## 3 Results
### Processing the Signals and Modal Parameters  
From the three known dynamic vibration tests, i.e., forced, ambient and combined, the first was used with an excitaion induced by the impact hammer. In general, the well-known experimental modal analysis consists of: (1) recording of the signals, (2) identification of the system and (3) approximation of the modal parameters. The last step can be performed by free vibration analysing of the identified system model from step (2), i.e., by modal decomposition. The model is a mathematical solution, estimated on a basis of measured data and can be of parametric or non-parametric type. The latter can be described in a tablularized form, as for example, the frequency response functions (FRF). Using the Laplace transform of (7) and neglecting the initial conditions provides the frequency-domain method for analysis of response of linear systems to excitations varying arbitrarily with time in the matrix equation:  
\[\mathbf{Z}(s)\mathbf{U}(s)=\mathbf{P}(s), \tag{10}\]  
with the dynamic stiffness \(\mathbf{Z}(s)=\mathbf{M}\,s^{2}+\mathbf{C}\,s+\mathbf{K}_{T}\) and \(s=i\omega\), \(i=\sqrt{-1}\). Inverting above equation yields:  
\[\mathbf{U}(s)=\mathbf{H}(s)\mathbf{P}(s), \tag{11}\]  
with the transfer function matrix \(\mathbf{H}(s)=\mathbf{Z}^{-1}(s)\). The frequency-domain method is an alternative approach to the time-domain method and provides an efficient means of a predicting response. The frequency response analysis can be particularly useful if the linear response of a system subjected to a continuous series of harmonic excitations, i.e., to the periodic forcing function with a frequency \(\omega\) is sought. Steady-state response is then given as a frequency sweep through a specified range of frequencies. The response for each excitation frequency \(\omega\) can be determined from (11). The'response function' \(\mathbf{H}(\omega)\) is the Fourier transformation of the response matrix. Each element of the matrix \(\mathbf{H}(\omega)\) can be itself a frequency response function (FRF) and it is most likely to be able to measure in practice. From FRFs it is possible to determine modal characteristics of structure, which are amenable to direct measurement. However, the measured frequency response functions ought to be subjected to a range of curve-fitting procedures in an attempt to find the mathematical model, which provides the closest description of actually observed behavior. According to the modal theory of mechanical systems, the FRF matrix can be decomposed as:  
\[\mathbf{H}(\omega)=\sum_{r=1}^{N}\biggl{(}\frac{\phi_{r}\mathbf{L}_{r}^{T}}{i \omega-\lambda_{r}}+\frac{\phi_{r}^{*}\mathbf{L}_{r}^{H}}{i\omega-\lambda_{r }^{*}}\biggr{)}, \tag{12}\]  
with such modal parameters as the poles \(\lambda_{r}=\sigma_{r}+i\omega_{r}\), vectors of the mode \(r\), the mode shape \(\phi_{r}\) and modal participation factors \(\mathbf{L}_{r}\). One element \(\lambda_{r}\) contains both the natural frequencies \(f_{r}\) and damping ratios \(d_{r}\) for the \(r\)th normal mode of vibration. They can be determined as \(f_{r}=\omega_{r}/(2\pi)\), \(d_{r}=-\sigma_{r}/\sqrt{\sigma_{r}^{2}+\omega_{r}^{2}}\), where the number of modes may differ from the number of measured output degrees of freedom and the number of input forces. The meanings of symbols used in (12) are: \((. )^{*}\)--a complex conjugate, \((. )^{T}\)--a transpose of the matrix, \((. )^{H}\)--a complex conjugate transpose of the matrix (a Hermitian transpose). To identify modal characteristics of the simplex three steps have been chosen: (1) the hammer test, (2) the method pLSCE and (3) a stabilisation diagram with peak picking. All steps of the experimental modal analysis (EMA) were performed using the Macec toolbox [29], using the deterministic poly-reference least squares complex frequency domain method (pLSCF). The natural frequencies identified are gathered in Table 4, while natural modes are presented in Figure 5. The modal parameters are obtained by connecting the results of modal testing through all setups.