Interface Damping: Characterization and Implementation

Transcription

1 Interface Damping: Characterization and Implementation Ravi Varma Nadampalli Licentiate Thesis Stockholm April 2012 The Marcus Wallenberg Laboratory for Sound and Vibration Research Department of Aeronautical and Vehicle Engineering Postal address Visiting address Contact Royal Institute of Technology Teknikringen 8 Tel: Aeronautical and Stockholm ravin@kth.se Vehicle Engineering SE Stockholm Sweden

2 Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framläggs till oentlig granskning för avläggande av teknologie licentiatexamen Friday den 20 April 2012, 13:00 i sal D41, Lindstedtsvägen 17, KTH, Stockholm. TRITA-AVE-2012:13 ISSN ISBN Ravi Varma Nadampalli, April 2012

3 Abstract Material damping in a structure is well dened and documented. However, dissipation due to mechanical contact (surface contact) in a complex built-up structure is not as well represented, in particular in large scale noise and vibration simulations. The present work is dealing with the understanding of the physical behaviour of losses that take place at such complex interfaces. The objective is to investigate, if, these mechanical loss phenomena can be modelled using linear response simulation techniques and implemented using commercially available nite element software. In a rst step, the losses at the interfaces were experimentally investigated using an experimental setup capable of in-vacuo conditions. Following this, the second step was aimed at dierent ways of representing the proposed boundary conditions in a linear response simulation of a built-up structure. Two dierent approaches were studied, one using a continuous surface approach and one using a discrete element method.

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5 Dissertation A Licentiate of Technology is an intermediate Swedish academic degree that can be obtained half-way between the MSc and the PhD, while less formal than a Doctoral Dissertation, examination for the degree includes writing a thesis and a public presentation. This thesis consists of two parts. The rst part gives an overview of the research with a summary of the performed work. The second part collects the following scientic articles: Paper A. Ravi V. Nadampalli, K. Dovstam, P. Göransson and C. Glandier, "Damping Modelling in Complex Built-up Structures", To be submitted for publication in Journal of Sound and Vibration. Paper B. Ravi V. Nadampalli, P. Göransson and C. Glandier, "Implementing Linear Modelling of Interface Damping in a Finite Element Software". To be submitted for publication in Finite Elements in Analysis and Design. Division of Work Between the Authors Paper A. Nadampalli performed the measurements, computations and analysis. He wrote the paper under the supervision of Göransson P., Dovstam K. and Glandier C. Paper B. Nadampalli performed the computations and analysis. He wrote the paper under the supervision of Göransson P. and Glandier C. iii

6 iv Ravi V. Nadampalli Acknowledgements The study presented in this thesis has been performed at the CAE-NVH department (EP/SNB) of DAIMLER AG and at the Marcus Wallenberg Laboratory (MWL), KTH Royal Institute of Technology. This research is funded by the EU FP7 Marie Curie Initial Training Network CAE Methodologies for Mid-Frequency Analysis in Vibration and Acoustics under grant agreement The nancial support is gratefully acknowledged. First of all, I would like to thank my supervisors at KTH, Peter Göransson and Krister Dovstam as well as my supervisors at DAIMLER, Christian Glandier and Otto Gartmeier, for being a great support and guiding me through the world of research. Also thank you to my colleagues at DAIMLER and KTH for all those discussions of, noise, vibration and harshness, on life in general. A special thank you to Eric Bauer from DAIMLER for supporting me with the Nastran. Last but not least, I would like to thank my wife and my family for supporting me. And to all of my friends; life would be pretty boring without your involvement.

