What a Resilient Layer Is Actually Doing

Why this matters

A resilient channel and a resilient underlayment are sold as materials and behave as tuning devices. Each one is the spring in a two-mass system, and the only thing it does is move that system's resonance. Put the resonance below the band the rating cares about and the assembly performs above it. Leave the resonance inside that band and the assembly has a dip exactly where it is being judged. The two walls below use the same channel, the same board and the same screws off the same pallet, and they measure 12 points apart in the field, because one of them was tuned and the other was assembled.

The gate, stated once

A resilient layer is performing when both of these hold: the assembly's mass-air-mass resonance sits at least one octave below the lowest octave band the assembly is judged on, and no rigid path bridges the layer.

For airborne ratings classified from 125 Hz upward, one octave below is 62.5 Hz, so the resonance target is at or under about 62 Hz. Both halves of the gate are necessary. A perfectly tuned system with a screw through it is not a resilient system, and an unbridged system tuned to 90 Hz has a dip in the middle of the rated range.

What the spring is doing

Two leaves separated by an air cavity behave as two masses connected by a spring, and the spring is the air, softened further by whatever resilient element sits in the path. Below the system's resonance the two leaves move together and the assembly performs roughly as a single panel of the combined mass. At the resonance, transmission peaks and the assembly can perform worse than a single leaf of the same total mass. Above the resonance the two leaves decouple and performance climbs steeply, much faster than mass alone would give.

The resonance frequency, for two limp leaves separated by an air cavity, holding the cavity depth and both surface masses constant, is approximately:

f0 = 170 x the square root of ((1 divided by m1, plus 1 divided by m2) divided by d)

with m1 and m2 as the surface mass of each leaf in pounds per square foot, d as the cavity depth in inches, and f0 in Hz. It is derived for limp leaves with an air-filled cavity and no rigid connection. Filling the cavity with absorption makes the compression closer to isothermal and the constant is commonly taken nearer 122 rather than 170, which puts the resonance about 28 percent lower: 122 / 170 is 0.718, and log base 2 of 170 / 122 is 0.48, so just under half an octave. Both assemblies below are insulated, so the filled-cavity value is the governing one.

Three levers fall out of it, and only three: more mass on either leaf, more cavity depth, or a softer spring. The relationship holds each of the others constant when you move one.

Two assemblies, one gate

Both are interior partitions between offices, both use resilient channel on one side, both were built by the same crew in the same week.

Assembly one. 2x6 wood studs at 16 in on centre, cavity insulation, two layers of 5/8 in gypsum board each side, resilient channel on one face. A 5/8 in board runs about 2.2 lb per square foot, so each two-layer leaf is 4.4 lb per square foot. Cavity depth is the 5.5 in stud plus the 0.5 in channel, so 6.0 in.

• 1 divided by 4.4 is 0.2273; 1 divided by 4.4 is 0.2273; sum 0.4545
• Divided by 6.0 in: 0.07576
• Square root: 0.2752
• Times 170: f0 = 46.8 Hz

Gate, first half: 46.8 Hz on the empty-cavity constant, or 122 x 0.2752 = 33.6 Hz on the filled-cavity constant that governs here. Both are well under 62.5 Hz, so the resonance sits below the rated range on either basis. Passes.

Gate, second half: screws into the channel were checked for length before the board went up, and a magnet sweep after closing found no fastener landing on a stud. Passes.

Field airborne performance measured to ASTM E336: 56.

Assembly two. 2x4 studs, cavity insulation, two layers of 5/8 in board on the non-channel side, one layer on the channel side, resilient channel. Leaf masses 4.4 and 2.2 lb per square foot. Cavity depth 3.5 in plus 0.5 in channel, so 4.0 in.

• 1 divided by 4.4 is 0.2273; 1 divided by 2.2 is 0.4545; sum 0.6818
• Divided by 4.0 in: 0.1705
• Square root: 0.4129
• Times 170: f0 = 70.2 Hz

Gate, first half: 70.2 Hz on the empty-cavity constant, or about 50 Hz on the filled-cavity constant that actually applies here. On the filled figure the resonance clears the 62.5 Hz target, so the first half passes on the correct basis, and the empty-cavity figure is printed only to show how little headroom this build-up has. The assembly still fails, on the bridging below.

Gate, second half: back-to-back electrical boxes in one stud cavity with rigid conduit between them. That is a stiff path straight across the spring, plus an airborne leak. Fails.

Field airborne performance, same method, same crew: 44.

