Proceedings of the IMAC-XXVIII February 1–4, 2010, Jacksonville, Florida USA ©2010 Society for Experimental Mechanics Inc. Model Reduction and Substructuring Techniques for the Vibro-Acoustic Simulation of Automotive Piping and Exhaust Systems

Jan Herrmann, Michael Junge and Lothar Gaul Institute of Applied and Experimental Mechanics, University of Stuttgart Pfaffenwaldring 9, 70569 Stuttgart, Germany

ABSTRACT

The influence of the acoustic field on the is a common issue in automotive applications. An example is the pressure-induced structure-borne of piping and exhaust systems. Efficient model order reduction and sub- structuring techniques accelerate the finite element analysis and enable the vibro-acoustic optimization of such complex systems with acoustic fluid-structure interaction. This research reviews the application of the Craig-Bampton and Rubin method to fluid-structure coupled systems and presents two automotive applications. First, a fluid-filled brake-pipe system is assembled by substructures or superelements according to the Craig-Bampton method. Fluid and structural partitions are fully coupled in order to capture the interaction between the pipe shell and the heavy fluid inside the pipe. Second, a rear muffler with an air-borne excitation is analyzed. Here, the Rubin and the Craig-Bampton method are used to separately compute the uncoupled component modes of both the acoustic and structural domain. These modes are then used to compute a reduced model which incorporates full acoustic-structure coupling. For both applications, transfer functions are computed and compared to the results of dynamic measurements.

Nomenclature

M, K, D, C Mass matrix, stiffness matrix, damping matrix, acoustic-structure coupling matrix s, a Index for solid partition, index for acoustic partition f(t), q(t) Structural forces, nodal acoustic fluxes p, u Nodal acoustic excess pressures, nodal displacements q Modal coordinates I, F Index for interface DOF, index for free (inner) DOF ρ0 Fluid mass density Φ Eigenspace of the constrained problem – fixed interface modes ⋄ Superscript for reduced component model matrices CB Craig-Bampton method Φˆ Free-interface modes used for Rubin method Ψˆ Attachment modes used for Rubin method Hp→u Transfer function between pressure at inlet and structural deflection

1 Introduction

Elastic piping and exhaust systems are often characterized by (hydro-)acoustic sources. An example for a hydroacoustic excitation in hydraulic pipes such as fuel and brake-pipes is the operation of pumps and valves which leads to oscillating pressure pulsations within the pipe. As a result, pressure waves propagate along the pipe and excite the pipe shell due to the heavy fluid-structure coupling [1, 2, 3]. Finally, the pressure-induced structure-borne sound is transmitted to attachment structures which leads to undesired noise and levels [4]. A similar excitation scenario is found in automotive exhaust systems where the exhaust gas acts as a strong acoustic source which also leads to pressure-induced structure-borne sound and undesired sound radiation [5]. To predict the vibro-acoustic behavior of such mechanical systems, three-dimensional models including full coupling of the two-field problem are needed. It is particularly important to include bending modes of the structure, which are predominantly responsible for sound and vibration harshness. The finite element method [6] is considered as the appropriate discretization method to investigate the dynamics of the interior vibro-acoustic problem including the coupling between the inner fluid and the pipe shell. The might be used to determine the sound radiation in the exterior field [7]. The main problem of fully discretized models are large computation times and extensive computer memory. Model order reduction and substructuring techniques such as the well-known component mode synthesis overcome this limitation. This research shows how the Craig-Bampton [8] and the Rubin method [9] are applied to efficiently compute the hydro- and vibro-acoustic response of two automotive applications. First, a fluid-filled brake-pipe system is analyzed which is characterized by a heavy fluid-structure coupling between the water inside the pipe and the flexible pipe shell. The Craig- Bampton method is applied which leads to a considerable model order reduction and to moderate computation times. Moreover, the influence of a cross-section change on the hydraulic transfer function is analyzed and the results are validated by a hydraulic test bench operating in the kHz-range. Secondly, an automotive exhaust system is analyzed which is an example of light fluid-structure coupling between the exhaust gas and the structure of the expansion chamber. Here, the Rubin and the Craig-Bampton are used to separately determine the uncoupled component modes of both the acoustic and structural domain. These modes are then used to compute a reduced model including full acoustic-structure coupling. Measurements are performed and the vibro-acoustic response is compared to the results of the numerical simulation including the proposed model reduction technique.

