Open Access

Table 1

Basic quantities and their values.

Quantity Symbol Value Unit
Upper plate made of steel
 Mass density ϱ 8.0 × 103 kg/m3
 Young’s modulus E 2.0 × 1011 N/m2
 Poisson’s ratio ν 0.33 1
 Thickness h 0.025 m

Upper plate made of concrete
 Mass density ϱ 2.0 × 103 kg/m3
 Young’s modulus E 1.0 × 1010 N/m2
 Poisson’s ratio ν 0.33 1
 Thickness h 0.060 m

Underlay of porous material
 Porosity ε 0.50 1
 Structure factor χ 1.0 1
 Flow resistivity σ 1.0 × 104 Pa s/m2
 Stiffness per unit area of the solid structure 1.0 × 106 Pa/m
 Thickness d 0.020 m

Air inside the underlay
 Mass density ϱ 0 1.20 kg/m3
 Static air pressure p 0 1013.25 × 102 Pa
 Adiabatic exponent κ 1.4 1

Overall geometry
 Half edge length L 0.10 m
 Outer radius R 0.10 m
 Inner radius r in 1.0 × 10−3 m

Harmonic excitation at the centre of the upper plate
 Angular frequency ω Varies 1/s
 Force amplitude Varies, complex N
 Deflection amplitude Varies, complex m

Derived quantities
 Mass per unit area of the upper plate ϱh kg/m2
 Bending stiffness of the upper plate B Nm
 A scaling factor α 1/m
 A factor γ iωχϱ 0 + εσ Pa s/m2
 A factor δ ω 2 −  Pa/m
 Imaginary unit i 1

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