Single Reference Modal Test

The most common type of Experimental Modal Analysis (EMA EMA is an acronym for Experimental Modal Analysis. During an EMA, the test article is artificially excited with either an impactor, or using one or more shakers. The excitation force(s) and one or more responses caused by the force(s) are simultaneously measured, and a set of FRFs is calculated The FRFs are then curve fit to obtain experimental modal parameters for the test article.) is done using a single reference.  A single reference EMA can be performed in two ways;

• Using a fixed (reference) exciter and a roving response sensor

• Using a fixed  (reference) response sensor and a roving exciter.

MIMO Model

A MIMO model A MIMO model is a Multiple Input Multiple Output frequency domain matrix model containing a vector of Inputs, a matrix of Transfer functions and a vector of Outputs. The MIMO model is an equation where the Transfer function matrix is post-multiplied by the vector of Input DFTs to obtain the vector of Output DFTs. Inputs, Outputs & Transfer functions can be calculated using different forms of the MIMO model equation. of a structure completely represents the dynamic properties of the structure between all pairs of Input (excitation) and Output (response) DOFs for which it is defined.  A FRF An FRF (Frequency Response Function) is a cross-channel frequency domain function that defines the dynamic properties of a structure between an excitation Force and the Response caused by that force. An FRF is defined as the ratio (Response DFT / Force DFT). The FRF is a special case of a Transfer Function, where the response is the numerator (Output) and the force is the denominator (Input). matrix of a MIMO model contains rows & columns of FRFs.  Each FRF defines the Output (response) of the structure at a DOF DOF is an acronym for degree-of-freedom. A DOF includes a Point number & direction. If each measurement (M#) in a Data Block, Shape Table or Acquisition window has a DOF defined for it, the DOF can be used to create Animation equations by assigning M#s to matching Points & directions on the model in the connected Structure window. Each Point number should correspond to a numbered Point on the model. Each DOF direction should correspond to a Measurement Axis direction at the Point on the model. Scalar data has no direction associated with it. due to the force Input (excitation) at another DOF.

Roving Response Test

In a roving response test, a single fixed (reference) exciter is used to excite the structure, and a roving response transducer is used to measure its response.  Each FRF measurement is calculated between the excitation force signal applied to the structure and the response signal from a response transducer.  The FRFs correspond to measuring elements from a single column of the MIMO model for the structure. (See the Multi-Input Multi-Output Modeling & Simulation chapter for details.)  The excitation force can be provided in two ways,

1. Attaching a shaker to the structure and driving it with a broad band signal.

2. Impacting the structure at the same DOF (point & direction) for each measurement.

Roving Impact Test

In a roving impact test, a single fixed (reference) response transducer is used, and the structure is excited using a roving impacter.  Each FRF is calculated between the response signal from the same DOF and the excitation signal from a different roving DOF.  The FRFs correspond to measuring elements from a single row of the MIMO matrix for the structure.  The impact hammer applies a broad band impulsive force to the structure, which excites many resonances at a time.  The excitation force is measured with a load cell attached to the head of the hammer.

Maxwell's Reciprocity

Maxwell’s Reciprocity: The structural response at DOF A due to the excitation force at DOF B is the same as the structural response at DOF B due to the excitation force at DOF A. In modal testing, Maxwell’s Reciprocity is usually assumed to be valid.

When Maxwell’s Reciprocity is valid,

• An FRF calculated when excitation is provided at DOF A and response s measured at DOF B is the same as the FRF calculated when excitation is provided at DOF B and response is measured at DOF A.  The structure is dynamically symmetrical.

• Measuring elements from a column of the MIMO model of the structure is the same as measuring elements from its corresponding row.  This also means that the MIMO model contains a symmetric matrix of FRFs.

• Curve fitting FRF from any row or any column of the MIMO model will yield the same modal parameters for the structure.

When Maxwell’s Reciprocity is valid,

• Any (fixed) Reference DOF (any row or any column of the MIMO model) can be used in a modal test

• Only one Reference DOF is required to obtain all of the modal parameters of the structure