7 Contents I Overview and Summary 1 1 Introduction Background Objective Overview Damping Material Damping Interface Damping Theoretical Background Power dissipated at the interface Interface damping Losses due to mechanical contact and air pumping Testing, Modelling and Implementation Approaches Testing Modelling and Implementation Assumed contact area Relative displacement Model comparisons Results Discussion 16 6 Conclusion and Future scope 18 7 Summary of Appended Papers Paper A Paper B II Appended Papers 25 v

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9 Part I Overview and Summary 1

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11 Chapter 1 Introduction 1.1 Background Figure 1.1: Benz Patent Motorwagen. The automobile is perhaps one of the greatest inventions that man has conceived. It changed the way human mobility took place on the planet earth. Last year Mercedes- Benz celebrated its 125th birthday as the inventor of the automobile back in Since 125 years of inception, the automobile and its internal combustion engine has evolved and great progress has been achieved in improving the technology that has been put in today's cars. At present, the automotive industry is facing a new challenge in going towards the zero CO2 emissions target. The race for the next generation of power units is in its full, for example electric/hydrogen fuel cell mobility, among the manufacturers, bringing even more pressure and emphasis in advancements on the technological front. A greater eort will be placed on reducing and optimizing the weight of the car body in order to reduce the CO2 emissions along with improving the fuel consumption. So, all means to reduce weight is being tested during the product development cycle while keeping all crucial qualities of the car, intact. In power train development, interior design, vehicle electronics, crash, and acoustics, this has a consequence that more emphasis is being placed on reducing the overall weight of the vehicle. The noise, vibration and harshness (NVH), which comes at the later phase of the product development cycle of a vehicle, is seen as one important area where there 3

12 4 Ravi V. Nadampalli is huge conict in reducing the weight still keeping the core qualities of the car. While measurements are widely used in the NVH eld during the product development phase, due to cost reasons, there is a tendency towards modelling as an integral part of the daily process and it is being used to predict the vehicle behaviour well in advance during the product development cycle. However, expensive measurements are still seen as a reference for the virtual modelling work that is carried on. This is a cumbersome fact as, high variability among similar car bodies is a known fact in the industry. Virtual modelling of a car body is well documented, developed and implemented into the daily practice in the automotive industry. Finite element modelling is vastly used in the simulations and it is a routine process in the industry. However, the delity of the models used need to be continuously improved, so more research and development eort is being put into this area. Though virtual modelling tools are well developed and used routinely, there are certain areas where more eort is needed in understanding the physical behaviour, especially related to the frequency response of complex builtup structures like a body-in-white car structure. A car structure is built-up of many complex parts and the losses that take place at the interfaces are not well understood. There is further eort needed in this direction where the physical understanding of the loss mechanism lacks in the industry as a whole. Previously, work has been done on built-up structures where the importance of understanding the losses at the interfaces, [1, 2, 3], is emphasised. Material damping is very well researched and there exists an extensive literature for one to understand and implement it in a structure. But very few studies have been noticed highlighting the interface damping in built-up structures. Recent research done on interface damping, [3, 4, 5, 6, 7], is such an eort in understanding the physical behaviour of the losses that take place at complex interfaces. In the industry, global damping is applied as a factor of losses that takes place on the whole car body. But the localised losses that arise at complex interfaces are not well represented in the implemented global damping; this brings more uncertainties in the simulation model, and thus needs to be studied. So there is a need for physical understanding, modelling and implementing of such interface losses in an industrial structure. 1.2 Objective Modelling and implementation of material (structural) damping is well established but modelling of the losses at the interfaces is not well understood. This research is focused on understanding the physical dissipation of the losses that takes place at the interfaces of a complex built-up structure. The main focus is to be able to model it using simple linear modelling techniques and also to implement it in commercially available FE software. A body-in-white (BIW) car structure consists of many spot-welded parts, on average a typical BIW will have 5000 spot-welds, gure 1.2, and each spot-weld will be 4-5 mm in diameter. Estimating losses at these interfaces along the anges is

13 Interface Damping: Characterization and Implementation 5 Figure 1.2: Car body-in-white structure a challenging task. There are many such auxiliary parts in a car body where current industrial modelling practice does not take the local dissipation into account. This brings more uncertainty in optimizing the vehicle characteristics, of for example, the vehicle dashboard, the plastics inside a car cabin, the structural glue and the spot-welds. As a step forward in this eld, the focus of the present study will be on a spot-welded structure, gure 1.3. A better understanding of the physical loss phenomena will help Figure 1.3: Test Structure in optimizing the spot-welds and increase the delity of the virtual model, so time can be saved during the testing and the modelling. The spot-weld connection, mix damping related to the mechanical contact taking place around the spot-welds with the losses due to the visco-thermal eects that are caused due to the air movement through the gaps formed between the spot-welds, which is modelled using the interface damping principle. 1.3 Overview The present work builds on recent research done on interface damping, [3, 4, 5, 6, 7], to generalise the ndings presented to a more complex built-up structure. To be able to characterize the losses at the interfaces, experimental work was performed initially using an in-vacuo set-up. Losses at the interfaces were characterized as dissipation due to the mechanical contact and the air pumping. For the simulations, the Comsol multiphysics 3.5a software was used to handle the proposed boundary conditions. The NXNastran 7 was used for implementation in a more conventional nite element software.

