Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Audiology in Brazil

The profession of audiology took root in Brazil nearly a half a century ago and has since blossomed into a flourishing, well-developed field. Currently, audiologists in Brazil work at private institutions, including private medical practices and dedicated speech and hearing clinics. They are also employed in a wide array of public institutions, including community clinics, elementary schools, colleges, and universities. In both the private sector and health clinics, audiologists perform diagnostic evaluations of auditory and vestibular disorders, select and fit hearing aids, and provide aural rehabilitation. At the public level, they assist with workers` health programs, dispense hearing aids, and aural rehabilitation. There is always room to grow, however, and the future of audiology in Brazil holds both challenges and opportunity. The following article will sketch the development of audiology training and practice in Brazil, provide a picture of how the field stands today, and summarize the unique challenges which the profession faces in this large and diverse nation.