Modal Frequencies Study

Overview#

Every structure has natural frequencies at which it prefers to vibrate. If an external excitation (a motor, propeller, road input) matches one of those frequencies, the response can be large and destructive, a phenomenon called resonance. The Modal Frequencies study computes the natural frequencies and the associated mode shapes of your design. It does not tell you how large the vibration will be (that requires damping and excitation data); it tells you where the danger zones are.

The study needs geometry, material (stiffness and density) and, normally, constraints that match how the part is mounted. Loads are optional: Autodesk notes that tension or compression from loads changes natural frequencies, but loads are only considered if you activate Compute Preloaded Modes.

Licensing: only Linear Static Stress cloud solves are covered by the Fusion subscription. Modal Frequencies is a basic study that costs 3 tokens per solve, or is covered without limits by the Fusion Simulation Extension (Autodesk token and extension topics). The Solve dialog shows the live cost. Personal-use availability is not stated in the Simulation help.

Where to find it#

• Simulation workspace > Setup tab > Study panel > New Simulation Study, then set the Study Type to Modal Frequencies (or choose it in the New Study dialog).
• Constraints and materials work as in static stress. Structural constraints are not required, and a modal study can solve with no constraints or only partial constraints.
• Results are in the browser: Total Modal Displacement (default, first mode), Natural frequencies (the Mode dropdown above the legend) and Mass Participation Factors (Results tab > Mass Participation panel).

Step by step#

1. Create a Modal Frequencies study. Avoid partial modelling with symmetry: Autodesk warns it would limit results to symmetrical vibration modes.
2. Assign materials. Density and Young's modulus drive frequency: frequency scales approximately with the square root of stiffness divided by mass.
3. Add constraints that reflect the mounting. A Fixed constraint is generally stiffer than a real bolted mount, so predicted frequencies will tend to be too high. For a free-free analysis, leave the model unconstrained: a fully unconstrained model has six rigid-body modes (three translations, three rotations) with no deformation, and the seventh and later modes involve deformation. A partially constrained model has fewer than six.
4. Optionally add a Point Mass (Manual) for items you are not modelling (a motor, a lens), attached to faces at the mass centre. Point masses affect frequencies and mode shapes, and do not need Compute Preloaded Modes.
5. In the study Settings, set Number of Modes (default 8) and optionally the Frequency Range [Hz]; modes outside the range are not output even if the requested number is not yet reached. Activate Compute Preloaded Modes if applied loads should affect the result.
6. Generate the mesh (the model is also meshed automatically when you solve). Adaptive Mesh Refinement is available for modal frequencies, with a Frequency Mode setting that chooses which mode drives the refinement.
7. Run Pre-check and then Solve.
8. In Results, choose a mode from the Mode dropdown above the legend (each entry shows the mode number and frequency in Hz, such as Mode 1: 440 Hz). Use the animation to see the shape. Modal displacement is normalized: the maximum is always one length unit and the minimum zero, so amplitude is relative, not absolute, and the legend has no units.
9. Compare the mode frequencies with excitation sources. Autodesk says ideally the first mode is above any driving frequency, or, if the operating speed is above it, the design must withstand the momentary resonance while accelerating. A separation margin such as 20 percent is a common general rule of thumb, not an Autodesk requirement.
10. Modify the design to shift the mode: add ribs, change thickness, change mass, stiffen the mounting.

Options reference#

Tips and pitfalls#

Warning: Boundary conditions dominate the answer. A cantilever with a perfectly fixed end has a higher first frequency than the same bracket on a flexible bolt pattern. Calibrate with a test if you can.

Tip: Add the mass of components you left out. Omitted motor or battery mass shifts frequencies upward and can make you miss a resonance.

Warning: Modal displacements are normalized and are not physical deflections; the Modal Frequencies results are natural frequencies, mode shapes and mass participation factors, not a design stress.

Tip: Rigid-body modes occur only when the model is unconstrained in one or more directions. They are expected in a free-free model, but in a model you meant to constrain they indicate a missing constraint.

Tip: Modal results are ranges. Material tolerances and mount stiffness variation move frequencies by several percent; design margin accordingly.

Practice exercise#

Build a 200 mm x 20 mm x 3 mm steel strip. Fix one end. Run a modal study with 6 modes. Compare the first bending frequency to f = (1.875^2 / (2 pi L^2)) sqrt(E I / (rho A)). Then add a 50 g remote mass at the tip. Expected result: the first mode frequency drops noticeably; the hand calculation should agree closely on the unloaded strip (the amount depends on your mesh).

