The spectral approach is employed for spectral analysis of a beam subjected to an arbitrary force traveling along the beam with constant speed. First, an expression for exact frequency response of a beam subjected to moving arbitrary force and general boundary conditions has been constructed. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 4 (2016), pp. 223 – 238 DOI: FREQUENCY RESPONSE OF A BEAM-LIKE STRUCTURE TO MOVING HARMONIC FORCES Nguyen Tien Khiem1,∗ , Phi Thi Hang2 1 Institute of Mechanics, VAST, Hanoi, Vietnam 2 Electric Power University, Hanoi, Vietnam ∗ E-mail: ntkhiem@ Received May 23, 2015 Abstract. The spectral approach is employed for spectral analysis of a beam subjected to an arbitrary force traveling along the beam with constant speed. First, an expression for exact frequency response of a beam subjected to moving arbitrary force and general boundary conditions has been constructed. The obtained frequency domain response allows straightforwardly exhibiting response vibration components governed by different frequencies such as the natural, loading and driving ones and their interaction. This provides also alternative insight to the cancellation of response at natural frequency. The theoretical development is illustrated and validated by numerical examination on a simply supported beam under moving harmonic forces. Keywords: Moving force, frequency response, spectral analysis, resonance, cancellation. 1. INTRODUCTION The moving load problem for a long time 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 fundamentals of the problem were formulated in [1–5] and intensively studied in the widespread literature, for example, the references [6–11]. In the most of the studies, the problem has been investigated by using the analytical method based mainly on the superposition principle. Latter, the FEM [12, 13] and, recently, the spectral approach [14–16] has been developed for dynamic analysis of beams subjected to various types of moving load. However, the moving load problem was mostly solved in the time domain even when the spectral element method has been employed. There are very few works .
