FORCED VIBRATION ANALYSIS OF PRESTRESSED EULER-BERNOULLI BEAM WITH DISCONTINUITIES BY MEANS OF DISTRIBUTIONS WITHOUT USING MODAL ANALYSIS

Abstract eng:
This paper is a continuation of the previous paper in which the author published the generalized mathematical model for forced vibration of Euler-Bernoulli beam covering discontinuities caused by concentrated loading, concentrated support, concentrated inertia forces or internal hinges. In this new paper, the generalized mathematical model is augmented to cover geometric nonlinearity of stress stiffening or weakening of the beam with the same type of discontinuities. This new analytic approach can offer three advantages. Firstly, steady-state responses of the beam can be found directly without doing modal analysis. Secondly, these responses of the beam are expressed in closed form. Thirdly, remaining continuity conditions at points of the discontinuities are fulfilled automatically. To give an example of using this new approach based on distributions, new closed-form expressions for forced steady-state response of pre-stressed simply supported beam with concentrated harmonic loading are presented.

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