Worked example: a motor mount and a resonance margin#

The motor, speed and bracket dimensions are illustrative assumptions, and the aluminium modulus is a typical value. A small brushless motor spins at 6000 rpm, so the fundamental excitation is 100 Hz, with a blade-pass or slot harmonic at 2 x or 7 x. A bracket (aluminium, 3 mm plate, 80 mm cantilever) carries the 0.35 kg motor.

1. Estimate the first mode: the bracket's tip stiffness k = 3 E I / L^3. With width 30 mm, I = 30 x 27 / 12 = 67.5 mm^4, so k = 3 x 68900 x 67.5 / 512000 = 27.3 N/mm = 27300 N/m. With a 0.35 kg tip mass, f = (1 / 2 pi) sqrt(k / m) = 0.159 x sqrt(27300 / 0.35) = 0.159 x 279 = 44 Hz (ignoring the bracket's own mass, which lowers it a little).
2. 44 Hz is below the 100 Hz excitation, so the motor runs above resonance; during spin-up it passes through 44 Hz. That is acceptable if the pass is quick, but the bracket will see a short resonance.
3. In Fusion: fix the bolt holes, add the motor as a Point Mass (Manual) of 0.35 kg attached to the mounting face at the motor's centre of mass, request six modes, and solve. The hand estimate suggests the first mode near 40 to 44 Hz.
4. Design change: thickening to 5 mm multiplies I by (5/3)^3 = 4.63 and the frequency by sqrt(4.63) = 2.15, giving about 90 Hz. That moves the mode to within 10 percent of the 100 Hz excitation, which is worse. Going to 6 mm gives f x sqrt(8) = 2.83, about 125 Hz, 25 percent above the excitation, which meets a 20 percent margin (a rule of thumb, not an Autodesk requirement).

The example shows that more stiffness is not automatically better: aim to move the mode away from the excitation.

Choosing constraints for realistic modal results#

A free-free uniform beam's first bending mode is f = (22.37 / (2 pi L^2)) sqrt(E I / (rho A)); a steel bar 300 x 20 x 5 mm gives about 290 Hz (E I = 41.7 N m^2, rho A = 0.785 kg/m, L = 0.3 m); a tap test with a phone microphone and a spectrum app is a cheap way to check.

Number of modes and mass participation#

Request enough modes to cover the frequency range of interest. General practice: if excitation reaches 500 Hz, compute modes well above that (the factor is your choice, not an Autodesk rule). Solve with a modest number of modes, look at the highest frequency, and extend if needed.

Mass Participation Factors indicate the effective percentage of total mass moving in each global direction for each mode; modes with relatively high participation are readily excited by an external stimulus, and those with low participation are not. Autodesk notes that design standards often dictate a minimum total participation (such as 85% or 90%) and therefore how many modes to compute. If a model is unconstrained in a direction, the rigid-body modes already account for 100% of the mass participation there and the other modes show 0%, so constrain the model to see which flexible modes are susceptible to excitation.

Understanding mode shapes#

Normalized amplitudes mean you should compare shapes, not values. A mode that mostly moves the motor mount in the direction of the motor's imbalance force is the dangerous one.

Prestress, damping and next steps#

Autodesk states that tension increases vibration frequencies and compression lowers them, and that Compute Preloaded Modes must be on for applied loads to count. The relation f_loaded = f_0 x sqrt(1 - P / P_cr) is a general engineering approximation for axial compression, not an Autodesk formula. Damping is not computed, so response amplitude needs a separate estimate: at resonance, amplification is Q = 1 / (2 zeta) in the standard single-degree-of-freedom model; with 2 percent damping, Q = 25 (illustrative value).

Failure modes and fixes#

Practice exercise#

Verify and then design for a margin.

1. Build the 80 mm cantilever (30 mm wide, 3 mm thick aluminium) with a 0.35 kg Point Mass at the tip, and solve for six modes. Compare mode 1 with 44 Hz (a few percent difference is acceptable because the bracket's own mass and the finite mass patch matter).
2. Increase the thickness to 6 mm and predict the new frequency (about 125 Hz) before solving.
3. Remove the point mass and compare with the bare cantilever formula f = (1.875^2 / (2 pi L^2)) sqrt(E I / (rho A)).
4. Change the constraint from Fixed to Pin on the two bolt holes and record the frequency drop.
5. State whether the design now has a 20 percent margin from 100 Hz and from 200 Hz.

Related#

• Simulation Workspace Overview
• Loads and Constraints
• Cloud Solve and Credits