## Structural dynamics

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Belgium## Objectif

A.BACKGROUND

For fifty years, the finite element method has been developed for structural computations. It is now currently used in industry for the modelization and the calculation of mechanical components. For the same period, vibration measurement devices and experimental modal analysis techniques have known large improvements due to hardware and software developments. The correlation between theoretical computations and experimental data has become a sensitive problem for industrials. In most cases, the interaction between theory and experiment is limited to the simple comparison of computation and measurement results. Thus correcting the model in order to get computation results closer to experimental data is usually done by "hand" adjustments using a heuristic approach. During the last twenty years, attempts have been made to correlate rather than simply compare experimental and theoretical results. In this context, it becomes important to develop European collaboration and to intensify and coordinate research in the field of structural testing, dynamic analysis and model updating.

Carrying out the proposed research program within the framework of the COST coordination seems highly desirable for the following reasons. First, the proposed COST Action requires competence in different topics such as structural dynamics, structural testing, modal analysis, numerical analysis, mechanical and civil engineering as well as a markedly experience for numerical and experimental work. This panel of expertise can be found only via international coordination. Secondly, the proposed research needs frequent exchanges of scientific information to which the COST Action is perfectly adapted. Finally, international workshops and conferences related to the topics of the proposed research (such as the International Seminar on Modal Analysis organized annually by the Katholieke Universiteit Leuven (Belgium), or the International Modal Analysis Conference organized annually by the Society for Experimental Mechanics) reveal that numerous European research institutions tend to work on similar problems in parallel without always exchanging information with others and/or being aware of similar research programs. The COST framework seems at the very least an efficient way of gathering a database and diffusing that information among many European partners. However, we also believe that the COST cooperation enables the definition of coherent research objectives and provides a unique opportunity to coordinate research efforts between many research groups with complementary domains of expertise.

B.OBJECTIVES AND BENEFITS

The main objective of this COST Action is to increase the knowledge required for improving the structural design, the mechanical reliability and the safety of structures in the field of linear and non-linear dynamics.

Regarding the increased demand for construction or equipment performance in terms of mechanical reliability, lightness, carrying capacity, speed, safety, etc., modern design methods become more and more sophisticated. New design objectives need powerful computers, precise description of material behaviour and efficient modelization methods.

As model updating procedures are used to build a representative model of structural dynamics, they can also be used to detect damage on structures and monitor the health conditions in general. For example, if the parameters related to a crack geometry in composite materials are chosen as model updating variables, the updating procedures can be used to predict the crack propagation during the life of the structure. In this way, updating methods open new possibilities in the field of predictive maintenance, default diagnosis and characterization of the mechanical signature of structures.

Furthermore, the complexity of today's mechanical systems and their increased level of performance make it necessary to model effects that were not predominantly important in previous analyses. Failure to do so could result in inadequate models and could lead to large discrepancies between the estimation of the structure's dynamics and its real behaviour. These effects include non-linear dynamics, mechanisms of damping and dissipation of the energy and phenomena of energy localization. The secondary objectives would include investigating modal techniques (that is, procedures for ground testing and identification of the structure's dynamics from test data) for non-linear structural systems.

Benefits

The proposed research action will lead to the development of more accurate analytical models for structural systems and thus will help engineers to improve design methods. The experimental part of this work will lead to better insight into measurement techniques and testing procedures, especially in traditionally avoided circumstances such as non-linear systems. It will therefore provide engineers with guidelines for improving the quality of testing procedures. Both aspects should impact positively, for example, a large variety of test-analysis correlation studies realized during various structural applications that span different industries. It will also allow the development of new diagnostic methods to solve vibration problems what will result in incommensurable benefits to industries.

This COST Action should benefit research institutions (whether in the academia or industry) by:

-improving the communication between laboratories with common research interests,

-helping to define coherent research objectives,

-and providing a framework for co-ordinating common research efforts.

The overall consequence will be an increased efficiency of the research in the areas of analytical and experimental structural analysis and a better competitivity compared to research groups from non-European countries (in particular, Japan, Taiwan and the USA).

Finally, it is expected that many industries will benefit from the COST Action by transferring directly the research and technology developed by COST partners to practical problems encountered in many applications. In the following, domains primarily involved and typical examples of application are listed:

-measurement standards and testing procedures (type of instrumentation, optimum sensor location, signal conditioning for testing large structural systems and/or non-linear structures),

-health monitoring of structural systems (damage detection and localization in structures; safety assessment of the residual dynamics of potentially damaged structures; monitoring of buildings during and after earthquakes; health monitoring of pipeline joints from their vibration signatures; in-situ monitoring and diagnosis of mechanical equipment, rotating machinery, etc.),

-modelling of damage mechanisms affecting materials, such as delamination and crack propagation,

-noise cancellation (development of tools used for the technology of noise cancellation in industrial environments or transportation vehicles, such as on-line system identification and structural-acoustics interaction),

-active control of structures (deployment and control of large and high precision space structures such as antennas; vibration attenuation of civil engineering structures during earthquakes; "smart" structures capable of adapting their geometry to the loading conditions),

-modelling of complex industrial manufacturing processes (development of modelling and diagnosis tools for advanced automotive systems such as geared systems with backlash, steering and active suspension; industrial safety),

-non-linear modal analysis for structural dynamics via perturbation technique (Normal Forms Methods),

-application of probabilistic methods in establishing design and evaluation criteria.

