Vibration Isolation Transmissibility Calculator mechanism

Model scope

The core transmissibility equation is standard for a steady-state linear single-degree-of-freedom isolator. The specification is not complete enough to verify the required-static-deflection output: it needs an explicit design equation, target-TR input, unit convention, fixed design variables, and branch/feasibility rules. The honest label is appropriate only if the excitation type and steady-state assumptions are made explicit.

• The stated TR formula is standard for harmonic force transmissibility and, with the same mathematical expression, for absolute motion transmissibility under harmonic base excitation, but the excitation definition must be stated because force transmissibility and motion transmissibility are different physical quantities.
• The isolation percentage formula is valid only when TR<1; for this model that occurs for r>sqrt(2). The formula should explicitly define r=f/f_n and f_n=(1/(2*pi))*sqrt(k/m).
• The claimed output 'required static deflection for target TR' has no formula, target-TR input definition, damping-dependent inversion method, or specification of whether frequency and mass are fixed while k is changed.
• For nonzero damping, solving a target TR requires selecting the physically relevant high-frequency isolation branch and checking whether the requested target is attainable. This constraint is not specified.

Units and conventions

• Disturbing frequency is in Hz, not rad/s; therefore r=2*pi*f*sqrt(m/k). If frequency is supplied in rad/s, use r=omega*sqrt(m/k) without the extra 2*pi.
• Mass m is in kg, stiffness k is in N/m, and static deflection is in m.
• Damping ratio zeta is dimensionless and should normally satisfy zeta>=0.
• The numerical vectors below use g=9.81 m/s^2 where static deflection is shown.
• TR is dimensionless and isolation percentage is reported as a percent.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "disturbing_frequency_hz": 2,
    "isolator_stiffness_N_per_m": 3947.84176,
    "mass_kg": 100,
    "damping_ratio": 0.05
  },
  "expected_outputs": {
    "natural_frequency_hz": 1,
    "frequency_ratio_r": 2,
    "TR": 0.339181733,
    "isolation_percent": 66.081827,
    "required_static_deflection_m": "not defined by the supplied specification"
  },
  "working": "f_n=(1/(2*pi))*sqrt(k/m)=(1/(2*pi))*sqrt(3947.841760/100)=(1/(2*pi))*6.283185307=1 Hz. r=f/f_n=2/1=2. 2*zeta*r=2*0.05*2=0.2. Numerator=sqrt(1+0.2^2)=sqrt(1.04)=1.019803903. Denominator=sqrt((1-2^2)^2+0.2^2)=sqrt(9+0.04)=sqrt(9.04)=3.006659276. TR=1.019803903/3.006659276=sqrt(1.04/9.04)=0.339181733. Since r>sqrt(2), isolation=(1-0.339181733)*100=66.081827%."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification leaves frequency units ambiguous, causing substantially different transmissibility results, and it does not explicitly define rejection behavior for zero stiffness or the exact r=sqrt(2) boundary.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json