Antonio Culla

Uncertainty model for contact instability prediction.

Contact between sliding bodies can cause vibrations leading to instability. The problem of squeal due to high frequency noise from brake systems is due to unstable vibrations generated at the contact interface between the pad and disk. Squeal noise is characterized by extreme unpredictability due to large uncertainties on the values of parameters of the system. Parametrical complex eigenvalue analysis is a common tool used to predict squeal instability. In this paper a substructured linear finite element model of a simplified brake system is studied. A parametrical analysis is focused on a test case and compared to experimental results. The analysis is developed as a function of the parameters assumed to be the most influential but also the most uncertain: friction coefficient and the parameters driving the dynamics of the system. The uncertainties are accounted for by considering parameters such as random variables. A Monte Carlo simulation and a probabilistic technique are performed simultaneously to study the probability of squeal occurrence. Finally, a reduced model based on the transfer function calculated at the contact is developed to perform the analysis with reduced computational effort.

High Frequency Vibroacoustic Analyses on VEGA Launch Vehicle

VEGA, the future European small launch vehicle, is a single-body launcher composed of three solid-propellant stages and a liquid propellant upper module. It is approximately 30 metres high, has a maximum diameter of 3 metres, and weights a total of 137 tons at lift – off. The acoustic loads applied to the launch vehicle upon the lift-off and the transonic flight, are broad band and random loads which may be dangerous for the payload and the equipment. A fast and cheap prediction may be obtained by numerical procedures rather than performing measurements on real prototypes. The classical numerical techniques (finite elements (FEM), boundary elements (BEM)) allow to predict the response of the mechanical systems at low frequency ranges, typically under 200 Hz. A high frequency problem happens when the ratio between the characteristic wave length and the characteristic dimension of the system is very little respect the unity. It happens, for example, when a broad-band load forces a large and lightweight structure. The classical numerical techniques fail to solve high-frequency dynamic problems, because the computational burden grows excessively, but also because the sensitivity of the numerical algorithms to uncertainties in the modal parameters increases with frequency so that the predicted response becomes meaningless. In this case a statistical approach is more appropriate. The Statistical Energy Analysis (SEA) is, at present, the most useful method for solving this kind of vibroacoustic problems, by providing information on the stored mechanical energy and on the dissipated mechanical power between modal subsystems. The energy of the subsystems is calculated by solving a set of algebraic energy-balance linear equations: the right-hand side quantities are the powers injected into each subsystem and the coefficients depend on the coupling loss factor (CLF) and the internal loss factor (ILF). These parameters depend on the kind of studied mechanical system and they are independent by the imposed forces. Two different load cases have been analysed: ae Lift – off Manoeuvre

Selection of Interface DoFs in Hub-Blade(s) Coupling of Ampair Wind Turbine Test Bed

Substructure coupling is an important tool in several applications of modal analysis. It is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs, especially in an experimental context. Furthermore, the reverse problem, the decoupling of a substructure from an assembled system, arises when a substructure cannot be tested separately but only when coupled to neighboring substructures, a situation often encountered in practice. In this paper, the dynamic behavior of the Ampair test bed wind turbine rotor, made by three blades – each one bolted to the hub at three points – is analyzed. The aim is both to identify the dynamic behavior of the rotor starting from the frequency response functions (FRFs) of blades and hub, and to select a reduced set of relevant DoFs to represent the interface between blades and hub. FRFs to be used in the coupling procedure are obtained starting from FE model of each substructure, by using a super-element based computational approach. The decoupling problem, with the aim of identifying the dynamic behavior of each blade from the FRFs of the assembled rotor and of the hub, is also considered.

Experimental Dynamic Substructuring of the Ampair Wind Turbine Test Bed

In a recent paper, the authors discussed the selection of a reduced set of interface DoFs in order to describe the coupling between the blades and the hub of the Ampair test bed wind turbine rotor. The study was conducted using simulated FRFs obtained from Finite Element model of the blades and the hub, but in view of using experimental FRFs. In this paper, test data measured on the turbine by the UW-Madison participants in the IMAC Focus Group on Experimental Dynamic Substructuring, and posted on the Wiki page of the group, are used for dynamic substructuring of the wind turbine test bed.

Estimation of Rotational Degrees of Freedom by EMA and FEM Mode Shapes

In this paper a new technique is presented to estimate the rotational degrees of freedom of a flexural structure, using only a limited number of sensors that measure the translational DoFs of the system. A set of flexural mode shapes in a limited number of nodes is obtained by modal testing, while a different set of approximated mode is calculated by a Finite Element Model (FEM) at all the nodes and degrees of freedom of the structure. The technique is based on the classical assumption that the response can be determined by a linear combination of the structure’s mode shapes. The structure’s mode shapes are approximated by using the local correspondence principle for mode shapes, i.e. by using an optimally selected set of finite element mode shapes as Ritz vectors for the true mode shapes. This allows to obtain the rotational response at unmeasured DoFs. The technique is validated by comparing predicted and experimental results.

