Transverse Vibrations of Elastically Connected Double-String Complex System, Part I: Free Vibrations

Abstract

A theoretical vibration analysis of an elastically connected double-string system is presented. The double-string system is the simplest model of a complex continuous system, which is composed of two one-dimensional elastic solids attached by a Winkler elastic layer. The free and forced transverse vibrations of this system are considered. The present paper develops the free vibration theory, and a companion paper analyzes the forced vibrations. The motion of the system considered is described [1] by a non-homogeneous set of two partial di!erential equations, which are solved by using classical mathematical methods. The solutions of the free vibrations are derived from the Bernoulli}Fourier method. The boundary-value and initial-value problems are solved. The natural frequencies and natural mode shapes of vibration are determined. The free vibrations of an elastically connected double-string system are realized by synchronous and asynchronous de#ections.

Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads

“…However, many researchers reject this assumption due to the limitations of identical beam systems. Based on previous studies for double-string systems [12], Oniszczuk [13] provided analytical solutions for the free and forced vibrations of an elastically connected complex double-beam system with a simply supported boundary condition. Li and Hua [14] reported a spectral finite-element method for a general double-beam system with unequal flexural rigidities, unequal masses, and arbitrary boundary conditions to investigate the free vibration characteristics.…”

Exact eigensolution of a class of multi-level elastically connected members

“…In contrast, relatively little work has been undertaken on the class of structures considered below. Perhaps most interest has been directed towards double string systems, which have generated a number of papers [4][5][6][7], as have problems associated with the longitudinal motion of spring linked bars [8][9][10][11]. In contrast, the torsional vibration problem has seen less activity [12][13] and there is little evidence of any related work on the motion of beams vibrating in shear.…”

Vibrations of String due to a Uniform Partially Distributed Moving Load: Closed Solutions

“…The analogies between a string and the beams have been considered in papers [2][3][4]. Various aspects of the dynamics response of a string under a moving load have been considered, among others, in the papers [5][6][7][8][9][10][11][12][13][14]. The classical solution of the response of a finite string subjected to a load moving with a constant velocity has a form of an infinite series.…”