**4.1. Detection and identification of non-linearities**

The above test concept allows the identification of non-linearities if some conditions are fulfilled: The response to harmonic excitation should be dominated by the excitation frequency and the mode shapes of the associated linear system should remain nearly unchanged at different force levels.

In order to characterize the non-linearities of a large complex structure, it is first required to detect the non-linearities. This can be done by simply increasing the force level. However, more detailed investigations are beneficial. The book (Worden & Tomlinson, 2001) gives a broad survey of non-linearities in structural dynamics. The detection, identification and modeling is described in great detail. Numerous suitable methods are presented and elucidated. The article (Gloth & Goege) proposes some methods for the fast detection of non-linearities within the described advanced modal survey test concept.

The step following the detection is the identification of the non-linearities. For complex lightly damped structures with weak non-linearities, the mode shapes can be divided into different groups as shown in (Wright, Platten, Cooper, & Sarmast, 2001):


**Figure 1.** Test concept for modal identification of complex structures in a Ground Vibration Test (GVT)

The above test concept allows the identification of non-linearities if some conditions are fulfilled: The response to harmonic excitation should be dominated by the excitation frequency and the mode shapes of the associated linear system should remain nearly

In order to characterize the non-linearities of a large complex structure, it is first required to detect the non-linearities. This can be done by simply increasing the force level. However, more detailed investigations are beneficial. The book (Worden & Tomlinson, 2001) gives a broad survey of non-linearities in structural dynamics. The detection, identification and modeling is described in great detail. Numerous suitable methods are presented and elucidated. The article (Gloth & Goege) proposes some methods for the fast detection of

The step following the detection is the identification of the non-linearities. For complex lightly damped structures with weak non-linearities, the mode shapes can be divided into

non-linearities within the described advanced modal survey test concept.

different groups as shown in (Wright, Platten, Cooper, & Sarmast, 2001):

Linear proportionally damped modes, which are well separated in frequency.

 Linear proportionally damped modes, which are very close or identical in frequency. Linear non-proportionally damped modes, which are usually fairly close in frequency

**4.1. Detection and identification of non-linearities** 

unchanged at different force levels.

(significant damping coupling)

Most of the modes of real structures behave linear so that an identification using the classical linear methods and the test concept described above is still possible. Nevertheless, some modes show significant non-linear behaviour, which makes it impossible to adopt linear theory. A solution to this problem is a non-linear identification which can be based on the Masri-Caughey approach (Masri & Caughey, 1979), the force-state mapping (Crawley & Aubert, 1986) and a variant of it (Al\_Hadid & Wright, 1989). The idea and basics of the nonlinear resonant decay method (NLRDM) (Wright, Platten, Cooper, & Sarmast, 2001), (Platten, Wright, Cooper, & Sarmast, 2002), (Wrigth, Platten, Cooper, & Sarmast, 2003), (Platten, Wrigth, Worden, Cooper, & Dimitriadis, 2005), (Platten, Wrigth, Dimitriadis, & Cooper, 2009) appear to be an appropriated method for applying it to large and complex structures.
