Nomenclature a, b = plate length, width a nm , a = deflection modal coordinate E = Young's modulus F = Airy stress function f nm = stress function modal coordinate h = plate thickness K Fd = dimensionless unidirectional (compressive) elastic foundation stiffness, ka 4 ∕D k Fd = unidirectional (compressive) elastic foundation stiffness, or linear foundation stiffness M = Mach number m = plate mass per area N x , N y , N xy = in-plane stress resultants q = flow dynamic pressure U ∞ = freestream velocity ν = Poisson's ratio w = deflection Δp = dynamic pressure λ = dimensionless dynamic pressure, 2qa 3 ∕D ω ma 4 ∕D p ξ, η = dimensionless plate length, width ϕ nm = mode shape ω = angular frequency ω = dimensionless frequency, ω ma 4 ∕D p