An analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented. Free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non-uniform displacement or stress on the boundaries are considered. Three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion. The terms in the expressions for components of displacement and stress are products of Bessel and sinusoidal functions and are orthogonal to each other. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is therefore possible to satisfy arbitrary boundary conditions. It is shown that two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions. The error is less than 1% for free cylinders. Numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress. Excellent agreement with finite element results is obtained at all frequencies up to 1 MHz. Convergence of the series is also discussed.
A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.
Electrode fabrication and membrane electrode assembly (MEA) processes are critical steps in polymer electrolyte membrane fuel cell (PEMFC) technology. The properties of decal substrate material are important in decal coating technique for efficient transfer of catalyst layer. In the present study, MEAs are fabricated in decal method using 6 different decal substrates among which polypropylene (PP) is found ideal. Morphological, thermal, spectroscopic and sessile drop measurements are conducted for 6 decal substrates to evaluate the thermal and physicochemical properties. Studies indicate PP is thermally stable at hot-press conditions, having optimal hydrophobicity that hinders the coagulation of catalyst ink slurry cast. The pristine PP film has been identified to showcase 100% transfer yield onto the Nafion membrane without contamination and delamination of catalyst layer from membrane. The PP based MEAs are evaluated underconstant current mode in a hydrogen-oxygen fuel cell test fixture. The performance is found to be of 0.6 V at a constant current density of 1.2 A.cm−2. Besides, the cost of PP-film is only 7.5% of Kapton-film, and hence the current research work enables the high throughput electrode fabrication process for PEMFC commercialization.
A method is presented to determine power dissipation in one-dimensional piezoelectric slabs with internal losses and the resulting temperature distribution. The length of the slab is much greater than the lateral dimensions. Losses are represented using complex piezoelectric coefficients. It is shown that the spatially non-uniform power dissipation density in the slab can be determined by considering either hysteresis loops or the Poynting vector. The total power dissipated in the slab is obtained by integrating the power dissipation density over the slab and is shown to be equal to the power input to the slab for special cases of mechanically and electrically excited slabs. The one-dimensional heat equation that includes the effect of conduction and convection, and the boundary conditions, are then used to determine the temperature distribution. When the analytical expression for the power dissipation density is simple, direct integration is used. It is shown that a modified Fourier series approach yields the same results. For other cases, the temperature distribution is determined using only the latter approach. Numerical results are presented to illustrate the effects of internal losses, heat conduction and convection coefficients, and boundary conditions on the temperature distribution.
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