In particular, benefits in the area of adaptive structures (sometimes also referred to as "intelligent" or "smart" structures) would be expected to impact positively a large number of applications in the civil engineering, mechanical and aerospace industries.

C.SCIENTIFIC PROGRAMME

In order to achieve the main objective of this COST Action, the following research tasks have been identified.

Many efforts have been undertaken by scientific institutions to develop finite element model updating methods but their outcome is still limited to linear elasto-dynamics.

C.1.Updating methods to adjust analytical models

Updating methods are used to adjust analytical models to test results. The field of application of these methods includes:

-the correction of approximation errors; this type of error is related to assumptions regarding the physics of the model as for example, the linear behaviour of the structure, the physical behaviour laws (model of elasticity, etc.), the limitations of the mathematical formulations used for deriving particular finite elements and the representation of non-accessible structural data (dissipative phenomena),

-the correction of discretization errors related to errors in modelling connections and boundary conditions or using a model that is too small for capturing some of the significant dynamics of the system; this type of error is related to the optimization and automatization of finite element meshing for dynamic computations,

-the correction of parametric errors caused by the differences in measured material properties (elasticity modulus, density, section and thickness, etc.), especially for complex new material systems.

Updating methods can be classified in two groups: global and local methods. Global methods are based on the correction of the global stiffness and/or mass matrices of the finite element model. These methods use optimization tools for deriving an updated model that is not always physically meaningful even if it reproduces the test data with accuracy. Local methods are usually preferred to global methods because they offer a better potential. They are based on the calculation of modal parameters (frequencies, damping ratios and mode shapes) or frequency response sensitivities with respect to the physical variables of the model (elasticity modulus, density, section and thickness, etc.). The advantages of local methods are the following:

-the ability to locate erroneous regions of the analytical model,

-the ability to select the relevant physical or structural parameters for model updating.

Whether the methods are global or local in nature, several "families" emerge depending on the mathematical formulations adopted for formulating the updating problem.

An important research task of this COST Action will therefore be to select updating methods which are computationally efficient and address practical difficulties of model updating (incomplete measurement sets, selection of the optimum data sets for the updating, capability to control the numerical difficulties, etc.); to define guidelines regarding the updating of finite element models; and to apply these methods or develop new ones for the updating of damped and non-linear systems.

C.2.Health monitoring, damage detection and force identification

Health monitoring is very similar mathematically to model updating even though objectives of the two problems are different. Model updating seeks the correlation of a mathematical model to experimental data collected from the instrumentation of a structure whereas health monitoring is mostly concerned with the variations in time of a structural system. Very often, the system to monitor is represented via mathematical models such as finite element models, which provides a clear link with updating methods. For example, assuming that data are collected periodically, successive updatings of the mathematical models may be performed and comparison of the correlated models to the baseline (undamaged) model provides a practical tool for damage detection.

Practical difficulties of health monitoring include non-proportional damping, non-linear identification and updating, modelling of joints, optimum sensor and actuator placement, most of which will be addressed in the research. The long-term goal is the ability to realize on-line diagnosis systems which would perform modal tests of the structure throughout its life time, identify an experimental model, correlate this model to the analytical one and assess the probability of damage from the comparison between various correlated models in time. The advantage of such a methodology is that a probability density function per structural component would be available, making it straightforward to locate and assess the extent of structural damage. For example, bridges can be tested using the natural source of excitation of wind and traffic, and cracks can be located before leading to safety concerns. Clearly, health monitoring syntheses techniques of both experimental and analytical domains and the integrated approach proposed here is the only valid approach for reaching significant advances of the state-of-the-art.

In damage detection the structure must be considered under realistic environmental conditions, loading conditions and measurement conditions. Thus, addressing the practical problems of developing long-term, stable, highly-sensitive transducers, systems for easy data transfer and data manipulation, and problems of filtering out changes in environmental conditions and loading conditions are essential. Highly accurate (especially bias-free) system identification procedures must be implemented in a module oriented software system, and experience must be gathered using these techniques on large civil engineering structures using only a few sensors. Probabilistic measures must be developed for indication of damage and location and type of damage, and ways of taking a priori information into account must be developed. Further, ways of using the information gathered from analysis of the measured response in updating the reliability of the structure, must be developed to have an appropriate tool for decision making concerning maintenance and visual inspection.