High frequency optimisation of an aerospace structure through sensitivity to SEA parameters

Classical (FEM, BEM) structural optimisation techniques fail to solve medium high frequency dynamic problems because too many DoFs are involved and eigenvalues and eigenvectors loose the significance due to high modal density. Using a SEA model, the subsystem energies are controlled by (coupling) loss factors, under the same loading conditions. In turn, coupling loss factors (CLF) depend on physical parameters of the subsystems. The idea is to determine an approximate relation between CLF and physical parameters that can be modified in the structural optimisation process, for instance, by using Design of Experiment (DoE). Starting from this relation, an optimisation problem can be formulated in order to bring the subsystem energies under prescribed levels. A preliminary analysis of subsystem energy sensitivity to CLF can be performed to save time in looking for the approximate relationship between CLF’s and physical parameters. The approach is applied on a typical aerospace structure.

Interplay Between Local Frictional Contact Dynamics and Global Dynamics of a Mechanical System

Friction affects almost the entirety of the mechanical systems in relative motion. In spite of intense and long-time research activities many aspects of this phenomenon still lack of a meaningful interpretation. Some of them could be explained by not focusing only on the interface properties. In fact recent literature confirms the picture of a macroscopic frictional behaviour of a mechanical system as the outcome of a complex interaction between the local dynamics at the frictional interface (wave and rupture nucleation and propagation) and the global dynamics of the system. This paper presents the results of a 2D non-linear finite element analysis under large transformations of the onset and evolution of sliding between two isotropic elastic bodies separated by a frictional interface. The aim is to investigate the trigger of the dynamic rupture at the interface, which preludes and goes with the sliding and its interaction with the global dynamics to determine the observed macroscopic frictional behaviour (stick-slip, continuous sliding). The analysis is focused on the observed phenomena during the onset of the sliding (micro-slips, precursors, macro-slips), accounting for the frictional properties and the inertial and elastic properties of the system.

Nonlinear unsteady energy analysis of structural systems

The problem of vibration of large systems undergoing shocks and unsteady loads is one of the field of great interest in vibro-acoustic engineering. Statistical Energy Analysis-SEA is one of the most acknowledged methods in this field. However, SEA has many limitations, and is based on several questionable hypotheses. In the present paper, on the basis of a new theory of vibration thermodynamics, the authors consider a set of systems characterized by (i) unsteady loads, such as shocks, (ii) nonlinear coupling between the different subcomponents. The analysis is carried on considering different prototype systems, starting from a very simple pair of nonlinear resonators, a 2-dof system, up to consider a system of plates coupled through nonlinear joints. It is shown how the energy flow relationship between subsystems pair, comes out to be a power series of the energy storage difference. These results are systematically considered in the light of the thermodynamic theory of vibrating systems, showing how a gen...

Structural health monitoring under random flow loading

The aim of the work is the analysis of fluid-structure systems, when excited by a flow consisting of an incompressible potential fluid with embedded vortexes. In fact, in many problems of relevant application interests, the monitoring and the potentially detection of structural damages in structures undergoing loads in operative conditions is important. The present method tries to identify simultaneously the load characteristics together with the structural damage. The flow is characterized by the average velocity of the fluid conveying the vortexes and by the position and intensity of the conveyed vortexes. A method for the identification of these flow parameters, based on vibration signals measured at the elastic fluid-structure interface, is proposed. Vibration signals are numerically generated and then processed with time-frequency techniques, such as the ensemble empirical mode decomposition and the normalized Hilbert transform. The sensitivity of the algorithm to the measurement position and to sing...

Load identification by coherence analysis of structural response

Aim of this paper is the identification of uncorrelated forces acting on a structure based on a coherence analysis of the structure response, performed entirely in operative condition. In order to identify the position and the amplitude of the applied load only the responses of the structure and the experimental FRF are required. The proposed procedure consists of three steps. First, the number of acting loads is established by the analysis of the responses coherence, second the position of the acting forces is identified using an index obtained by the knowledge of experimental FRF and of the responses of the structure, then, the amplitude of the acting forces is computed in correspondence of the excited points. The procedure is tested by two experiments. First experiment consists in the excitation of a complex structure in several places with an instrumented hammer. The identification is performed by the accelerations measured on a set of points of the structure itself. The second experiment is carried o...