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Determination of mode shapes of a multiple cracked beam element and its application for free vibration analysis of a multi-span continuous beam

This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyze changes of natural mode shapes of multiple cracked beams have been carried out. | Volume 35 Number 4 4 Vietnam Journal of Mechanics, VAST, Vol. 35, No. 4 (2013), pp. 313 – 323 DETERMINATION OF MODE SHAPES OF A MULTIPLE CRACKED BEAM ELEMENT AND ITS APPLICATION FOR FREE VIBRATION ANALYSIS OF A MULTI-SPAN CONTINUOUS BEAM Tran Van Lien∗ , Trinh Anh Hao University of Civil Engineering, Hanoi, Vietnam ∗ E-mail: lientv@hotmail.com Abstract. This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyze changes of natural mode shapes of multiple cracked beams have been carried out. Numerical analysis of natural mode shapes of cracked simple support beams using the obtained expression shows a good agreement in comparison with the well-known analytical methods. The methodology approach and results presented in this article are new and basic for building an efficient method to identify cracks in beam structures using wavelet analysis of mode shapes. Keywords: Shape function, cracked beam, transfer matrix, natural frequency, mode shape. 1. INTRODUCTION Current researches on the identification of cracks or damages in a structure using non-destructive test method have been developed primarily based on the dynamic characteristics of the structure such as natural frequency, mode shapes, response spectrum function [1–11]. These dynamic characteristics are normally determined by analytical method, semi-analytical method, finite element method (FEM), and dynamic stiffness method (DSM). The analytical and semi-analytical methods are limited in a simple beam [1, 5, 6] and not applicable for a complex structure such as multi-span continuous beam or frame structure. Therefore, identification of dynamic characteristics of a structure is mainly based on the FEM and the DSM: - In the FEM, a multiple-cracked beam element has been modeled as an assembly .