Ignoring rotational DoFs in decoupling structures connected through flexotorsional joints

Substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). The degrees of freedom (DoFs) of the coupled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In direct decoupling, a fictitious subsystem that is the negative of the residual subsystem is added to the coupled system, and appropriate compatibility and equilibrium conditions are enforced at interface DoFs. Compatibility and equilibrium can be required either at coupling DoFs only (standard interface), or at additional internal DoFs of the residual subsystem (extended interface), or at some coupling DoFs and some internal DoFs of the residual subsystem (mixed interface). In this paper, a test bench is considered made by a cantilever column with two staggered short arms coupled to a horizontal beam. This involves both flexural and torsional DoFs, on which rotational FRFs are quite difficult to measure. Using a mixed interface, rotational DoFs are neglected and substituted by internal translational DoFs. Experimental results are presented and discussed

A unified approach to substructuring and structural modification problems

Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs. This paper analyzes the possibility of assembling together different substructures' models. The important role of rotational DoFs is highlighted, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DoFs are not available. Expansion techniques can be used to provide this information as well as appropriate modelling of joints. With this information FRF models, modal models and FE models can be appropriately combined together and solutions for several cases of practical interest are presented. The analyzed procedures are tested on purpose-built benchmarks, showing limits and capabilities of each of them

Dynamic Model Updating Using Virtual Antiresonances

This paper considers an extension of the model updating method that minimizes the antiresonance error, besides the natural frequency error. By defining virtual antiresonances, this extension allows the use of previously identified modal data. Virtual antiresonances can be evaluated from a truncated modal expansion, and do not correspond to any physical system. The method is applied to the Finite Element model updating of the GARTEUR benchmark, used within an European project on updating. Results are compared with those previously obtained by estimating actual antiresonances after computing low and high frequency residuals, and with results obtained by using the correlation (MAC) between identified and analytical mode shapes

Substructure decoupling without using rotational DoFs: fact or fiction?

In the framework of experimental dynamic substructuring, substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). On the contrary, substructure coupling identifies an assembled system starting from the component subsystems. The degrees of freedom (DoFs) of the assembled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In substructure coupling, whenever coupling DoFs include rotational DoFs, the related rotational FRFs must be obtained experimentally. Does this requirement holds for substructure decoupling too, as it is commonly believed? Decoupling can be ideally accomplished by adding the negative of the residual subsystem to the assembled system (direct decoupling) and by enforcing compatibility and equilibrium at enough interface DoFs. Ideally, every DoF of the residual subsystem belongs to the interface between the assembled system and the residual subsystem. Hopefully, not all the coupling DoFs are necessary to enforce compatibility and equilibrium. This may allow us to skip coupling DoFs and specifically rotational DoFs. The goal of the paper is indeed to establish if rotational FRFs at coupling DoFs can be neglected in substructure decoupling. To this aim, after highlighting the possibility of avoiding the use of coupling DoFs from a theoretical standpoint, a test bed coupled through flexural and torsional DoFs is considered. Experimental results are presented and discussed

AN ITERATIVE RATIONAL FRACTION POLYNOMIAL TECHNIQUE FOR MODAL IDENTIFICATION

The rational fraction polynomial (RFP) modal identification procedure is a well known frequency domain fitting technique. To deal with a linear problem, the RFP procedure does not directly minimize the fitting error, i.e, the difference between the experimental and the analytical frequency response function, but a frequency weighted function of it: this causes bias in the modal parameter estimates. In this paper an iteration procedure is proposed which uses the output of the RFP technique as a starting estimate, and minimizes the true fitting error, expressed as a first order Taylor expansion of the identified parameters. Results are quite satisfactory: the fitting error is notably reduced after few iterations. Moreover, less computational modes with respect to the original RFP method are needed to obtain a good fit in a given frequency band

Vibroacoustic optimization using a statistical energy analysis model

In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF) and coupling loss factors (CLF), which in turn depend on the physical parameters of the subsystems. A preliminary sensitivity analysis of subsystem energy to CLFs is performed to select CLFs that are most effective on subsystem energies. Since the injected power depends not only on the external loads but on the physical parameters of the subsystems as well, it must be taken into account under certain conditions. This is accomplished in the optimization procedure, where approximate relationships between CLFs, injected power and physical parameters are derived. The approach is applied on a typical aeronautical structure: the cabin of a helicopter

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

International audienceSubstructure coupling is an important tool in several applications ofmodal 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

Numerical investigation on the mode coupling contact dynamic instabilities.

