PSI - Issue 58

Victor Rizov et al. / Procedia Structural Integrity 58 (2024) 137–143 V. Rizov / Structural Integrity Procedia 00 (2019) 000–000

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coordinates (Chikh (2019), Han et al. (2001), Kou et al. (2012), Rizov and Altenbach (2020)). The functionally graded materials are preferred in many applications in different areas of modern engineering (Kieback et al. (2003), Mahamood and Akinlabi (2017), Yan et al. (2020), Hao et al. (2002)). This is because of their superior properties in comparison to the conventional materials. The wide impingement of functionally graded materials in the engineering practice in the recent decades is closely related to analyzing of various aspects of the mechanical behaviour and performance of structural components under different loadings. One of the important problems is the energy dissipation in structural components made of functionally graded materials with non-linear viscoelastic mechanical behaviour. Energy dissipation has bearing on issues like integrity, reliability and life of engineering structures. The present theoretical paper deals with analyzing of the energy dissipation in a beam structural component made of a functionally graded material. There are two novelties in the present paper: (i) the beam exhibits non-linear viscoelastic behaviour and (ii) the beam is under time-dependent skew bending. It should be underlined here that previous energy dissipation studies deal usually with linear viscoelastic beam structures subjected to bending around the horizontal axis of the cross-section (Narisawa (1987), Rizov (2021)). In the present paper, the non-linear viscoelastic behaviour of the beam is treated by a model representing a combination of linear as well as non-linear springs and dashpots. A solution of the energy dissipation problem is derived. The influence of the distribution of material properties, the beam size and the parameters of the loading on the dissipated energy is clarified. 2. Analytical model Fig. 1 shows the static schema of a beam structural component of rectangular cross-section.

Fig. 1. Static schema of beam loaded in skew bending. The beam is loaded in skew bending so that the beam free end angle of rotation,  , presented as a vector in Fig. 1 is inclined under angle,  , with respect to the horizontal centric axis, y , of the beam. The variation of  with time,