In present paper, the spectral approach is proposed for analysis of multiple cracked beam subjected to general moving load that allows us to obtain explicitly dynamic response of the beam in frequency domain. The obtained frequency response is traightforward to calculate time history response by using the FFT algorithm and provides a novel tool to investigate effect of position and depth of multiple cracks on the dynamic response. | Volume 36 Number 4 4 2014 Vietnam Journal of Mechanics, VAST, Vol. 36, No. 4 (2014), pp. 245 – 254 SPECTRAL ANALYSIS OF MULTIPLE CRACKED BEAM SUBJECTED TO MOVING LOAD N. T. Khiem1,∗ , P. T. Hang2 1 Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam 2 Electric Power University, Hanoi, Viet Nam ∗ E-mail: ntkhiem@ Received October 15, 2013 Abstract. In present paper, the spectral approach is proposed for analysis of multiple cracked beam subjected to general moving load that allows us to obtain explicitly dynamic response of the beam in frequency domain. The obtained frequency response is traightforward to calculate time history response by using the FFT algorithm and provides a novel tool to investigate effect of position and depth of multiple cracks on the dynamic response. The analysis is important to develop the spectral method for identification of multiple cracked beam by using its response to moving load. The theoretical development is illustrated and validated by numerical case study. Keywords: Multiple cracked beam, moving load problem, frequency domain solution, modal method, spectral analysis. 1. INTRODUCTION The moving load problem has attracted attention of researchers and engineers in the field of structural engineering and it is so far an actual topic in dynamics of structures. The mathematical fundamentals of the problem were formulated in [1–3]. The mathematical representation of the problem is strictly associated with the model adopted for moving load and structure subjected to the load. The models adopted for moving load are constant or harmonic force [4]; moving mass [5, 6] and more complicated vehicle system [7, 8]. The structure taken into this issue is firstly the simple and intact beam like structures and, recently, more complicated structures [9–14]. Most of the aforementioned studies have investigated the moving load problem in time domain by using either the mode superposition (modal) method or the finite .
