**7. References**


temperature-independent material properties case than for the temperature-dependent

Three-dimensional FE models of SOFC anode and cathode microstructures were constructed from a stack of two-dimensional SEM images of actual cross-sections of anode and cathode microstructures. The models were subjected to spatially uniform predefined temperature fields of increasing magnitude and the resulting distribution of stresses was obtained using FEA. The obtained stresses were subjected to Weibull analyses to determine the failure probability of the anode and cathode as a function of temperature. *The novelties of this work include FE analysis of the mechanical response of microstructure-based anode and cathode models to temperature loads, consideration of temperature-dependent material properties of the anode and cathode materials, and consideration of nonlinear elastic-plastic behavior of the nickel phase of the Ni-YSZ anode*. The Weibull analyses showed that the linear elastic material models underestimate the failure probability of the anode at high temperatures; hence, it is important to consider the nonlinear behavior of the nickel phase of the Ni-YSZ anode. Also, it was found that consideration of temperature-independent material properties of the cathode materials results in higher failure probability values than those obtained with

We acknowledge the financial support for this work from the National Science Foundation under the Faculty Early Career Development (CAREER) Grant CMMI-0546225 (Material Design & Surface Engineering Program). We also acknowledge the technical support from Dr. Scott Barnett at the Department of Materials Science and Engineering at Northwestern University who generously provided a series of 2-D SEM images of anode and cathode

Anandakumar, G., Li, N., Verma, A., Singh, P., & Kim, J.-H. (2010). Thermal stress and

Atkinson, A., & Selcuk, A. (2000). Mechanical behavior of ceramic oxygen ion-conducting

Ebrahimi, F., Bourne, G., Kelly, M., & Matthews, T. (1999). Mechanical properties of

Giraud, S., & Canel, J. (2008). Young's modulus of some SOFCs materials as a function of temperature. *Journal of the European Ceramic Society*, Vol. 28, (2008), pp. (77-83). Johnson, J., & Qu, J. (2008). Effective modulus and coefficient of thermal expansion of Ni-YSZ porous cermets. *Journal of Power Sources*, Vol. 181, (2008), pp. (85-92).

*of Power Sources,* Vol. 195, (2010), pp. (6659-6670).

Vol. 11, No. 3, (1999), pp. (343-350).

membranes. *Solid State Ionics,* Vol. 134, (2000), pp. (59-66).

probability of failure analyses of functionally graded solid oxide fuel cells. *Journal* 

nanocrystalline nickel produced by electrodeposition. *NanoStructured Materials*,

material properties case, as is indeed observed.

temperature-dependent material properties.

**6. Acknowledgements** 

microstructures.

**7. References** 

**5. Conclusions**


**5** 

*USA* 

**Noise and Vibration** 

*Mechanical Engineering Department,* 

*California State Polytechnic University Pomona,* 

Chuan-Chiang Chen

**in Complex Hydraulic Tubing Systems** 

In hydraulic systems, pumps are the major source of noise and vibration. It generates flow ripples which interact with other hydraulic components, such as transmission lines and valves to create harmonic pressure waves, *i.e.*, fluid-borne noise (FBN). Fig. 1 shows a typical oscillating pressure measured at the outlet of a ten-vane pump running at 1500 rpm. Fig. 2 gives the frequency spectrum for the pressure signal which contains harmonic components of the fundamental frequency, 25 Hz, which correlates with the pump operating speed. The largest peak is at 250 Hz, which corresponds to the shaft speed times the number of the pumping elements (10 vanes in this case). The FBN propagates along as well as interacts with the tubing and other components to result in airborne noise (ABN) and structure-borne noise (SBN, *i.e.*, structural vibration). These noises can become excessive, and lead to damage the tubing system and other components. Therefore, to study the pressure wave propagation in the hydraulic tubing system, it is important to take the fluid-structure interaction into account to further the understanding of noise transmission

Fluid-structure interaction can be divided into three categories: junction coupling, Poisson coupling, and Bourdon coupling. Junction coupling occurs at discontinuities, such as bends and tees, where the pressure interacts with the structure to cause structural vibration. In unsteady flow, the pressure varies along the tube. Differences in pressure exert axial and transverse forces during power transmission at bends and other locations where the diametrical geometry changes. Moreover, the pressure is related to the longitudinal stresses in the pipe because of the radial contraction or expansion via Poisson coupling (Hatfield & Davidson, 1983). Furthermore, the cross-sectional shape of the line in a bend is not circular because of action by the bending forces. This effect, known as the Bourdon effect (Tentarelli,

Several approaches have been used (To & Kaladi, 1985; Everstine 1986; Nanayakkara & Perreia, 1986), such as the transfer matrix and finite element (FEM) methods, to model the fluid-structural coupling. In this study, the transfer matrix method (TMM) is used because of its simplicity. Even though FEM may offer better accuracy, it is more complicated and

1990), influences the structural modes at low frequencies.

**1. Introduction** 

mechanism.

time-consuming than TMM.