2 Finite Element Based Substructuring Techniques

This chapter briefly summarizes the application of the Craig-Bampton and the Rubin method on fluid-structure coupled systems. Both methods are used to reduce the order of the corresponding finite element model of each component and to assemble the overall mechanical system. The linear wave equation for a fluid at rest is used for low Mach numbers as encountered in most piping and exhaust systems [1]. The acoustic field is coupled to the structural dynamic equations at the fluid-structure interface [6], where two coupling conditions hold, namely the Euler equation and the reaction force axiom. The corresponding finite element formulation leads to coupled discretized equations in terms of nodal structural displacements u and nodal acoustic excess pressures p 0 M s u¨ Ds 0 u˙ Ks −C u f(t) T + + 0 = . (1)  ρ0 C M a   p¨   0 Da   p˙   Ka   p   q(t) 

In the above equation, index “s” denotes the structural partition, whereas index “a” characterizes the acoustic fluid. The discretized equations include mass matrices M s,a, stiffness matrices Ks,a, viscous damping matrices Ds,a, as well as the coupling matrix C. Forces and fluxes are given as f(t) and q(t). Hereby, the classical unsymmetric formulation with displacements and pressures as field variables is used. It is worthy of note that alternative representations use the acoustic velocity potential as field variable [10] which leads to a symmetric formulation of Eq. (1).

2.1 Craig-Bampton Method

The adaptation of the Craig-Bampton method to mechanical systems with acoustic fluid-structure coupling has been developed in [11]. For clarity, the critical steps are briefly summarized in this section. To apply the Craig-Bampton method to the acoustic-structure coupled problem, displacement and pressure DOFs are both separated into interface DOFs with T T T T T T index “I” and inner (free) DOFs denoted by index “F”, i.e. u = [uI uF ] and p = [pI pF ] , respectively. The matrices are partitioned accordingly. As explained in [8], the Craig-Bampton reduction basis consists of fixed interface modes and constraint modes. The fixed interface modes are obtained by solving the eigenvalue problem for the system with constrained interface DOFs 0 Ks,FF −CFF 2 M s,FF uˆ j,F 0 0 − ωj T = . (2)  Ka,FF   ρ0 CFF M a,FF   pˆj,F 

The reduction bases Φ are enriched by the fixed interface modes up to the m-th eigenvector or a cer- tain threshold (which is usually at least two times the maximum frequency of interest), such that Φ Φ s = [uˆ1,F , ... , uˆ m,F] and a = pˆ1,F , ... , pˆm,F . A modification of an iterative subspace solver is applied to compute the eigenvectors [12, 1]. The eigenspaces are mass-normalized in order to avoid ill-conditioning or numerical break-down. The constraint modes follow from a static of Guyan condensation [13]. The resulting reduction bases Γs and Γa are built according to Craig-Bampton method by discarding any coupling terms, i.e. 0 uI I uI Γ = −1 Φ = s qs (3)  uF   −Ks,FFKs,FI s,FF   ud  for the structural domain and I 0 pI pI Γ = −1 Φ = a qa (4)  pF   −Ka,FFKa,FI a,FF   pd  for the fluid domain, respectively. Hereby, index “d” denotes dominant modal coordinates as compared to neglected or truncated modal coordinates. Hence, qs and qa are the generalized coordinates of the reduced system. The overall reduction basis is assembled by Γ 0 u s qs = 0 Γ (5)  p   a   qa 

Γ∈Rn×nr | {z } and reduces the coupled system in Eq. (1) to nr ≪ n DOFs ⋄ 0 ⋄ ⋄ M s q¨s Ks −C qs f s ⋄T ⋄ + 0 ⋄ = (6)  ρ0 C M a   q¨a   Ka   qa   f a  where ⋄ ΓT Γ ⋄ ΓT Γ ⋄ ΓT Γ ⋄ ΓT Γ M s = s M s s, M a = a M a a, Ks = s Ks s, Ka = a Ka a, (7) ⋄ ΓT Γ ΓT ΓT C = a C s, f s = s f f a = a q. Eq. (6) describes the superelement for the component mode synthesis. It is important to note that both structural and fluid interface DOFs are kept as physical DOFs which simplifies the component coupling procedure and which allows the integration of an impedance boundary condition in the reduced equations. The Craig-Bampton method is particularly efficient for piping systems, where the number of interface DOFs between the components is small compared to the inner DOFs and where repeating superelements occur. An additional reduction of the remaining interface DOFs leads to a further computational speedup and may be applied as explained in [3, 14, 15]. The coupling between the reduced component models is defined by single point contraints on the component interfaces. This holds for both the solid and the fluid domain, and implicit coupling conditions are established. They are used for the generation of an explicit transformation matrix Q to transform the component coordinates in coordinates of the assembled piping system [16]. This coupling procedure allows the subsequent summation of nsub substructure contributions. An alternative way to couple the superelements using Lagrangian multipliers is shown in [17]. The global dynamic system of T equations with the global reduced coordinates q = [qs qa] is given as

