PSI - Issue 58

Victor Rizov et al. / Procedia Structural Integrity 58 (2024) 150–156 V. Rizov / Structural Integrity Procedia 00 (2019) 000–000

151

2

materials which offer very good chances for tailoring of the distribution of material properties in a structural member to meet complex operational requirements (Mahamood and Akinlabi (2017), Yan et al. (2020), Hao et al. (2002)). That’s why it is not surpassing that functionally graded materials are widely used in various load-bearing structures and engineering facilities including frame structures. The damping phenomenon is important in the context of safety and reliability of engineering structures (Dowling (2007)). The main aim of the present theoretical study is to contribute for clarifying the question of the influence of the non-linear viscoelastic behaviour and varying temperature on the damping energy in load-carrying functionally graded frame structures under a cyclic side load. It should be mentioned here that previous analyses of the damping phenomenon usually deal with beam structures (Dowling (2007)). Therefore, the present paper is focused on damping in non-linear viscoelastic frames with emphasis on the effect of material inhomogeneity and varying temperature. A solution of the damping energy is found-out by integrating of the damping energy density in the volume of the frame structure members. A parametric investigation of the damping is performed. Results illustrating the influence of frame geometry, loading and temperature on the damping phenomenon are presented. 2. Analysis We investigate the damping phenomenon in a load-bearing frame structure depicted in Fig. 1. The frame is constructed by two vertical members, 1 2 BB and 3 4 B B , with heights, 1 s and 2 s , and a horizontal member, 2 3 B B , with length, l . The supports of the frame are located on different levels in points, 1 B and 4 B , as shown in Fig. 1. The frame is subjected to a cyclic side load, a F , about zero mean with simultaneous variation of the temperature.

Fig. 1. Schema of frame structure.

The frame has non-linear viscoelastic mechanical behaviour. We apply the non-linear stress-strain-time relationship (1) to treat the frame behaviour (Dowling (2007)).

1

  

  

C n  

a 

a  

a

,

(1)

E H

C

a  are the half ranges of the strain and stress, respectively, E is the modulus of elasticity,

C H and

where a  and

C n are material parameters defined by Dowling (2007)