Second order generalized linear systems arising in analysis of flexible beams

The analysis of a one-link flexible beam using a power series solution with respect to the spatial variable is discussed. The Euler-Bernoulli beam with payload mass and moment of inertia at the right end is clamped at the left end or driven by a torque applied by an actuator located at the base of the beam. The former case results in a second-order state-space equation, while the latter results in a second-order singular equation. For both models, an extended Leverrier-Faddeev algorithm is derived in order to invert the matrix polynomial R(s)=Es/sup 2/+A, where s epsilon C, E and A are constant matrices and E max be singular. Extension of the algorithm for beams with energy dissipation yielding a matrix polynomial R(s)=Es/sup 2/+A/sub 1/s+A/sub 2/ is given.<
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