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R. Beigelbeck, M. Stifter, M. Schneider, F. Keplinger, U. Schmid, T. Voglhuber-Brunnmaier, B. Jakoby:
"Rigorous Analytical Analysis of Resonant Euler-Bernoulli Beams with Constant Thickness and Polynomial Width";
Talk: IEEE Ultrasonics Symposium, Illinois, USA; 09-03-2014 - 09-06-2014; in: "2014 IEEE Ultrasonics Symposium Proceedings", IEEE, (2014), 2095 - 2099.

We report a novel exact closed-form solution of the
Euler-Bernoulli beam equation expressible in terms of Meijer G-
functions. This solution allows for analytically studying the
natural frequencies and mode shapes of a very general class
of beams characterized by both a polynomially varying flexural
beam bending stiffness EI.x/ and beam cross section A.x/,
but a constant EI.x/=A.x/-ratio. Its application is exemplarily
demonstrated on cantilevers characterized by a uniform thickness
and a spatially narrowing width of either linear form (i. e.,
trapezoid cantilevers) or describable by a power function of
higher order. The analytically deduced results are validated by
computer numerical simulations and compared to test measure-
ments carried out on micromachined thin-film cantilevers.

We report a novel exact closed-form solution of the
Euler-Bernoulli beam equation expressible in terms of Meijer G-
functions. This solution allows for analytically studying the
natural frequencies and mode shapes of a very general class
of beams characterized by both a polynomially varying flexural
beam bending stiffness EI.x/ and beam cross section A.x/,
but a constant EI.x/=A.x/-ratio. Its application is exemplarily
demonstrated on cantilevers characterized by a uniform thickness
and a spatially narrowing width of either linear form (i. e.,
trapezoid cantilevers) or describable by a power function of
higher order. The analytically deduced results are validated by
computer numerical simulations and compared to test measure-
ments carried out on micromachined thin-film cantilevers.