Modal analysis

Applications of experimental modal analysis

During an experimental modal test, first the vibration response of a structure is measured over frequency. The excitation should be spectrally broad to excite all relevant natural frequencies. Typically, the excitation spectrum is acquired as well, so that transfer function's (FRFs) response-input force can be recorded. The setup should be well defined to avoid any unwanted influences from the environment or the excitation process itself. A typical setup could be attachment of the structure to some soft rubber strings or putting it onto soft foam to decouple it from the environment and to excite it with e.g. a modal hammer.

Next, the measured FRFs are curve fitted to a mathematical model involving the inherent modes of the structure under test. The result of this process are the natural frequencies, the damping and the mode shapes of the structure. These modes reveal valuable insights for any engineer and developer, e.g. for simulation in an early stage when designing new products or optimizing the design e.g. with increased lightweight constructions in engineering and construction. Examples of modal analysis typically include entire car-bodies, a wide range of precision components in automotive, aerospace and mechanical engineering, but also cover small parts in microtechnology.

SIMO vs MIMO modal testing approach

The standard test is a single-input multiple output SIMO test. One excitation source and multiple response channels either with multiple acceleration sensors or in the case of a Scanning Laser Doppler vibrometer (SLDV) with a laser beam scanned over the surface is the most common test setup. The results can be directly analyzed and fed into a curve fitting software to extract the individual modes. MIMO – multiple-input multiple-output – setups are applied with highly damped larger structures or in cases where not all modes can be excited with one location of excitation like for symmetric structures, e.g. brake disks.

Modal testing of structures with closely coupled modes is a very frequent task. Structures often have modes that have almost the same resonant frequency. For example, a plate’s specific bending mode might occur at almost the same frequency as its torsion mode. This “accidental” frequency degeneracy is common among more complex geometries and structures. On the other hand, when a structure is planned to be highly symmetric, the coupled modes are expected “by design.” In finite element (FE) simulations, all of these modes appear separately. However, in real world testing, extracting the modes from measurement data can be challenging. This application note introduces a novel approach to separate closely spaced modes with MIMO testing (multiple input, multiple output) using a 3D scanning laser vibrometer and two automated modal hammers. Sign up for reading the full paper.

Experimental modal analysis (EMA) software

As a result of the experimental modal test the operational deflection shapes as answers to this special modal test excitation are available. To compare these results with the calculated results from a numeric modal analysis based on a FE model a second step called curve fitting is required. In the pure measurement results, the modes are potentially still coupled. The dynamic behavior of a mechanical system can be described as the superposition of the Eigen-modes, one mode being considered as a single degree of freedom (SDOF). In curve fitting the SDOF results are extracted with various methods, typically based on single value decomposition (SVD).
Experimental modal analysis software packages like PolyWave allow for curve fitting and the comparison of the EMA test results with the FEA results in MAC analysis. The findings like damping values, Eigen-frequencies and Eigen-vectors are fed back into the model to update the FE model parameters.