Vibration of beams on partial elastic foundations

Abstract

The natural response of a beam or pile having only a portion of its span supported by an elastic foundation is investigated for the two cases when both ends are either simply supported or free. The derivation of the shape functions and the computed natural frequencies are compared with the extreme cases where the element is either completely supported by, or fully detached from, the elastic foundation.

Modal Analysis of Tapered Beam-Column Embedded in Winkler Elastic Foundation

“…Winkler foundation model is extensively used by engineers and researchers because of its simplicity. The analysis of beamcolumns on elastic foundations have been carried out in the literature, namely by Zhaohua and Cook [1], Yankelevsky and Eisenberger [2], Doyle and Pavlovic [3], Yokoyama [4], Valsangkar and Pradhanang [5], De Rosa and Maurizi [6], Halabe and Jain [7], West and Mafi [8], Matsunaga [9] and Kameswara et al [10]. In this paper, discrete singular convolution method technique is presented for computation of the free vibration analysis of a pile embedded in elastic foundation.…”

Beam Dynamic Stresses Increments After Partial Deconstruction of Foundation

“…In particular, in papers [2][3][4] considers the transition dynamic process caused by the sudden formation of transverse cracks in a loaded beam. Beam modeled conjugation of two segments connected by a torsion spring whose stiffness is determined by the depth of cracks.…”

“…In [12][13][14] solved the problem of the vibrations of the beam when it is sudden partial destruction. In [4,6,11,16] studied transients dynamical process caused by sudden transformation of the internal structure of rod systems: coupling and bearing conditions their elements. In [17] is modeled by a sudden breaking of the reinforcing bar and the longitudinal vibrations caused by this defect.…”

“…Absence and lack of knowledge about deformation and stress state of structural elements during dynamic processes initiated by a sudden damage, constrain the development of the theory and design techniques that take into account the possibility and potential consequences of beyond design impacts and ensure a high level of safety of their maintenance. As an example of work performed in the discussed direction, we note a number of publications [1][2][3][4] containing the results of the modeling of transient dynamic processes that occur in stressed beams at the sudden breakage of the support links, formation of transverse and longitudinal cracks, delamination and exfoliation, change conditions interfaces parts construction and others. All these works are made in relation to the free beams, that are not supported by solid foundations.…”

An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

“…The free and forced vibrations of a three span continuous beam resting on a Winkler-Pasternak foundation are studied by means of the general dynamic slope-deflection equations. In addition, the natural response of an Euler-Bernoulli beam supported by an elastic foundation is investigated by Doyle and Pavlovic (Doyle and Pavlovic, 1982). Ultimately, this paper considers the vibration problem of EulerBernoulli beam partially supported by a Winkler foundation.…”