14 Chapter 2 Damping Damping is dened as an eect that converts mechanical vibration energy into heat and thus reduces the amplitude levels of an oscillating structure. When a structure possess no damping, there exists no mechanisms to remove the vibration energy in it, implying that any motion that is set will go on for ever. In reality this might not happen though there are some exceptional cases with very low damping. Most of the engineering structures posses some kind of loss mechanisms. The simple model shown below illustrates the case when damping is introduced as a structural loss factor, proportional to the stiness element, gure 2.1, and commonly referred to as structural, proportional damping. However, it is seldom the case that the damping in a structure is distributed as the stiness itself. For a built-up structure with complex interfaces and joints, the damping associated to these needs to be accounted for. The increased level Figure 2.1: Single degree of freedom system with structural damping. of complexity which arises in such cases is then related to two aspects. First, along such interfaces between parts, the damping is caused by relative motion illustrated with a 6

15 Interface Damping: Characterization and Implementation 7 system as shown in gure 2.2, with the interface loss mechanisms then introduced as, Figure 2.2: Two degree of freedom system with structural damping. Figure 2.3: System with interface losses. gure 2.3, (K ω 2 M)u = F. (2.1) The equations of motion for this system of two masses, then may be written as M 1 ω 2 u 1 + i C ω (u 1) + K 1 (1 + iη)(u 1 ) = 0, (2.2) M 2 ω 2 u 2 + i C ω (u 2 u 1 ) + (K 2 K 1 )(1 + iη)(u 2 u 1 ) = F, (2.3) which in matrix form reads { [K1 ] [ ] [ ] } [ ] [ ] (1 + iη) + K 2 (1 + iη) K 2 (1 + iη) ω 2 M1 0 C C u 1 F i K 2 (1 + iη) K 1 (1 + iη) 0 M 2 C C u 2 =. 0 (2.4) where [M j ], [C j ], [K j ] are the mass, damping, stiness matrices, [u j ] is the nodal displacement and F is the external force on the structure. Even though the concept of interface damping is trivial in this simple model, it still serves the purpose of illustrating the dierence in localising the sources of damping to dierent parts of the system and with dierent motion related characteristics. Typically, η could be viewed as resulting from internal material damping, while the quantity C, and its assumed action dependent on the relative motion between the two masses, could be interpreted as resulting from the (local) interfaces between dierent parts.

16 8 Ravi V. Nadampalli Damping can be varied into dierent mechanisms like material damping and non material damping. Extensive research has been done on estimating the material damping in a structure from the measured data, [1, 2]. A few damping mechanisms which are of interest will be explained in some detail below. 2.1 Material Damping Material damping is dened as the volume of the material element in which the vibrational energy is dissipated, see [1] where a detailed description is given on various mechanisms that eect the material damping. Previously, research has been performed on understanding and implementing the losses in a structure, i.e. material damping, and with classical methods like half-power bandwidth, Nyquist diagram, Hysteresis loops etc, to determine the damping in a structure from the measured data. In the automotive industry estimating material damping is implemented as a routine task where the loss factor estimation is done for a car body by taking into account all the losses that might take place in a heuristic way. However, the losses are in such an approximate model, not localized and this could potentially cause discrepancies in the simulated responses. 2.2 Interface Damping Dissipation that takes place at the interfaces due to mechanisms like acoustic radiation, linear air pumping, friction are examples of the damping mechanisms that occur at the interfaces, [1, 2], schematically illustrated in gure 2.3. Though structural damping is well understood and implemented, interface damping lacks such understanding; where one major reason is due to the complexity in understanding the physical loss mechanisms that takes place in the intricate spaces. Dissipation at the interfaces for a built-up structure might depend on the construction of the object. Previously, [1, 2], research has indicated that the dissipation through the spot-welds is minimal when compared to the losses through other joining mechanisms like rivet/ bolted joints. However they highlighted the importance of losses that takes place along these complex interfaces, which is of major focus in this study. To the author's knowledge there is very few physical explanation existing where such losses could be understood and modelled. Recently, research has been focused on the interface damping, [3], where the losses at the interfaces is studied with good results. But there is more eort needed in estimating the losses at the interfaces of a complex structure and in the end implementing it in commercially available FE software. A spot-welded structure is studied where the losses at the interfaces were explained. To be able to characterize and implement the interface losses, tests were performed, in-vacuo and in ambient pressure conditions. After characterizing the losses at the interfaces due to various physical mechanisms, the interface damping principle is applied in estimating and modelling the losses. The mechanical contact around the spot-welds, caused due

