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. 2025 Nov 26;25(23):7222. doi: 10.3390/s25237222
Symbol Description
A Circle plate (leaf) cross-sectional area
Ab beam cross-sectional area
Cp Capacitance of the PZT
Cf Piezoelectric coupling coefficient
E Young’s modulus of the elastic beam
F Slapping force (acting on the root of the main structure)
Fb Wind force acting on both the circular plate and the rectangular plate.
I Beam area moment of inertia
I¯A Dimensionless mass moment of inertia of the circle plate (leaf)
I¯b mby2mbl2 Dimensionless beam mass moment of inertia
l Length of beam
M¯ Mass ratio of the circle plate to the beam
mb beam mass
q distributed external force
q¯ Dimensionless distributed external force
T Slapping period
T¯ Dimensionless slapping period
t Dimensional time
V Voltage
αn Eigenvalue of nth mode
ε Time scale of small perturbations.
η Von Kármán nonlinear strain
μw Dimensionless damping coefficient
ξ Generalized coordinate (time-dependent variable)
ν Dimensionless voltage
ρ Density
τ Dimensionless time
ϕn Mode shape of nth mode
σ Tuned frequency
ζn The nth mode phase
ωn Natural frequency of nth mode