M gq¨ + Dgq˙ + Kgq = f g, (8) whereas the system matrices M g and Kg are assembled as

nsub T ⋄ 0 Qs,iM s,iQs,i M g = T ⋄T T ⋄ , (9) ρ0Q C Q Q M Q  Xi=1 a,i i s,i a,i a,i a,i

nsub T ⋄ T ⋄ Qs,iKs,iQs,i −Qs,iCi Qa,i Kg = ⋄ . (10)  0 QT K Q  Xi=1 a,i a,i a,i The global damping matrix is given as

nsub T ⋄ T ⋄ 0 αs,iQs,iM s,iQs,i + βs,iQs,iKs,iQs,i Dg = T ⋄ , (11)  0 βa,iQ K Q  Xi=1 a,i a,i a,i assuming a Rayleigh damping model for each substructure with the corresponding Rayleigh damping parameters αs and βs for the structural domain and βa for the fluid partition. For fluid-filled pipes, a considerable improvement of the fluid damping model is achieved using an advanced modeling approach including wall friction effects which is the dominant damping mechanism in thin pipes. The advanced fluid damping model is based on a complex wave number and incorporates the frequency dependent wall friction between the acoustic fluid and the pipe shell. A complete derivation of the improved fluid damping model and its integration in the finite element analysis is beyond the scope of this paper. The interested reader is refered to [18, 19]. In the , Eq. (8) is given as

2 ˆ −M gω + iωDg + Kg qˆ = f g, (12)  such that a harmonic analysis is performed using the inverse of the dynamic stiffness matrix as transfer function. The results are expanded to full space in order to obtain the transfer function of interest.

2.2 Rubin Method

In contrast to the Craig-Bampton method, the Rubin method is a free-interface method, i.e. neither the interface DOFs nor the free DOFs are additionally constrained for the computation of the component modes in Γˆ, which is assembled by free-interface normal modes and attachment modes [9]. In what follows, the basic principle of the Rubin method is explained on behalf of the structural domain. The free-interface normal modes are computed by solving the eigenvalue problem of the unconstrained system

2 Φˆ −ωj M s + Ks sj = 0 . (13)  Analogue to the Craig-Bampton method, only a small number of free-interface normal modes are retained. Attachment ˆ modes, Ψs, augment the component modes matrix accounting for the modal truncation error. The i-th attachment mode is defined by the static solution vector due to a single unit force applied to the i-th interface DOF

−1 ˆ Ks,II Ks,IF T Ψsi = [0 . . . 1 . . . 0] . (14) Ks,FI Ks,FF

In other words, attachment modes are columns of the associated flexibility matrix. The reduction basis Γˆ is then given by ˆ ˆ ˆ Γs = Φs Ψs . (15)   Attachment modes cannot be computed directly, if the structure pocesses rigid body degrees of freedom. Then, instead of the standard attachment modes, inertia-relief attachment modes represent one alternative [20]. The coupling between the reduced component models is analogue to the Craig-Bampton method. Since for the Craig- Bampton method all interface DOFs are retained, the displacement coupling conditions are typically fulfilled more accurately than with the Rubin method. Yet, if experimentally determined modal damping ratios are to be incorporated in the simulation model, the Rubin method is favorable. The free-floating boundary conditions of the free-interface normal modes can be realized in an experimental setup. Thus, the obtained modal damping ratios may be mapped directly.