17 Interface Damping: Characterization and Implementation 9 to the relative sliding of the plates, is one major cause for dissipation. Also the viscous behaviour of the air, caused due to the out-of-plane motion, in the open spaces between the spot-welds cause dissipation. These interface loss mechanisms were explained in detail in the present study.

18 Chapter 3 Theoretical Background 3.1 Power dissipated at the interface The interface damping principle in a simple and a complex structure, is given in more detail in, Dovstam, [3], and Nadampalli, [4, 5, 6, 7]. The linearised Cauchy equations of motion for a 3D continuum, can be shown as P int + P ext = iωk + U o, (3.1) where P int describes the dissipation at the interface between the structures and P ext denotes the input power on a boundary with external vibration excitation. In Equation (3.1), K denotes the frequency domain (real) kinetic energy and U o is mean stress power at circular frequency ω. 3.2 Interface damping Figure 3.1: Generic principle at a contact point with pairwise opposing damping forces in x direction. 10

19 Interface Damping: Characterization and Implementation 11 The approach for modelling the interface losses is as follows, from Equation (3.1), P int = 1 1 t n.vda + t n.vda, (3.2) 2 2 A int1 A int2 where t n is the 3D traction vector eld and v is the velocity. Damping occurs at the sub-surfaces A int1 and A int2 which are distinct but nominally and pairwise coinciding interfaces. The mean power loss P int at the interfaces for time harmonic vibrations is expressed as 1 P int Re[ 2 F o.(v o(1) v o(2) ) ]da. (3.3) A int Here F o is an assumed damping force. 3.3 Losses due to mechanical contact and air pumping The assumed damping force F o is here introduced as two dierent forces in order to dierentiate between the two mechanisms i.e, (F o ) Mech for the mechanical contact and (F o ) Air for the air pumping. For the mechanical contact, losses due to relative sliding of the plates is described by the damping constant (c x ) Mech and similarly the losses due to out-of-plane motion of the plates, at the contact interface, is described by the damping constant (c z ) Mech. It is assumed that the damping forces F ox, in x-direction, for ω > 0 is given by an expression (F ox ) Mech = (c x ) Mech i (u o ) x = (c x) Mech (v o ) x (3.4) ω where (F ox ) Mech is the complex traction amplitude (stress in Pa) and (c x ) Mech is a real constant (given in Pa/m) and v o is the vibration velocity dierence. From Equation (3.4) it is clear that the damping force amplitude (F ox ) Mech is assumed to be proportional to the vibration velocity dierence (v o ) x with a real, frequency dependent, proportionality factor (c x ) Mech /ω. Similarly, for the air pumping case, the damping constant (c z ) Air is used to represent the losses at the interface due to out-of-plane motion of the plates causing air movement due to the change of the volume of the air cavities formed in the gaps. It is specied as (F oz ) Air = (c z ) Air i (u o ) z = (c z) Air ω (v o) z (3.5) where (F oz ) Air is a complex traction amplitude and (c z ) Air is a real constant. The assumed damping forces are thus, in the present study, linearly dependent on the vibration velocities both in time and frequency domain in analogy to the mechanical contact damping case explained earlier.

