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Calculation of Composite Natural Frequency of a Floating Floor Over an Airspace    1/1,1/3

Strutt|Vibration|Building Vibration|Natual Frequency of Floating Floor calculates the effect of airspace stiffness on the overall natural frequencies of floating floors according to the following formula:

f_a = 1/(2 pi)sqrt((gamma P_0 (m_1 + m_2)) / (phi h m_1 m_2))

f_(nat) = sqrt(f_m^2 + f_a^2)

where:
f_a is the natural frequency of floating floor on airspace (excluding effect of isolation pads), Hz
gamma is the ratio of specific heats: 1.4 where adiabatic conditions apply (normal case), 1.0 for isothermal conditions (i.e. where a fibreglass quilt is provided in cavity)
P_0 is the equilibrium pressure in void (Pa or \text(psi)): normally P_0 = atmospheric pressure = 101325 Pa or 14.696 \text(psi)
m_1 is the mass per unit area of the floating floor - surface density, kg//m^2 or lb//ft^2
m_2 is the mass per unit area of the base slab - surface density, kg//m^2 or lb//ft^2
phi is the porosity (constant factor (0 - 1) of how porous the absorber is, typically 0.95 - 0.99 for rockwool)
h is the thickness of the airgap, m or ft
f_(nat) is the overall vertical natural frequency, Hz
f_m is the natural frequency due to stiffness of supporting mounts, Hz

If m_2 is excluded from the calculation using the check box on the user form (which effectively sets m_2 = \infty) and if phi=1, the equation simplifies to:
f_a = 1/(2 pi)sqrt((gamma P_0) / (m_1 h))

References:

• Floating Floors - an appraisal, Journal of Society of Environmental Engineers, June 1977, P Allaway
• Design of Floated Slabs to Avoid Stiffness Effect of Entrapped Air, Eric Ungar, Noise Control Engineering, Vol 5, No1, July/Aug 1975