2.3 Combination of Craig-Bampton and Rubin Method for Light Fluid-Structure Coupling

It is observed, that for structures with high impedance mismatch between the structure and the contained fluid, the coupled eigenfrequencies and eigenvectors are altered only marginally compared to the uncoupled ones. Therefore, in such a case, the reduced-order model is constructed by using the uncoupled eigenvectors, since they span approximately the same subspace as the coupled eigenvectors This is equivalent to reducing each domain separately. Please note, that the reduced-order model is still a fully coupled system. This approach has the advantage that for each domain the favorable reduction method might be applied. If for example, the Rubin method is applied for the reduction of the structure and the Craig-Bampton method is used for the fluid the reduction basis reads

Φˆ Ψˆ 0 0 Γˆ = s s . (16)  0 0 Φa Ψa

Please note, that all component modes vectors in Γˆ are obtained by the solution of the uncoupled problem. 3 Applications

So far, the application of substructuring techniques to problems with acoustic-structure coupling has been elaborated. Now, two industrial applications are presented, where the different model reduction techniques are applied.

3.1 Hydroacoustic Analysis of Automotive Piping Systems

The first example is a fluid-filled piping system which is characterized by a heavy fluid-structure coupling between water inside the pipe and the flexible shell. The Craig-Bampton method as explained in Section 2.1 is used as model reduction and substructuring technique to solve the fully coupled system equations. The focus of this section is the hydroacoustic analysis of thin piping systems as found in brake and fuel pipes.

3.1.1 Straight Pipe With a Cross Section Change

A water-filled piping system with a cross section change is assembled using three substructures as shown in Fig. 1 (steel 3 3 pipe: E=206 GPa, ρs=7900 kg/m , water: c = 1460 m/s, ρ0=1000 kg/m ). The first superelement is a straight pipe section (length 262 mm) with an outer radius of 3 mm and a wall thickness of 0.7 mm. The second substructure is an orifice with a length of l = 4 mm which is characterized by a cross section change as depicted in Fig. 1. The inner diameter of the orifice is d = 1.2 mm. The third component is another straight pipe section (length 305 mm) with the same uniform cross section as the first substructure and a closed end. To achieve a compatible mesh between the component interfaces, the substructure with the small inner pipe radius includes a thin element layer at both ends to enable the transition between the two different pipe diameters as illustrated in Fig. 1(a). It is also important to model the casing around the orifice which is needed according to the design. The piping system is clamped on the left end and an acoustic pressure excitation is applied as boundary condition. The reduced system has 550 DOFs as opposed to 8762 DOFs of the full FE model. The additional interface reduction as introduced in [3] further reduces the model order to 389 DOFs. 1 2 3 p1 p2 pipe PC measurement system + Matlab-interface solid charge ampl.

di da l d

p1 vacuum- p0 pump orifice p2 pipe pressure source fluid FSI power ampl. pump function generator (a) substructuring (b) experimental setup for validation

Figure 1: Left: assembled piping system using three substructures including boundary conditions and cut through the discretized Substructure 2 with the cross section change. Right: experimental setup of the hydraulic test bench.

The experimental setup of the hydraulic test bench is illustrated in Fig. 1(b) and is also described in [21, 3]. The setup consists of a hydroacoustic pressure source and a fluid-filled steel pipe with the dimensions mentioned before. The pipe is characterized by a cross section change due to an orifice as shown in the technical drawing of Fig. 1(b). The pressure source consists of two piezo stack-actuators which are arranged perpendicularly to the direction of wave propagation and on opposite sides of the hydraulic pipe. The actuators are driven by a power amplifier and a function generator and oscillate with opposite phase in order to excite pressure pulsations in the fluid column. The supply pipe with the additional pump is required to fill and compress the fluid to ensure a stable fluid column without any air bubbles, which is a challenging task especially for small orifice diameters. The dynamic pressure pulsations are measured with piezoelectric pressure sensors. A sweep excitation is chosen in order to excite a wide frequency range. The repeated sweep signals have a cycle duration of 200 ms. The hydraulic transfer function between the pressure p1 and the pressure p2 is estimated using the averaged auto-power and cross-power spectra of 15 swept pressure signals. The hydraulic transfer function Hp1→p2 is measured using the hydraulic test bench and the result is compared to the finite element simulation using the substructuring technique as described before. The result of the hydraulic or hydroacoustic transfer function for the pipe with an orifice diameter of d = 1.2 mm and an orifice length of l = 4 mm is shown in Fig. 2. The coherence of the measurement is plotted in the same figure. The correlation between and simulation is very good, both for the hydraulic resonances and the predicted damping. A kinematic viscosity of ν = 1 · 10−6 m2/s is assumed for the advanced fluid damping model [18]. Two coupled modes are visible where a structural resonance of the pipe shell interacts with the acoustic fluid. The first coupled peak around 1.5 kHz is characterized by a longitudinal mode of the pipe structure. The second coupled mode with the typical antiresonance behavior around 5 kHz strongly depends on the pipe section with the orifice. It is worthy to note that a cross section change as investigated in this section leads to a shift of the hydraulic resonance to lower frequencies when compared with a uniform pipe. The reason for this phenomenon is the increasing hydraulic inertia for decreasing orifice diameters. The frequency shift is particularly strong for odd-order modes.

