dimensionless transverse displacement (w/a)
S r Dimensionless radial stress (σr/E)
S t Dimensionless circumferential stress (σt/E)
H 0 Dimensionless height H (H/a)
G Dimensionless quantity (ρga2/Eh)
x Dimensionless radial coordinate (r/a)
C Capacitance of a non-parallel plate capacitor
D Initial gap of the non-parallel plate capacitor
b i Coefficients of the power series for capacitance C
c i Coefficients of the power series for Sr
d i Coefficients of the power series for W