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Frequency response function of an Euler-Bernoulli beam with arbitrary linear damping, nonuniformities, discontinuities and constraints
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DOI：10.1016/j.jsv.2026.120014.png)
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Abstract
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This paper develops a method to compute the frequency response of a nonuniform Euler-Bernoulli beam without modal decomposition or finite elements discretization. This method is applicable to any types of linear damping, nonuniformities, discontinuities or constraints. The method utilizes the concept of spatial state transition matrix, which is independent of boundary conditions of the beam. The steady state response is obtained by the solution of spatial state equations, which has two components: contributions from initial states, and convolution integral between spatial state transition matrix and amplitudes of sinusoidal external forcing functions. This approach yields the frequency response function of an infinite-dimensional Euler-Bernoulli beam from any applied input to any measured output. The method is illustrated via two numerical examples. The first example is a black hole attached to a fixed-free uniform beam with a viscous damper at the tip, which contains nonuniform geometry with a discontinuity, collocated input force and output transverse displacement. An algorithm is presented for the generation of a virtual black hole. The second example is the stepped piezoelectric cantilever beam with multiple discontinuities and non-collocated piezoelectric voltage input and transverse displacement output of the beam.
Keywords:
Frequency response without modal decomposition
EB beam with arbitrary nonuniformity
EB with arbitrary type of damping
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4.9
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1.7W
Citations:
4.8W
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