When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in the dynamic behavior of systems. The presence of frictional contact can give rise to mode-coupling instabilities that produce harmonic "friction induced vibrations". Unstable vibrations can reach large amplitude that could compromise the structural integrity of the system and are often associated with annoying noise emission. The study of this kind of dynamic instability has been object of many studies ranging from both theoretical and numerical study of simple lumped models to numerical and experimental study on real mechanical systems, such as automotive brakes, typically affected by such issue. In this paper the numerical analysis of a lumped system constituted by several degrees of freedom in frictional contact with a slider is presented, where the introduction of friction gives rise to an unstable dynamic behavior. Two different approaches are used to investigate the effects of friction forces. The linear Complex Eigenvalue Analysis (CEA) allows for calculating of the complex eigenvalues of the system that can be characterized by a positive real part (i.e. negative apparent modal damping). The effects of the main parameters on the system stability are investigated. In the second approach a non linear model has been developed that takes into account the stick slip behavior at the interface to solve the time-history solution and analyze the unstable vibration. The mode selection mechanism occurring in transient nonlinear analysis, when several unstable modes are predicted by the linear CEA, and driving the selection of the frequency of the unstable vibrations, is investigated. Furthermore, by means of the transient analysis, the influence of the type of perturbation at the equilibrium position on the time history of the system vibrations is analyzed. Results comparison between the two different approaches highlights how nonlinearities affect the time-history solution and how stable and unstable behavior can be predicted by the linear CEA. The obtained results have been extended to the finite element model of a simple mechanical system

Identification of bolted joint properties through substructure decoupling

Substructure decoupling techniques, defined in the frame of Frequency Based Substructuring, allow to identify the dynamic behaviour of a structural subsystem starting from the known dynamics of the coupled system and from information about the remaining components. The problem of joint identification can be approached in the substructuring framework by decoupling jointed substructures from the assembled system. In this case, information about the coupling DoFs of the assembled structure is necessary and this could be a problem if the interface is inaccessible for measurements. Expansion techniques can be used to obtain the dynamics on inaccessible (interface) DoFs starting from accessible (internal) DoFs. A promising technique is the System Equivalent Model Mixing (SEMM) that combines numerical and experimental models of the same component to obtain a hybrid model. This technique has been already used in an iterative coupling–decoupling procedure to identify the linear dynamic behaviour of a joint, with a Virtual Point description of the interface. In this work, a similar identification procedure is applied to the Brake Reus Beam benchmark to identify the linear dynamic behaviour of a three bolted connection at low levels of excitation. The joint is considered as a third independent substructure that accounts for the mass and stiffness properties of the three bolts, thus avoiding singularity in the decoupling process. Instead of using the Virtual Point Transformation, the interface is modelled by performing a modal condensation on remote points allowing deformation of the connecting surfaces between subcomponents. The purpose of the study is to highlight numerical and ill-conditioning problems that may arise in this kind of identification

Use of experimental dynamic substructuring to predict the low frequency structural dynamics under different boundary conditions

Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low frequency dynamics of the free-free structure. To overcome this problem, substructure decoupling can be used, that allows us to identify the dynamics of a substructure (i.e. the free-free structure) after measuring the frequency response functions on the complete structure (i.e. the structure plus the supports) and from a dynamic model of the residual substructure (i.e. the supporting structure). Subsequently, the effect of additional boundary conditions can be predicted using a frequency response function condensation technique. The procedure is tested on a reduced scale model of a space solar panel