Why a Rigid Connection Defeats an Isolator

Why this matters

Vibration paths run in parallel, and parallel paths are dominated by the stiffest one, not averaged. That single fact decides most isolation jobs, and it runs against intuition in a way that costs money: a set of mounts stopping 95 percent of the force can be reduced to stopping about 30 percent by one length of rigid conduit, on the conservative reading of that conduit's stiffness, and softening the mounts to fix it makes the bypass share of the load go up rather than down. The paths an isolator cannot reach are what set the result, so the useful skill is not selecting a better mount, it is finding the bridges.

Before you touch anything under a mounted machine

A loaded spring isolator is stored mechanical energy. Take the machine's weight on rigging or jacks and set cribbing under it before releasing any mount, stay out of the plane a spring would travel in if it let go, and isolate and lock the machine under 29 CFR 1910.147 first.

Cutting into a conduit or fitting a flexible whip is electrical work: de-energize, lock, tag and verify absence of voltage under 29 CFR 1910.333(b)(2) for general industry, or 29 CFR 1926.417 for construction, and prove the instrument live, dead and live again per NFPA 70E-2021, 120.5, which reaches you through your employer's electrical safety program in the edition it adopted. Where a variable frequency drive feeds the machine, wait the bus discharge time the drive's manual states and verify the bus discharged with an instrument before opening anything.

Rooftop work near an unprotected edge needs fall protection under 29 CFR 1910.28 for general industry low-slope roof work, or 29 CFR 1926 Subpart M where the job is construction, and it needs it before the first trip out, not after the first measurement.

Paths add in parallel, and the stiffest one wins

At frequencies well above the isolated system's own natural frequency, and with both paths driven by the same relative motion between machine and structure, the force each path carries is roughly proportional to that path's stiffness. So with an isolator set of total stiffness k-iso and a rigid bypass of stiffness k-bypass in parallel, the best achievable transmission is bounded below by:

k-bypass divided by (k-bypass plus k-iso)

That expression holds the receiving structure much stiffer than either path, treats both paths as driven by the same relative displacement, and applies above the isolated resonance. It says nothing about airborne noise, which travels a different path entirely and is not an isolator's job in the first place.

The consequence is not a small penalty. It is a floor. No amount of mount quality gets you below it, because the bypass is not in series with the isolator, it is beside it.

What an isolator cannot reach

The negative space is the article. An isolator controls exactly one path: the one through the isolator. Everything on this list is a path in parallel with it, and every one of them has been found carrying the load on a job where the mounts were correct.

• Rigid conduit from the machine to a curb-mounted or structure-mounted disconnect.
• Hard-piped condensate or drain lines clamped to the curb or the deck.
• A flexible connector installed taut. A flexible pipe or duct connector is a soft link only when it is slack. Pulled straight it is a rod with a bellows in the middle.
• A duct connection made up solid, or a flexible section compressed hard enough to bear.
• A curb seal or gasket packed to bearing, which turns a weather detail into a structural one.
• Seismic snubbers set to contact rather than with the gap their submittal calls for.
• Grout or shims under a rail or a foot that were meant to be temporary and were never pulled.
• A pipe hanger a few feet downstream that is rigid, which returns the pipe's motion to the building after a perfectly good flexible connector at the machine.
• An anchor bolt run through a pad and torqued down, which compresses the pad out of its working range and turns it into a washer.
• Standing water that freezes across a mount, which is seasonal and produces a complaint that arrives every winter and leaves every spring.

Worked example: one conduit against four mounts

A 4,000 lb rooftop machine on four spring mounts, 1,000 lb per mount, each with 1.0 in of static deflection under its share of load. Stiffness is load divided by deflection, so 1,000 lb per inch per mount, 4,000 lb per inch for the set.

What the mounts do on their own. At a forcing frequency well above the isolated resonance, this set was selected to transmit about 4.5 percent of the machine's force, which is the figure the vibration-isolating-connection article derives from the frequency ratio; that arithmetic belongs to that article and is not repeated here.

The bypass. A run of 3/4 in rigid metal conduit, nominal published dimensions 1.050 in outside diameter and 0.113 in wall, spanning 18 in between the machine and a curb-mounted disconnect. Second moment of area for a tube is pi divided by 64, times outside diameter to the fourth minus inside diameter to the fourth: 0.0491 x (1.2155 minus 0.4611) = 0.0370 in to the fourth. Steel modulus 29,000,000 psi.

