### Strutt Help

Calculation of Composite Natural Frequency of a Floating Floor Over an Airspace
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**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

Comments or suggestions to
strutt@arup.com