Abstract
An exact solution for free vibrations of a series of uniform Euler-Bernoulli beams connected by Kelvin-Voigt is developed. The beams have the same length and end conditions but can have different material or geometric properties. An example of five concentric beams connected by viscoelastic layers is considered.
Highlights
This paper presents an exact solution to the problem of the free vibrations of an arbitrary number of beams connected by viscoelastic layers of the Kelvin-Voigt type
The free vibrations of a set of n beams connected by viscoelastic layers of the Kelvin-Voigt type are considered
When substituted into the partial differential equations, it leads to a set of ordinary differential equations which is solved by assuming the solution is a vector times the undamped spatial mode shape of the first beam
Summary
This paper presents an exact solution to the problem of the free vibrations of an arbitrary number of beams connected by viscoelastic layers of the Kelvin-Voigt type. Selig and Hoppmann [4], Osborne [5], and Oniszczuk [6] studied the free or forced response of elastically connected Euler-Bernoulli beams They each used a normalmode analysis resulting in coupled sets of fourth-order differential equations whose eigenvalues were related to the natural frequencies. Oniszczuk [15] used a normal-mode solution in considering the vibration of two strings connected by a viscoelastic layer of the Kelvin-Voigt type. Hongxing [17] used a dynamic stiffness matrix to analyze free vibrations of three beams connected by viscoelastic layers Their analysis does not require the beams to have the same end conditions but does require the use of computational tools to determine the natural frequencies. The results are applied to a series of five concentric beams
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