20 Chapter 4 Testing, Modelling and Implementation Approaches 4.1 Testing Figure 4.1: Measurement set-up invacuo. Figure 4.2: Structure with response points. Red: On the spot-weld Green: Between the spot-welds Blue: Away from the ange To characterize the losses that take place at the interfaces, tests were performed on a complex spot-welded structure inside a vacuum chamber, gure 4.1. A typical spotwelded structure is studied as it is commonly used in the automotive industry, gure 4.2. The structure is made of standard steel where the two steel plates are bonded together with 24 spot-welds, 12 on each ange, measuring 3 mm diameter each. In [4] a detailed description of the test structure is shown. Since characterization of losses at the interfaces is a challenging task, tests were performed under in-vacuo and ambient 12

21 Interface Damping: Characterization and Implementation 13 pressure conditions. Experiments were carried out in the frequency band of Hz with a frequency resolution of 0.15 Hz. Frequency response functions (FRF's) were measured on the spot-welds (points 1, 7, 9), between the spot-welds (points 8, 11) and a few points away from the ange (points 2, 3, 10) as shown in gure 4.2. The selection of these points was made in order to illustrate the global damping resulting for the localised modelling applied in the present study. 4.2 Modelling and Implementation Figure 4.3: Generic principle dening, pair-wise opposing damping forces, similar damping forces are applied in Fz, for mechanical contact area. The same principle is followed for the air pumping in gaps. The Comsol multiphysics 3.5a nite element (FE) software was used in order to simulate a real measurement test set-up situation, including the input excitation device, [8]. Since the dynamics of the test set-up has some inuence on the test results, the inuence of the suspension, the stinger and the shaker attachments were all taken into consideration, [9, 10], in the numerical model. The numerical model is intended to resemble the test structure, [4], as far as possible and gure 4.3 shows the generic principle for interface damping, where the assumed area where damping takes place around the spot-welds that come into mechanical contact is shown. The assumed damping forces, Equations (3.4 and 3.5), were applied using the proposed method at these areas around the spot-welds. As discussed above [4], the size of these areas determine together with the relative motion, the losses incurred. In the present model, the area that comes into contact was modelled using a trial and error approach where the mechanical contact area and the respective constants were varied until a satisfactory match was found. Note that all represented mechanical contact areas were assumed to be identical with the same damping forces applied. The remaining areas at the anges of the spot-welded beam structure were then used to introduce the losses related to the air pumping through the cavities formed between the spot-welds. As a step towards an increased applicability of the proposed damping modelling, a nite element (FE) model was constructed using the NX Nastran 7 FE software in order to simulate a real measurement test set-up situation, including the input excitation

22 14 Ravi V. Nadampalli Figure 4.4: Nastran model with mechanical contact area around spot-welds device, gure 4.4. The Nastran simulation model included the same set-up in order to compare to the Comsol model and to the real measurement test set-up. The dierence lies in the way the damping forces are introduced. Figure 4.4 shows the area around the spot-welds that come into mechanical contact where the damping takes place. The mechanical contact in the Nastran model was represented by the CBUSH elements, [11]. The assumed mechanical contact area, as previously estimated from the Comsol simulations, was used also here, [4] Assumed contact area Choosing the area that comes into contact is some-what arbitrary. The two dierent physical loss mechanisms at the interfaces i.e. the mechanical contact and the air pumping, brings ambiguity in terms of the choices made for the area chosen. A trial and error approach is used in identifying the contact area, where, in the present work with an assumed mechanical contact area of 10 x 12 mm, a reasonable agreement was observed for damping loss factors at the 330 Hz resonance peak. There is however too high damping provided at the 280 Hz resonance peaks. Similar trial and error approach was used in nding the real constants. Also the resonance peaks are rather sensitive to the damping forces in vertical z direction. In the study, it was observed that once the assumed mechanical contact area is increased to 12 x 24 mm, there is better agreement found for the peaks at the 280 Hz, in the mechanical contact damping case. With the increase in assumed mechanical contact area, the assumed damping forces are reduced. This shows that there is a very complex combination between the real constants, the contact areas and the actual deformation shape, as the relative displacement magnitude in dierent directions inuences the actual damping occurring at certain frequencies Relative displacement In gure 4.2, response points 7 and 9 was divided into 9 equally distant sections in order to study the relative displacement dierence, for the undamped and the damped simulations. The 280 Hz and the 330 Hz resonance frequencies were studied. Reference [4] shows a detailed description with gures, where a higher relative displacement for the