40 experiment Craig−Bampton 30 [dB]

| 20 2 p

→ 10 1 p H | 0 −10 −20

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1

2 0.5 γ 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 frequency [Hz]

Figure 2: Top: hydraulic transfer function – comparison between experiment and simulation for a fluid-filled pipe with an orifice. Bottom: coherence of the measurement.

3.1.2 Elbow Pipe With Attachment Part

The Craig-Bampton method is now applied to a more complex piping system consisting of a curved brake pipe (E=206 GPa, 3 ρs = 7900 kg/m , ν = 0.3, lengths 0.7 + 0.3 m) with an outer radius of 3 mm and a wall thickness of 0.7 mm, two 3 steel joints (the so-called clips) and a plate as target structure (E=180 GPa, ρs = 7900 kg/m , ν = 0.3, lengths 3 0.3 x 0.3 x 0.001 m). The pipe is filled with water (c = 1460 m/s, ρ0 = 1000 kg/m ). The fluid wave strongly interacts with the flexible pipe shell, which leads to a fluid wave speed of 1408 m/s as opposed to the free sound speed of c = 1460 m/s. This phenomenon is described by Korteweg’s equation [22]. The investigated pipe configuration is of practical importance since pressure pulsations in the fluid and strong fluid-structure coupling result in a structural excitation of the brake pipe. The pressure-induced structure-borne sound is transferred to the target structure by the clips as explained in [4]. Fig. 3 shows the pipe configuration assembled by 9 substructures (five straight pipe sections, one elbow, two clips and the plate). The application of the Craig-Bampton method reduces the model order from 55818 DOFs to 2566 DOFs. The additional interface reduction leads to 1118 DOFs. To validate the overall simulation method, the measured and computed hydroacoustic (or hydraulic) transfer function

Hp1→p2 is shown in Fig. 3. The measurement is conducted with the same setup as explained before. Again, the correlation between experiment and simulation is very good, both for the obtained hydraulic resonances and the predicted damping in the fluid path. Strong acoustic-structure coupling is observed for a frequency around 1800 Hz, where a hydraulic and a structural resonance coincide. Another fluid-structure coupled mode is visible around 3600 Hz. Note that the observed coupled modes are very sensitive with respect to the structural configuration and the pipe mounting position. 30

20

[dB] 10

p2 | 2

p 0

full: 55818 DOFs → 1 −10 CB: 2566 DOFs p

H experiment | −20 CB+interface-red.: 1118 DOFs Craig−Bampton

−30 0 1000 2000 3000 4000 1

p1 2 γ 0 0 1000 2000 3000 4000 frequency [Hz]

(a) assembled piping system (b) result

Figure 3: Left: finite element model of the assembled brake-pipe system and boundary conditions (vibration mode at

1030 Hz). Right: measured and computed hydraulic transfer function |Hp1→p2 | (top) and coherence of the measurement (bottom).

3.2 Vibro-Acoustic Analysis of an Exhaust System

In this section, pressure-induced of a production series rear muffler as depicted in Fig. 4 are investigated. Please note, that for simplicity the inner structural parts of the rear muffler are removed. The periodically blown out exhaust gas leads to pressure pulsation within the exhaust system. These pulsations excite structural vibrations, which then additionally contribute to the sound radiation of the system. It is reported that this so-called surface radiated noise might dominate the noise radiated at the orifice [23, 24, 25, 5]. In this work, the focus is set on the pressure-induced vibrations and not on the sound radiation.

