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. 2024 Mar 20;15(3):415. doi: 10.3390/mi15030415
Subscripts
APG Amplified piezoelectric generator
BB Buckled beam
BR Bistable resonator
GB Guide beam
EH Energy harvester
HA Hydraulic amplifier
HC Hydraulic cylinder
HFT High frequency transducer
HV Hydraulic valve
LFA Low frequency absorber
PFF Piezoelectric force factor
Roman letters
a [m] HV bending lever arm
ah [-] Hydraulic amplification level
Cf [Pa·s2·m−6] Pressure loss coefficient
Cf0 [Pa·s2·m−6] Opened HV pressure loss coefficient
Cfc [Pa·s2·m−6] Closed HV pressure loss coefficient
Cp [F] APG internal capacity
D [m] Diameter of a random tube
Dh [m] Hydraulic diameter of the HV
Dhc [m] Hydraulic cylinder internal diameter
Dr [m] HV rigid sheath diameter
Dt [m] Kapton tube initial diameter
Ed [J] Global dissipated energy
Ee [J] Harvested electric energy
Ehyd [J] Available hydraulic energy from earplug
Fbr [N] BR counter reaction force
f0 [Hz] BR natural resonance frequency
fd [-] Dry friction loss coefficient
K [N/m] APG stiffness
Kbb [N/m] 8 BB’s stiffness
Keq [N/m] Equivalent stiffness seen from the APG
Kgb [N/m] GB stiffness
KHV [N/m/rad] HV stiffness
Ks [N/m] Spring stiffness
Kφ [N/m/rad] Single hinge stiffness
k2 [-] APG electromechanical coupling coefficient
ksys2 [-] Global electromechanical coupling coefficient
L [m] Distance between 2 BR adjacent hinges on x axis
l0 [m] Distance between 2 BR adjacent hinges
m [kg] BR dynamic mass
pc [Pa] Comfort pressure
phc [Pa] Hydraulic cylinder internal pressure
Pe [W] Harvested electric power
q [m3/s] Flow rate
qear [m3/s] Flow rate of the fluid exiting the earplug
Q [-] BR quality factor
rCf [-] Hydraulic restriction coefficient
Rl [Ω] Load resistance
Re [−] Reynolds number
Shc [Pa] Hydraulic cylinder internal section
xm [m] BR mass position
xhc [m] HC piston position
xm [m] BR mass position
x0 [m] BR buckling height
Up [V] APG tension
Greek letters
α [N/V] Piezoelectric force coefficient
Δpear [Pa] Earplug pressure variation
ΔVear [m3] Earplug volume variation
ϵ [-] BR buckling level
ηbr [-] BR energy conversion efficiency
ηg [-] EH energy conversion efficiency
θ [rad] HV bending angle
μair [N·s/m] Air dynamic viscosity
μw [N·s/m] Water dynamic viscosity
μhc [N·s/m] HC viscous loss coefficient
ρ [kg/m3] Water density
φ [rad] BR hinge rotational angle
ω0 [rad/s] BR natural angular frequency
Indexes
a Active hydraulic branch
b Bottom side hydraulic branch ( x<0 )
c Closed HV state
i Inactive hydraulic branch ( x>0 )
o Opened HV state
t Top side hydraulic branch
max Upper value
min Lowest value