Vibratory characteristics of flexural non-uniform Euler-Bernoulli beams carrying an arbitrary number of spring-mass systems

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Original languageEnglish
Pages (from-to)725-743
Journal / PublicationInternational Journal of Mechanical Sciences
Issue number4
Publication statusPublished - Apr 2002


A new exact method for the analysis of free flexural vibrations of non-uniform multi-step Euler-Bernoulli beams carrying an arbitrary number of single-degree-of-freedom and two-degree-of-freedom spring-mass systems is presented in this paper. The closed-form solutions for free vibrations of non-uniform Euler-Bernoulli beams are derived for five important cases. Then, using the massless equivalent springs to replace the spring-mass systems and the fundamental solutions developed in this paper, the frequency equation for free flexural vibrations of a multi-step non-uniform beam with any kind of support configurations and carrying an arbitrary number of spring-mass systems can be conveniently established from a second-order determinant. The proposed method is computationally efficient due to the significant decrease in the determinant order as compared with previously developed procedures. © 2002 Elsevier Science Ltd. All rights reserved.

Research Area(s)

  • Beam, Mode shape, Natural frequency, Spring-mass system, Vibration