C.2.2.Force identification

Even when the dynamics is not directly relevant for the design and maintenance of a structure, it might be a very important observation tool. The experimental modal analysis techniques are in many cases the easiest and most accurate ways of getting information about the properties of a structure. Even though the dynamical response is totally insignificant for the reliability of the structure, the dynamical response caused by natural loads might in many cases provide accurate information about the properties of the structure, its loading system and/or its interaction with the foundation. For instance, if a structure is well-known (if a model is calibrated), the response might be used to obtain information about the loads like traffic-loads and loads from wind and waves. Since in many cases these are the only ways of getting unbiased information about the loads, and since a lot of the uncertainty in modelling structural systems reliability is due to uncertainty of the loads, this is a very important application of experimental structural dynamics.

C.3.Identification of non-linear systems

Whenever non-linearities (e.g. damping effects that are not decoupled by the modal basis of the undamped equivalent system) are suspected, traditional modal analysis techniques collapse because their underlying mathematics are restricted essentially to the linear domain.

The problem of test-analysis reconciliation (model updating, health monitoring, etc.) exhibits several aspects depending upon the type of structure and the type of structural modification involved. In various situations, a local identification of the dynamics of a component may be extracted from the modal test of the structure. Therefore, the problem becomes that of "modal subtracting'' the behaviour of the known components from that of the whole system. A few attempts in this direction have been developed but a thorough investigation has not been proposed yet. This problem has numerous industrial applications, for example, the inspection of bolted joints in metallic structures or the control of joints in pipe networks. In other cases, for instance, when structural changes originate from localized damage, the problem must be investigated from a non-linear point of view. For example, untightening of bolted joints may determine particular vibrational patterns of the type "vibration with contact", due to joint free play. The analysis of these characteristics has been attempted by authors in the general framework of detection of non-linearities.

With respect to identification of non-linear systems for health monitoring, artificial intelligence based techniques should also be considered. During the recent years, many interesting attempts in this field have been proposed, but the subject needs a more systematic investigation. Also, the durability of recently proposed genetic algorithms for non-linear identification should be considered. These new techniques are not only interesting for health monitoring, but also for control purposes, i.e. active as well as non-active control of the dynamic response of structures.

It has to be noted that this COST Action could be considered in a second step as a framework for broader action since other specific research projects could be introduced afterwards, such as:

-flexible multibody dynamics,

-cable dynamics,

-fluid/structure interaction,

-structural dynamic sensitivity problems, structural optimization with aeroelastic constraints and aeroservoelasticity,

-vibro-acoustics,

-dynamic problems in injury biomechanics, ...

D.ORGANIZATION AND TIMETABLE

It is suggested that the proposed research action be carried out for the period of four years organized as follows:

6 months

12 months

12 months

12 months

6 months

-WGI: Working Group on task "C.1.Finite Element Model Updating Methods".

-WG2: Working Group on task "C.2. Health Monitoring and Damage Detection".

-WG3: Working group on task "C.3. Identification of Nonlinear Systems".

-year one, preliminary research and definition of coherent objectives between the COST partners:

the initial starting/planning period of the first six months should offer the opportunity to provide a state-of-the-art of existing problems; it would be beneficial to the structural dynamics community to offer a clear picture at a given point in time of what can reasonably be accomplished using the current technology and where open questions remain; in particular, the first six months of the COST Action should also be devoted to the definition of suitable benchmark structures and problems; it is also suggested to initiate a consultation regarding what could become a standard for input data; in the same idea, the use of a common software development platform could be examined in order to maximize interchangeability and communication effectiveness,

-years two and three, coordination of principal research and development efforts,

it should be noted that the many possible overlaps, which can be foreseen among tasks 1 and 2, should not be a drawback,

-year four, synthesis of the work accomplished, adjustment of the research objectives, definition of new goals and evaluation of the results of the research and their exploitation.

At the end of each organized seminar, the progress results of the COST Action will be published in the form of proceedings.

E.ECONOMIC DIMENSION

The following COST countries have actively participated in the preparation of the COST Action or otherwise indicated their interest:

Belgium, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.

On the basis of national estimates provided by the representatives of these countries and taking into account the coordination costs to be covered over the COST budget of the European Commission, the economic dimension of the project, estimated as the sum of the national efforts to support the participating laboratories, can be estimated at 800 man-years with a roughly estimated budget, at 1996 prices, of ECU 40 million.

This estimate is valid under the assumption that all the countries mentioned above but no other countries will participate in the COST Action. Any departure from this will change the total cost accordingly.

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**Dernière mise à jour le**: 2003-03-05

**Numéro d'enregistrement**: 69475

**Dernière mise à jour le**2003-03-05

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