Correction printed, boundary condition. Lateral stiffness of a beam depends on how its ends are held, and the choice changes the answer by a factor of four. Take the softest defensible case, pinned at both ends, 48 x modulus x second moment divided by span cubed, because taking the stiffest case would flatter the finding:

• 48 x 29,000,000 = 1.392 billion
• times 0.0370 = 51,560,000
• divided by 18 cubed, which is 5,832 = 8,841 lb per inch

Fixed at both ends, which is closer to a clamped conduit in practice, the same expression with 192 in place of 48 gives 35,363 lb per inch. The conservative number is used below.

What that does to the result. The bypass is 8,841 lb per inch against an isolator set at 4,000 lb per inch. Transmission floor is 8,841 divided by (8,841 plus 4,000), which is 0.689. About 69 percent of the force reaches the deck no matter what the mounts do.

The mounts alone gave about 4.5 percent. With the conduit in place the floor is about 69 percent. That is a factor of roughly 15, or about 12 dB of isolation thrown away by one conduit, and it is the conservative reading; on the clamped assumption it is 90 percent transmitted and worse.

How soft the bypass would have to be. For the bypass to cost less than half a decibel against the isolators' 4.5 percent, it would have to contribute under about 0.55 percent, which needs a stiffness under about 22 lb per inch. Nothing rigid is that soft. This is the calculation that tells you not to calculate: you break the path, you do not select around it.

Why softer mounts make this worse

The instinct when isolation disappoints is to buy a softer mount. Run it:

Replace the 1.0 in deflection mounts with 3.0 in deflection mounts under the same load. Stiffness per mount becomes 1,000 divided by 3, which is 333 lb per inch, so 1,333 lb per inch for the set.

• Bypass share before: 8,841 divided by 12,841 = 68.9 percent
• Bypass share after: 8,841 divided by 10,174 = 86.9 percent

The mounts got three times softer and the total force reaching the structure went up, because the bypass did not change and now carries a larger share of a stiffer overall path arrangement. The mount upgrade only pays once the bypass is gone, which is exactly why the rooftop case in the sibling article corrected the mounts and the flanking paths in one visit rather than sequentially.

Sibling-rule check. The transmissibility arithmetic is cited to the article that owns it rather than re-derived, and the numbers used here (4.5 percent transmission, 1.0 in and 3.0 in static deflection) are the same quantities that article uses, in the same direction: lower natural frequency improves isolation above the frequency ratio of 1.41, and a flanking path sets the floor on what any isolator can achieve. Every stiffness carries its units and its derivation, and the beam stiffness carries its boundary condition, with the softer of the two defensible cases used so the finding is not flattered. The parallel-path expression carries its held-constant conditions in the same clause. Nothing in this article claims an isolator addresses airborne sound. No rounding runs toward the more dramatic answer: the 12 dB figure comes from the pinned case, and the clamped case would have read larger.

How to break a path properly

A flexible whip, with a loop and slack. A liquidtight flexible whip is only soft in bending across the loop. Install a service loop, orient it so the machine's motion is across the loop rather than along the conduit axis, and anchor one end to the machine and the other to the building with genuine slack in between. Take the whip's own bending data from the manufacturer rather than assuming a flexible product is soft.

Flexible pipe connectors installed slack, and the first hanger resilient. A connector at the machine followed by a rigid hanger three feet away returns the motion to the building. The first two or three hangers downstream need to be resilient hangers, and the transition point is a design decision, not a field one.

A gap at every snubber and every restraint. Seismic and wind restraints exist to hold the machine in an event and must not touch in normal operation. The gap dimension comes from the restraint's own submittal, and it is a checkable item on a punch list.

A clear break at the curb. Weather sealing is compressible, not structural. A seal packed until it bears is a support, and once it is a support it is a path.

Verify by measurement, not by inspection. Take a reading on the structure at the complaint location with the machine running, with it off, and after each path is broken. The machine-off reading is what tells you how much of what you are measuring was never the machine, and skipping it is how a shop ends up chasing a path that was carrying nothing.

References

• 29 CFR 1910.147 for isolating and controlling the stored energy in a compressed isolator; 29 CFR 1910.28 for general industry low-slope roof work and 29 CFR 1926 Subpart M for construction fall protection.
• 29 CFR 1910.333(b)(2), general industry, and 29 CFR 1926.417, construction, for de-energizing and verifying, including a drive's stated bus discharge time; NFPA 70E-2021, 120.5, for live-dead-live, binding through the employer's electrical safety program in the edition adopted.
• Isolator and restraint manufacturer submittal data, which owns the rated static deflection under load, the snubber gap dimension and the bending characteristics of a flexible connector.
• See related: What a Vibration Isolating Connection Can and Cannot Do; What a Vibration Isolator Has to Be Tuned To; What a Resilient Layer Is Actually Doing.