This paper provides the formulation of the problem of forced vibrations of structures, which has the following peculiarities: equations of motion are formulated in absolute coordinates allowing to take into account the asynchronous excitations of the supports, smoothing of the time functions for forced displacements with the help of Hermite polynomials, and also the possibility of considering damping that does not obey the Rayleigh hypothesis.
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Fialko et al. (2018) studied this question.
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