Orientador: Michael John Brennan / Banca: Gilberto Pechoto de Melo / Banca: Paulo Jose Paupitz Gonçalves / Resumo: Nesta dissertação investiga-se o comportamento de um sistema de isolamento de vibrações de um grau de liberdade com amortecimento não linear. As transmissibilidades das forças e de movimento deste sistema são comparadas com as de um sistema de isolamento de vibrações linear. O sistema não linear é composto por uma mola e um amortecedor viscoso, ambos lineares, que estão acoplados a uma massa de modo tal que o amortecedor é perpendicular à mola. O sistema é excitado harmonicamente por um deslocamento da base ou por uma força na direção da mola. Quando o sistema é excitado por uma forca harmônica, as forças transmitidas através da mola e do amortecedor são analisadas separadamente, decompondo-as em termos dos seus harmônicos; permitindo assim determinar a contribuição individual de cada elemento no comportamento não linear do sistema como um todo. A transmissibilidade do sistema de isolamento não linear é calculada por meio de expressões analíticas validas para excitações com pequenas amplitudes, já para excitações com amplitudes grandes, calcula-se por meio de simulações numéricas. / Abstract: In this work the behaviour of a single degree of freedom (SDOF) passive vibration isolation system with a geometrically nonlinear damper is investigated, and its displacement and force transmissibilities are compared with that of a linear system. The nonlinear system is composed of a linear spring and a linear viscous damper which are connected to a mass so that the damper is perpendicular to the spring. The system is excited with either a harmonic force or an imposed displacement of the base in the direction of the spring. When excited with a harmonic force, the forces transmitted through the spring and the damper are analysed separately by decomposing the forces in terms of their harmonics. This enables the effects of these elements to be studied and to determine how they contribute individually to the nonlinear behaviour of the system as a whole. The transmissibilities of the nonlinear isolation system are calculated using analytical expressions for small amplitudes of excitation and by using numerical simulations for high amplitudes of excitation. / Mestre

This paper illustrates Winograd's approach to computing the Discrete Fourier Transform (DFT). This new approach changes the DFT into a cyclic convolution of 2 sequences, and illustrates shortcuts for computing this cyclic convolution. This method is known to reduce the number of multiplies required to about 20% less than the number of multiplies used by the techniques of the Fast Fourier Transform. Three approaches are discussed, one for prime numbers, one for products of primes, and lastly one for powers of odd primes. For powers of 2 Winograd's algorithm is, in general, inefficient and best if it is not used. A computer simulation is illustrated for the 35 point transform and its execution time is compared with that of the Fast Fourier Transform algorithm for 32 points.

Call number: LD2668 .T4 1938 G71

Master of Science / Department of Mathematics / Diego M. Maldonado / In this work we present the main concepts of Fourier Analysis (such as Fourier series, Fourier transforms, Parseval and Plancherel identities, correlation, and convolution) and illustrate them by means of examples and applications. Most of the concepts presented here can be found in the book "A First Course in Fourier Analysis" by David W.Kammler. Similarly, the examples correspond to over 15 problems posed in the same book which have been completely worked out in this report. As applications, we include Fourier's original approach to the heat flow using Fourier series and an application to filtering one-dimensional signals.

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Approved for public release; distribution is unlimited / A multiple frequency quaternary phase shift keyed signal is generated using a complex Fast Fourier Transform on an industry standard personal computer and is output using direct memory access through a digital to analog converter. The output is permitted at rates of up to the maximum direct memory access rate of the computer. An assembly language program loop, direct hardware output, and high level language output are compared as alternate solutions to the problem of outputting a data stream contained in the computer primary memory. / http://archive.org/details/highspeedoutputi00chil / Lieutenant, United States Navy

Summary The paper investigates the Gibbs’ phenomenon at a jump discontinuity for Fourier–Bessel series expansions. The unexpected thing is that the Gibbs’ constant for Fourier–Bessel series appears to be the same as that for Fourier series expansions. In order to compute the coefficients for Fourier–Bessel functionsefficiently, several integral formulasare derived and the Struve functions and their asymptotic expansions discussed, all of which significantly ease the computations. Three numerical examples are investigated. Findings suggest further investigations suitable for undergraduate research projects or small student group investigations.

Summary A result is discussed which permits the summing of series whose terms have more complicated sign patterns than simply alternating plus and minus. The Alternating Series Test, commonly taught in beginning calculus courses, is a corollary. This result, which is not difficult to prove, widens the series summable by beginning students and paves the way for understanding more advanced questions such as convergence of Fourier series. An elementary exposition is given of Dirichlet’s Test for the convergence of a series and an elementary example suitable for a beginning calculus class and a more advanced example involving a Fourier series which is appropriate for an advanced calculus class are provided. Finally, two examples are discussed for which Dirichlet’s Test does not apply and a general procedure is given for deciding the convergence or divergence of these and similar examples.