Modal Analysis
Natural frequencies, mode shapes, and what modal analysis tells you about a structure.
Modal analysis calculates the natural frequencies of a structure and the corresponding deformation patterns (mode shapes). It answers the question: at what frequencies does this structure want to vibrate?
Why natural frequencies matter
Every structure has natural frequencies. When an external excitation — a motor, a pump, road vibration, wind — matches a natural frequency, resonance occurs. At resonance, vibration amplitudes can grow very large, leading to fatigue failure or loss of function.
Modal analysis lets you identify whether a design is at risk of resonance before building the first prototype.
What modal analysis gives you
Natural frequencies (eigenfrequencies)
The frequencies at which the structure vibrates freely. Measured in Hz. The lowest frequency is the first mode (fundamental frequency); higher modes follow in order.
Mode shapes (eigenvectors)
The deformation pattern associated with each frequency. The absolute values are not meaningful — only the shape matters. Mode shapes show you where the structure deflects most for a given mode.
Mode shapes have no physical unit. They are normalized so the maximum displacement is 1 (or some other reference). Only the shape is meaningful, not the magnitude.
How to interpret results
Look at the first 5–10 modes. For each one, ask:
- Is the frequency close to any operating frequency in the system?
- Which part of the structure deforms most in this mode? That's where fatigue cracks will start if resonance occurs.
- Is the mode global (whole structure moves) or local (only a bracket or panel)? Local modes can often be suppressed with added mass or changed geometry.
Avoiding resonance
The two main strategies:
-
Move the natural frequency — change mass or stiffness. Adding stiffness (bracing, thicker wall) raises the frequency. Adding mass lowers it. Aim for a safety margin of at least 20% between the natural frequency and the excitation frequency.
-
Add damping — rubber mounts, visco-elastic materials, and structural damping all reduce vibration amplitude at resonance. Damping doesn't move the frequency, but it limits the peak amplitude.
Boundary conditions for modal analysis
Modal analysis is sensitive to boundary conditions. An unsupported structure has 6 zero-frequency rigid-body modes (3 translations + 3 rotations). These are normal and can be ignored — look at the first non-zero frequencies.
Use the same supports as the actual mounting condition. A structure mounted on soft rubber behaves very differently from one bolted rigidly to a steel frame.
Modal analysis vs. harmonic response
Modal analysis gives you frequencies and mode shapes — it does not tell you how large the vibration actually is under a real load. For that, you need harmonic response analysis or transient dynamics, which apply a frequency-dependent load and compute the actual displacement and stress amplitudes. Modal analysis is the necessary first step before any of those analyses.