White box / Analysis methods / Gyroscopic modal and Campbell

Frozen experimental boundary

Scope note · assumptions, essential equations, full derivation, algorithm, code and verification references.

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Scope noteNOT A GENERAL ROTORDYNAMICS SOLVER

The model is limited to a straight, connected, unbranched BEAM2 shaft, circular isotropic sections, centered rigid axisymmetric disks, fixed global axis, constant signed spin, no damping, and no prestress.

01 Model and scope

This card defines the model class for which the experimental rotor results are interpretable. Adding damping, prestress, eccentric disks, other element families or distributed gyroscopic effects changes the equations and invalidates a direct transfer of the current evidence.

This is a scope record. Its presence in the catalogue does not make the described route an ordinary supported capability.

Route assumptions and calculation checks

  1. No shells or solid rotor mesh; no eccentric/non-axisymmetric disks; no distributed shaft gyroscopy.
  2. No bearings or speed-dependent properties, centrifugal stiffening, unbalance forced response, contact, nonlinear rotor response, PETSc/SLEPc, or MPI.
  3. GYRO-06 is internal mesh-convergence evidence, not independent physical validation. Both routes remain EXPERIMENTAL.

02 Essential equations and symbols

This sheet records a scope or execution boundary. Its detailed steps explain the relevant conditions.

Definitions and conventions

BEAM2
Straight two-node shaft elements.
Ω\Omega{}
Constant signed spin speed.
Centered disk
Rigid axisymmetric disk attached to an existing shaft node.
EXPERIMENTAL
Maturity of these rotating routes, independent of release status.
Frozen experimental boundary · method mapThe current result is tied to a deliberately narrow beam-and-disk model with omitted physics listed explicitly.
3 detailed steps

03 Step by step derivation

Follow the assumptions, equations and discrete operations in order. The full explanation stays visible.

1 · Read the model class as a frozen contract

The experimental model is a straight, connected, unbranched BEAM2 shaft with circular isotropic sections, centered rigid axisymmetric disks, a fixed global spin axis, constant signed speed, no damping, and no prestress. These restrictions are inputs to the meaning of the equations, not administrative notes.

Mq¨+ΩGq˙+Kq=0,C=0\mathbf M\ddot{\mathbf q}+\Omega\mathbf G\dot{\mathbf q}+\mathbf K\mathbf q=\mathbf0,\qquad\mathbf C=\mathbf0

2 · Identify omitted physics

The model omits solid or shell rotor meshes, eccentric and non-axisymmetric disks, distributed shaft gyroscopy, bearings and speed-dependent properties, centrifugal stiffening, unbalance forcing, contact, and nonlinear rotor response. Adding any of these changes the governing operator or data contract.

current operator excludes   Cq˙,  funbalance(t),  Kcentrifugal(Ω),  and contact terms\text{current operator excludes }\;\mathbf C\dot{\mathbf q},\;\mathbf f_{unbalance}(t),\;\mathbf K_{centrifugal}(\Omega),\;\text{and contact terms}

3 · Separate solver verification from physical validation

GYRO-06 is an internal mesh-convergence record for its beam model, not independent physical validation. Both the single-speed and Campbell routes remain EXPERIMENTAL. Transfer requires a separately verified model, matching evidence, and a new maturity decision.

04 Algorithm and implementation

This sheet provides explanatory references rather than an inline source excerpt. Use the labeled sources to inspect the precise boundary.

05 Verification and limitations

NOT A GENERAL ROTORDYNAMICS SOLVER

Each reference supports its own model, observable and analysis route. Read the original contract and limitations before transferring a conclusion.

06 Sources and related sheets

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