23 Interface Damping: Characterization and Implementation 15 damped case at the 280 Hz peak in x direction was observed, compared to the undamped case. Similar observations were made at the 330 Hz peak. It was also observed that there is a non-zero relative displacement taking place at the spot-weld itself i.e, at response point 7. This is an artefact of the modelling of the spot-weld in the nite element model and could be the reason for the higher relative displacements found for the damped case, which is simulated using the applied assumed damping forces along the assumed mechanical contact areas Model comparisons In the Comsol model, the test structure was modelled as two dierent parts (two subdomains), where the two parts were connected along the ange, gure 4.3. At the ange, the two parts were divided by a common layer where the two assumed physical loss mechanisms were modelled. A surface integration was performed on the assumed mechanical contact areas and the air pumping areas. In the Nastran model, the test structure is modelled as two separate parts with spot-welds bonding them together. From the Comsol, the areas chosen for the two physical loss mechanisms were known, so the CBUSH elements were used in modelling the two loss mechanisms where element integration was performed.

24 Chapter 5 Results Discussion To be able to understand and explain the loss mechanisms that take place at the complex interfaces, a comparison of results from a Comsol simulation are shown, gure 5.1, between the test results in-vacuo, only material damping i.e. no interface damping, and mechanical contact damping. At the 330 Hz resonance frequency, reasonable agreement Point 8 : FRF Test: No Air Simulation: 0.1% Loss Factor Simulation: With Contact Damping 80 db (m/s) Frequency (Hz) Figure 5.1: Point 8 - Comsol simulation result with mechanical contact damping. Figure 5.2: Point 8 - Comsol simulation result with changed mechanical contact area. was found between the test and the simulation results with mechanical contact damping. The calculated loss factors, using half power band-width method, at these peaks showed good agreement. As expected, there is less damping provided, with only material damping case, at the peaks. There are certain dierence at the 270 Hz and the 280 Hz resonance peaks, but it is explained, [4], that the dierences in the assumed contact areas around the spot-weld is one of the main reasons for such variation. Figure 5.2 show a better agreement to the measurement results around the 280 Hz peaks by using the present interface damping principle but with increased (12 x 24 mm) mechanical 16

25 Interface Damping: Characterization and Implementation 17 contact area. A comparison of results is shown in gure 5.3 for the air damping case Point 8 : FRF Test: No Air Simulation: With Contact Damping Test: With Air Simulation: With Air Damping 100 db (m/s) Frequency (Hz) Figure 5.3: Point 8 - Comsol simulation result with air damping. Figure 5.4: Mechanical contact damping with new spot-weld area. The calculated damping loss factors at the 330 Hz resonance peak showed reasonably good agreement in the mechanical contact damping case. However, there are certain dierences observed at the 330 Hz resonance peak for the response points away from the ange i.e. points 2, 3 and 10. [4], by changing the spot-weld area to 5 mm diameter, a better agreement could be found for the response points away from the ange, gure 5.4. Also there are visual geometric discrepancies in the test structure which has a signicant eect on the response behaviour of the structure, [12, 13].

26 Chapter 6 Conclusion and Future scope The main focus of this study is to understand the physical loss mechanisms that take place at the interfaces of a complex built-up structure. Linear modelling and implementation of such loss mechanisms is also a part of this research as there is a gap in understanding such losses. The present research has contributed a step further in understanding, characterizing and implementing the losses that takes place at the interfaces i.e. the mechanical contact and the air pumping. This characterization of losses has helped in better modelling using simple linear techniques. Also the interface damping principle which is used and implemented in the Nastran has shown that such assumed damping forces can be applied in a conventional nite element tool. Implementation of interface damping into a complex spot-welded structure is a rst step, but the actual car body-in-white is made up of many such complex built-up of parts. Hence further eorts and a better understanding are required in order to implement it on a complete conventional vehicle. 18