(a) (b)

Figure 4: Picture of a production series rear muffler and corresponding CAE model. The system is depicted upside-down. The number on the right mark the location of the investigated nodes.

In order to quantify the pressure-induced vibrations of the rear muffler, the transfer function, Hp→u, between the acoustic pressure at the inlet and the structural deflection at 4 locations on the surface is determined (cf. Fig. 4(b)). The acoustic pressure at the inlet is measured by making use of the two-microphone-method [26]. For the simulation a finite element model is set up with 179808 structural DOFs and 143602 fluid DOFs. For an efficient simulation a reduced model is computed as described in Section 2.3. The Rubin method is applied for the structural domain. The modal damping values obtained from an experimental are incorporated in the damping matrix. The Craig-Bampton method is employed for the fluid domain. For each domain, 40 free-interface and fixed-interface normal modes are retained, respectively. The interface DOFs on the inlet and outlets sum up to 444 structural DOFs and 211 fluid DOFs yielding the same number of constraint modes and attachment modes, respectively. It is worth noting, that the interior acoustic fluid intersect with the surrounding fluid at the orifices. Previous investigation showed, that a radiation impedance condition approximates sufficiently accurate the occurring interaction at this cross-section [27]. The impedance condition yields complex entries in the damping matrix Da [28]. For the frequency sweep computations between 300 Hz and 600 Hz (with a step step size of 1 Hz) the reduced-order models clearly outperform the full-order solution. A speedup of approximately factor 100 is obtained. The plots in Fig. 5 show a comparison between the experimental (solid, black line) and simulative results (dashed, blue line). Each subplot represents the magnitude of the transfer function Hp→u for one node on the surface of the rear muffler as depicted in Fig 4(b). A strong excitability via the the acoustic path is observed for all points – Hp→u spans more than four orders of magnitude within the depicted frequency range between 300 Hz and 600 Hz. A comparison of the eigenfrequencies with the results of an experimental modal analysis reveals that the reasonance frequencies are reached at eigenfrequencies of the structure. This explains the fact that the surface radiated noise shows a strongly tonal characteristic. All four subplots show a good agreement between and simulations. It is worth noting, that the simulation is capable to predict the transfer function both qualitatively and quantitatively. The proposed method is thus suitable to efficiently predict pressure-induced vibrations in an early development stage and is capable to prevent cost-intensive modifications and time-consuming experiments.

measured measured simulated simulated ] ] -6 -6

N 10 N 10 / / 3 3 m m [ [ | | n n s s u u

→ -8 → -8 10 10 inlet inlet p p H H | |

-10 -10 10 10 300350 400 450 500550 600 300350 400 450 500550 600 frequency [Hz] frequency [Hz] (a) Node 3287 (b) Node 3290

measured measured simulated simulated ] ] -6 -6 N N 10 10 / / 3 3 m m [ [ | | n n s s u u

→ -8 → -8 10 10 inlet inlet p p H H | |

-10 -10 10 10 300 350400 450 500 550 600 300 350400 450 500 550 600 frequency [Hz] frequency [Hz] (c) Node 3756 (d) Node 3765

Figure 5: Pressure-induced structural vibrations. Comparison of experimental and simulative results.

4 Conclusion

The Craig-Bampton and the Rubin method are successfully applied to fluid-structure coupled systems in order to achieve moderate computation times and moderate computer memory. The hydro- and vibro-acoustic response of two automotive applications is analyzed in this research showing the applicability of the described component mode synthesis. For heavy fluid-structure coupling as in the case of fuel and brake pipes, the fluid and structural partition need to be fully coupled to compute the corresponding component modes and to capture the strong interaction between the fluid and the flexible pipe shell. For light acoustic fluid-structure coupling as in the case of an exhaust system, uncoupled component modes of both the acoustic and structural domain can be used to compute a reduced model. The results of the numerical simulation are compared to dynamic measurements. Good agreement is achieved with respect to hydro- and vibro-acoustic transfer functions of complex fluid-structure coupled systems.

5 Acknowledgement

The authors gratefully acknowledge the funding of this project by the German Research Society DFG in the transfer unit TFB 51 and by the Friedrich-und-Elisabeth-Boysen-Stiftung. Moreover, the authors wish to thank Dr. Matthias Maess at Robert Bosch GmbH for his ongoing advice.

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