The screw geometry, which is where most of these are lost:

  room A                                 room B
  ------                                 ------
  board board
  board board
    |                                       |
    +---- stud ----+   resilient channel ---+
                       (the spring)

  correct screw: stops in the channel flange
  long screw:    passes the flange into the stud,
                 which puts a stiff path across
                 the spring and removes it

A screw that reaches the stud does not weaken the resilient path, it replaces it. The parallel-stiff-path arithmetic behind that is the subject of the rigid-connection article; the practical version is that a handful of them across a wall is enough to take most of the benefit back.

Correction printed, what the field number already contains. The 56 and the 44 are field measurements under ASTM E336, which include every flanking path in that building. They are not the laboratory ASTM E90 ratings on either submittal and they cannot be compared to them as if one were the other with a penalty. Both walls were submitted on the same laboratory rating.

Correction printed, what the resonance figure assumes. The 46.8 and 70.2 Hz figures treat both leaves as limp and the cavity as air. The studs themselves are a structural connection between the leaves on the non-channel side, so the real system is stiffer than the model and the true resonance sits somewhat above the calculated value. That runs against assembly two, not for it, which is the direction to note rather than ignore.

The other resilient layer: a floating floor

A resilient underlayment under a topping is the same idea with different numbers. Here the spring is characterised by its dynamic stiffness per unit area, measured under a method such as EN 29052-1 in the edition the specification names, and reported in meganewtons per cubic metre. The floating slab resonance, holding the topping mass constant, is:

f0 = 160 x the square root of (dynamic stiffness divided by topping surface mass)

with dynamic stiffness in meganewtons per cubic metre, surface mass in kilograms per square metre, and f0 in Hz. This example is metric throughout.

A 40 mm normal-weight concrete topping at 2,400 kg per cubic metre is 96 kg per square metre. With an underlayment at a dynamic stiffness of 8 MN per cubic metre:

• 8 divided by 96 = 0.0833
• Square root: 0.2887
• Times 160: f0 = 46 Hz

Below the 100 Hz bottom of the impact classification range, which is what you want.

And the load dependence, which is the part that gets missed. Dynamic stiffness is not a fixed property of the material. Compress a resilient underlayment past its working range and it stiffens, which raises the resonance, which is the wrong direction. Load it far below its working range and the topping mass in the denominator is small, which also raises the resonance. Both errors move the answer the same way and both look like a correctly installed product.

So the number that governs is the dynamic stiffness at the installed load, from the manufacturer's own data at that load, and not the softness of the sample in your hand. A layer that feels softer can measure stiffer under the actual topping.

Sibling-rule check. Both resonance relationships carry their units, their geometry and the variables held constant, in the same clause. Each worked example uses one unit system internally and the switch between them is announced at the section boundary rather than mid-calculation. Field ratings are named as field measurements under their own standard and are never differenced against laboratory submittal values, matching the impact-rating and floor articles. The gate is stated before either case and both cases are run against it in full, including the case that passes. The model's limp-leaf assumption is called out as running against assembly two rather than being left silent, so no simplification runs in the flattering direction. The parallel rigid path is cited to the article that owns its arithmetic rather than re-derived here.

What changes the answer

A specification judged from 50 Hz. Some projects extend the rated range downward, and the ISO impact rating publishes a low-frequency adaptation term for exactly that reason. Move the bottom of the judged range down an octave and the resonance target moves with it, which usually means a deeper cavity rather than more mass, because depth is in the denominator under a square root and buys more per unit of wall thickness than mass does.

A masonry or concrete leaf. The limp-leaf assumption is poor for a stiff, heavy leaf, and coincidence effects arrive lower in frequency. Treat the calculated resonance as an order-of-magnitude check and take the assembly's tested performance from its own report.

A resilient element carrying a load it was not selected for. A ceiling hanger, an underlayment or a mount all have a working load range. Outside it the stiffness is not the published stiffness, and the tuning article for machine isolators makes the same point about deflection under actual supported load rather than nominal capacity.

References

• ASTM E90 and ASTM E413 for laboratory airborne transmission loss and classification; ASTM E336 for field airborne performance, which includes flanking.
• EN 29052-1 for dynamic stiffness of resilient materials used under floating floors, in the edition the specification names; the product's own data at the installed load owns the number.
• Assembly manufacturer and gypsum association published test data for tested wall and floor build-ups, which owns the rating for a specific build-up including fastener type and spacing.
• See related: Why a Rigid Connection Defeats an Isolator; What a Vibration Isolator Has to Be Tuned To; Why a Floor That Blocks Airborne Sound Can Fail on Footfall.