Understanding and dynamic stiffness measurement materials open up a field of practical applications, particularly in the area of under-screed insulation or acoustic linings.
La dynamic stiffness is an index and a measurement method that plays an important role in the characterization of certain materials. It allows, among other things, to evaluate the performance of insulation, an essential aspect in construction and interior design to guarantee acoustic comfort.
In particular, it determines the position of the resonance frequency of mass-spring-mass systems. This is essential for characterizing solutions, such as screed + underlay + concrete slab assemblies or elasticized EPS linings mounted on a concrete wall.
Its definition is: ratio between the force per unit area and the displacement under this force.
\[ \frac {F/S} {\Delta d} \]
with F the force, S the area and Δd the deflection.
The stiffness measurement procedure is based on an experimental method which makes it possible to obtain the resonance frequency spectrum of the mass-spring system.
So, to get a spectrum, place a spring (the complex material to be tested) under a steel plate weighing 4 or 8 kg (the mass), in a format of 20 cm x 20 cm (i.e. 1 or 2 kPa).
By hitting the plate with a hammer or by using a vibrating device (such as a vibrating pot delivering a broadband vibration), and by positioning an accelerometer, a vibration is caused.
Test bench example – ImpAcTool
This vibration (an oscillation which decreases in the case of an impact) is then analyzed by software to calculate a spectrum (FFT), thus revealing the resonance frequency (maximum peak on the curve).
Spectrum with ft, the resonant frequency
Temporal signal following an impact
The interest of this method lies in its ability to extract concrete and usable data from the resonance spectrum obtained.
The resonance frequency allows the dynamic stiffness (s't in MN/m3) to be calculated directly,
\[s'_t=4\times\pi^2\times f_r^2 \times m_{s}\]
Calculation of dynamic stiffness according to EN 29052-1 (ms, surface mass in kg/m² and fr, resonance frequency in Hz)
with “ms” the surface mass in kg/m² and “fr” the resonance frequency in Hz.
From the value (s't in MN/m3), it is possible to calculate the dynamic Young's modulus in MPa (MN/m²). This is essential because the dynamic Young's modulus is a measure of the elasticity of the material.
\[E=s_t' \times d \]
Calculation of dynamic Young's modulus in MPa (MN/m²) a measure of elasticity
with d, the thickness of the material in m
Warning !
In the case where the material contains a porous part, it is important to calculate the dynamic stiffness of the gas inside the pores (s'a) which depends on the resistance to the passage of air and the porosity. In this case, the stiffness is the sum of s'a and s't (s'=s't+s'a).
Beyond simple measurement, the spectrum also provides information about the loss factor, an indicator of how efficiently vibrational energy will be dissipated. The loss factor is calculated on the spectrum by taking the ratio of the difference in frequencies at -3dB from the maximum and the resonance frequency.
\[\eta=\frac{\Delta f}{f_r} = \frac{f_2-f_1}{f_r}\]
Loss factor
with f2 and f1 the frequencies at -3dB and fr the resonance frequency.
To learn more about calculating the Young's Dynamic Modulus, see our article on measuring Young Dynamics
Dynamic stiffness provides information for various practical applications:
In fact, this measurement conditions the resonance frequency position and the behavior of elements such as linings with plasterboard and EPS or thin underlays (SCAM) under a screed.
The lower the stiffness, the lower the resonance frequency will be, see figure below:
The isolation increases sharply once the resonant frequency is passed.
It is therefore in your best interest to properly identify dynamic stiffness!
This measurement approach is based on the NF EN 29052-1 standard [1], attesting to its reliability and recognition within the scientific and technical community.
It nevertheless requires careful implementation and the taking into account of several precautions to guarantee the accuracy of the results, including for porous materials whose characteristics require particular attention (porosity taken into account in the calculation of dynamic stiffness).
To help you measure dynamic stiffness in the best conditions, we have developed Impactool.
The table below shows dynamic Young's Modulus values for some materials. As a reminder, the dynamic Young's Modulus is calculated by multiplying the dynamic stiffness with the thickness (s't xh).
Some elasticized supports such as EPS can present different dynamic stiffnesses depending on the manufacturing processes and rigidity (Elasticization of EPS).
This data comes from Building Acoustics by Tor Erik Vigran and Sound Insulation by Carl Hopkins