27 Chapter 7 Summary of Appended Papers 7.1 Paper A Damping Modelling in Complex Built-up Structures Ravi V. Nadampalli, K. Dovstam, P. Göransson and C. Glandier Damping in a given structure can be characterized and attributed to mechanisms like internal material dissipation and non material damping. While material damping is well understood and rather straightforward to model, the losses occurring at interfaces are less accessible and representable in simulations of realistic built-up body structures. Here, an approach based on linear modelling is discussed. The main objective of the work is to investigate the modelling of interface damping in a spot-welded structure by numerical simulations. Damping due to surface contact and movement of air through unsealed gaps is included. The results are promising in terms of the losses predicted for a realistic structure. 7.2 Paper B Implementing Linear Modelling of Interface Damping in a Finite Element Software Ravi V. Nadampalli, P. Göransson and C. Glandier In the automotive industry virtual modelling of losses in a built-up structure is still a challenge. A body-in-white car structure consists of many spot-welded parts and the modelling of their associated losses is highly interesting. For this purpose, the dissipation of mechanical energy is here modelled in the frame of large scale computations using linear techniques with commercially available nite element software. Mechanical, 19

28 20 Ravi V. Nadampalli vibration damping is introduced through external forces which are pairwise applied such that they oppose the relative motion at the contact interfaces between two parts. Two aspects are investigated, rst if the proposed modelling captures the main mechanisms of the damping on a system level. Second, if the predicted local vibration responses at dierent locations correlate well between predicted and previously measured (in vacuo) spectra. Initial simulations show promising results and the level of damping observed in the predictions are similar to the measured spectra, for vibration shapes which involve signicant relative motion along the spot-welded surfaces. An advantage with this technique is that it helps in understanding of dierent sources of total system damping, i.e. due to material and other sources of damping. It is veried that nonmaterial damping due to mechanical contact is a signicant contributor to the losses in a built-up structure which may be simulated with the proposed technique. In the paper the overall approach is discussed together with the specic aspects of the nite element implementation technique proposed.

29 Bibliography [1] Nashif A D., Jones D I G., and Henderson J P. Vibration damping. John Wiley & Sons, New York, [2] Mead D J. Passive Vibration Control. John Wiley & Sons, Reprint, [3] Dovstam K., Göransson P., and Gartmeier O. On linear modeling of interface damping in vibrating structures. Journal of Sound and Vibration - Accepted for publication, March [4] Nadampalli R V., Dovstam K., Göransson P., and Glandier C. Damping modelling in complex built-up structures. To be submitted to Journal of Sound and Vibration. [5] Nadampalli R V., Dovstam K., Göransson P., and Glandier C. On linear modelling of interface damping in a complex vibrating structure. In COMVEBONOV, pages , Sussex, UK, March [6] Nadampalli R V., Göransson P., and Glandier C. Implementing linear modelling of interface damping in a nite element software. To be submitted to Finite Elements in Analysis and Design. [7] Nadampalli R V., Göransson P., and Glandier C. Modelling and implementation of interface loss models for linear response simulation in a complex structure. In NOVEM, Sorrento, Italy, April [8] COMSOL AB. Comsol Multiphysics User's Guide. Stockholm, [9] Dalenbring M. and Einarsson S P. A study of the sensitivity in vibration response due to uncertainties in input excitation and location. In Euromech 405 Colloquium, November 17-19, Valenciennes, France, [10] Olbrechts T., Vandepitte D., Sas P., and Heylen W. Inuence of excitation systems on the dynamic behaviour of test structures. In Proceedings of ISMA 21, pages , Leuven, Belgium, [11] Siemens Product Lifecycle Management Software Inc. NX Nastran 7, Quick Reference Guide

30 22 Ravi V. Nadampalli [12] Matteo Palmonella, Michael I. Friswell, John E. Mottershead, and Arthur W. Lees. Guidelines for the implementation of the cweld and acm2 spot weld models in structural dynamics. Finite Elements in Analysis and Design, 41:193210, [13] Fumiyasu Kuratani, Kazuhei Matsubara, and Takashi Yamauchi. Finite element model for spot welds using multi-point constraints and its dynamic characteristics. SAE International, 2011.

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