The modal identification of large and dynamically complex structures often requires a multi-point excitation. Sine sweep excitation runs are applied when it is necessary to concentrate more energy on each line of the frequency spectrum. The conventional estimation of FRFs from multi-point excitation requires uncorrelated excitation signals. In case of multi-point (correlated) sine sweep excitation, several sweep runs with altered excitation force patterns have to be performed to estimate the FRFs. An alternative way, which offers several advantages, is to process each sine sweep run separately. The paper first describes the conventional method for FRF estimation in case of multi-point excitation, followed by two alternative methods applicable in case of correlated excitation signals. Both methods generate a virtual single-point excitation from a single run with multi-point excitation. In the first method, an arbitrary structural point is defined as a virtual driving point. This approach requires a correction of the modal masses obtained from modal analysis. The second method utilizes the equality of complex power to generate virtual FRFs along with a single virtual driving point. The computation of FRFs and the modal identification using virtual single-point excitation are explained. It is shown that the correct set of modal parameters can be identified. The application of the methods is elucidated by an illustrative analytical example. It could be shown that the separate evaluation of symmetric and anti-symmetric multi-point excitation runs yield obviously better and more reliable results compared to the conventional method. In addition, the modal analysis of the separate symmetric and anti-symmetric excitation runs is easier, since the stabilization diagrams are easier to interpret. The described methods were successfully applied during the Ground Vibration Tests on Airbus A380 and delivered excellent results. The methods are highly advantageous and may thus be established as a new standard procedure for testing aerospace structures.

U. Fuellekrug

M. Boeswald

D. Goege

Y. Govers

Measurement of FRFs and Modal Identification in Case of Correlated Multi-Point Excitation

Nuno M.M. Maia

Special issue: International Conference on Engineering Dynamics &#x2013; ICED 2007

In several cases, laboratory-based modelling approaches such as Experimental Modal Analysis and Transfer Path Analysis run into limitations with respect to technical and economical feasibility (accessibility of the structure, excitation feasibility, measurement time, accuracy, &#x2026;) as well as model representativity. Therefore, approaches such as in-operation modal analysis (OMA) have been developed and are reaching a similar degree of acceptability as standard EMA, with all limitations regarding accuracy and observability of the structural dynamics. In the same line of reasoning fits the question of system characterization and identification using (or based on) other operation data types such as transmissibility functions and coherence functions and data analysis procedures such as principal component analysis. Using these testing and analysis paradigms instead of the classical load-FRF-response one, key analysis techniques such as transfer path and contribution analysis can be reconsidered.

H. Van der Auweraer

P. Mas

P. Peeters

K. Janssens

A. Vecchio

Modal and Path Contribution Models from In-Operation Data: Review and New Approaches

In this paper the recursive method for modal parameters estimation is formulated and verified. Formulated algorithms are implemented in the FPGA electronic chip. As a result, the modal parameters and confidence bounds for the modal parameters are obtained in real time. The algorithms and their implementations are tested on laboratory test rig data and applied to &#x2013; flight modal analysis of an airframe structure.

Tadeusz Uhl

Maciej Petko

Grzegorz Karpiel

Andrzej Klepka

Real Time Estimation of Modal Parameters and Their Quality Assessment

In this work, an inelastic beam macro-element that incorporates hysteretic damping is presented. Based on classical theory of plasticity, a Bouc-Wen type model is utilized that simulates the hysteretic behavior of an inelastic spring element. Using this model, an inelastic nonlinear beam element is formulated based on the appropriate combination of two coupled nonlinear spring elements. The equations of motion are determined and are cast in a state-space form for the vector of the end displacements, velocities and hysteretic forces. The system is solved by employing a Runge-Kutta type of algorithm. The proposed inelastic beam model is then employed to simulate the experimental dynamic behavior of steel beams. The model parameters are estimated with the aid of a nonlinear system identification algorithm using existing experimental data. The proposed element approximates the inelastic behavior of steel beams adequately within plastic regions that do not undergo substantial stiffness degradation, or other relevant phenomena. Finally, the hysteretic damping features of the model are demonstrated.

K.G. Papakonstantinou

P.C. Dimizas

V.K. Koumousis

An Inelastic Beam Element with Hysteretic Damping

In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.

Benjam&#x131;n Vazquez-Gonzalez

Gerardo Silva-Navarro

Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System

The object of this paper is to investigate computationally the possibility of damage prognosis in a structure under the most idealised circumstances. A simple isotropic material &#x2013; Titanium alloy Ti-6Al-4V &#x2013; is assumed. The structure is a simple finite plate under harmonic uniaxial loading and the damage is assumed to be a central mode 1 through crack for which various approximations to the stress intensity factor are known. The damage propagation model is the Paris-Erdogan law. Where the paper departs from complete simplicity is in the assumption that the parameters of the damage propagation law are uncertain. The paper investigates the effect of the parameter uncertainty on the estimated lifetime of the specimen. Two approaches are adopted for the uncertainty propagation, a statistical Monte Carlo scheme and one based on interval arithmetic.

Keith Worden

Graeme Manson

Prognosis under Uncertainty &#x2013; An Idealised Computational Case Study

A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.

P.P. Moita

J.B. Cardoso

A.J. Valido

A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response

One challenge in the numerical simulation of industrial structures is model validation based on experimental data. Among the indirect or parametric methods available, one is based on the &#x201C;mechanical&#x201D; concept of constitutive relation error estimator introduced in order to quantify the quality of finite element analyses. In the case of uncertain measurements obtained from a family of quasi-identical structures, parameters need to be modeled randomly. In this paper, we consider the case of a damped structure modeled with stochastic variables. Polynomial chaos expansion and reduced bases are used to solve the stochastic problems involved in the calculation of the error.

B. Faverjon

P. Ladev&#xe8;ze

F. Louf

An Updating Method for Structural Dynamics Models with Uncertainties

Vibration-based structural health monitoring of a vehicle crane was studied. The performance of different features to detect damage was investigated after eliminating the normal operational variations using factor analysis. Using eight accelerometers, ten AR parameters from each record were identified for damage detection. Also transmissibilities between sensors were estimated. Damage was introduced with additional masses at different locations of the structure. All damage cases could be detected from either features using control charts, but transmissibilities proved to be more sensitive to damage than the AR coefficients.

J. Kullaa

T. Heine

Feature Comparison in Structural Health Monitoring of a Vehicle Crane

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