A novel strategy to characterize and identify structural nonlinearities in MDOF systems based on reconstructing constant response tests from constant excitation tests is developed in this paper. Constant displacement frequency response functions (FRFs) can be measured by a stepped sine test where the displacement is controlled at every frequency of interest. In these FRFs the nonlinear restoring force is effectively linearized and natural frequencies can be estimated by linear modal analysis. Using a series of constant displacement tests, the relationship of equivalent stiffness versus displacement can be established by curve fitting and hence the nonlinear stiffness characterized. This paper proposes a method to reconstruct the constant displacement FRFs from stepped sine tests with constant excitation; this avoids the requirement to control either the response or force amplitude, leads to a faster and more stable testing programme. Similarly, damping nonlinearities in structures can be characterized and identified by constant velocity tests reconstructed in a similar way. This approach of FRF reconstruction is mathematically simple and suitable for structures with weak nonlinearities. The method is demonstrated on a framed structure with unknown weak nonlinearities, and the nonlinear stiffness and damping parameters of the structure are identified and validated. The results demonstrate the feasibility and effectiveness of the approach, and also show the potential for practical applications in engineering.

This paper is focused on the analysis of effects of mistuning on the forced response of gas-turbine bladed discs vibrating in the frequency ranges corresponding to higher modes. For high modes the blade aerofoils are deformed during vibrations and the blade mode shapes differ significantly from beam mode shapes. A model reduction technique is developed for the computationally efficient and accurate analysis of forced response for bladed discs vibrating in high frequency ranges. High-fidelity finite element models of a tuned bladed disc sector are used to provide primary information about dynamic properties of a bladed disc and the blade mistuning is modelled by specially defined mistuning matrices. The forced response displacement and stress amplitude levels are studied for high frequency ranges. The effects of different types of mistuning are examined and the existence of high amplifications of mistuned forced response levels is shown for high-mode vibrations: in some cases, the resonance peak response of a tuned structure can be lower than out-of-resonance amplitudes of its mistuned counterpart.

Rotational degrees of freedom (DOF) are usually indirectly derived from the measured translational DOF in structural dynamic tests by using the finite difference method. However, the noise of translational DOF measurement is easily propagated and further amplified when the finite difference method is employed to obtain the rotational DOF. Therefore, the accuracy of the obtained rotational DOF was rather poor. In order to overcome this disadvantage, a novel approach of using a dual sinusoidal-scan continuously scanning laser Doppler vibrometer (CSLDV) with the objective of obtaining the structural modal rotational DOFs is put forward in this paper. For plate structures, the operational deformation shape of the normal translational DOFs can be measured and described with polynomial functions through the modulation of CSLDV output signals. Then, rotational out-of-plane DOFs can be achieved with respect to the first derivatives of the polynomial functions along orthogonal directions. In such a way, the measurement noise that considerably affects the rotational out-of-plane DOFs derived from normal translational DOF can be significantly eliminated. The approach is validated experimentally with a cantilever plate structure, and a comparison with the results obtained from discrete point measurement is given. The results demonstrate the noticeable improvement in accuracy and spatial resolution of the proposed technique.

A scanning laser Doppler vibrometer (SLDV) directs the laser beam scanning over an object by using a galvanometer scanner system, which comprises two orthogonal mirrors and two driving motors. Hence, a control algorithm for the galvanometer scanner is essential to precisely direct the laser beam to the desired position. In this paper, a novel and easy-to-implement algorithm is put forward to determine the pose (orientation and position) of an SLDV. Firstly, a mathematical model is established to correlate the coordinates of the laser spot in the galvanometer mirrors’ coordinate system (MCS) and the rotation angles of the X and Y mirrors. Then, the spatial relationship between the MCS and the tested structure’s coordinate system (TSCS) is identified using an appropriate set of fitted polynomials through a number of reference points. The polynomial coefficients are derived by computing the Moore–Penrose pseudoinverse of the matrix composed of the coordinates of the reference points. Integrated into an SLDV, this algorithm has a strong capacity for dealing with complex testing objects with curved surfaces. Taking a compressor blade as an example, the novel algorithm was applied to an SLDV to direct the laser beam scanning over the measurement points arranged on the blade surface. Results show that the position of the laser spot controlled using the proposed algorithm is accurate, with the maximum deviation from the actual measurement points arranged on the surface being less than 1 mm. The mode shapes of the blade and the modal assurance criterion values also illustrate the feasibility and accuracy of the algorithm for determining the pose of the SLDV. The work presented in this paper has excellent potential for the further development of SLDVs.

During fast gas-turbine engine acceleration and deceleration the transient vibration effects in bladed disk vibration become significant and the transient response has to be calculated. In this paper an effective method is developed for efficient calculations of the transient vibration response for mistuned bladed disks under varying rotation speeds. The method uses the large-scale finite element modelling of the bladed disks allowing the accurate description of the dynamic properties of the mistuned bladed disks. The effects of the varying rotation speed on the natural frequencies and mode shapes of a mistuned bladed disk and its effects on the amplitude and the spectral composition of the loading are considered. The dependency of the modal characteristics on the rotation speed are based on the evaluation of these characteristics at reference points followed by the interpolation to obtain values at any rotation speed from the operating range. A new method has been developed for the interpolation of mode shapes while preserving the orthogonality and mass-normalization of the mode shapes. The method of mode shape interpolation is elaborated for tuned and mistuned bladed disks. The accuracy and efficiency of the method is demonstrated on test examples and on analysis of transient forced response of realistic bladed discs.