PSI - Issue 59

Olena Mikulich et al. / Procedia Structural Integrity 59 (2024) 466–470 Olena Mikulich et al. / Structural Integrity Procedia 00 (2024) 000 – 000

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2. Methods of experimental research For investigation of the influence of changes in the mechanical, physical, and microstructural characteristics of polyurethane foams on their vibration-absorbing properties, we study the change in the intensity of normalized normal stresses in foam media based on the method which used the indirect approach of the boundary element method within the framework of the couple stress elasticity (Mikulich et al., 2021). In the framework of the Cosserat elasticity with confined rotation (couple stress elasticity), the equations of motion of the classical theory of elasticity are supplemented with equations accounting for the influence of rotational-shear deformations. These equations in displacement form are written as (Mikulich et al., 2021): ( ) ⃗ ( ) ⃗⃗ (1) where is the displacement vector ,  is the material density, are the Lame’s constants, B is the microstructure’s characteristic of medium. The function ⃗⃗⃗ is the continuous function. The problem is solved using analytical and numerical approaches based on developed methods (Mikulich et al., 2021) within the framework of the indirect approach of the boundary element method, which allows for controlling the accuracy of calculations in the case of non-stationary loads. In the investigation of the vibration-absorbing properties of polyurethane foams, the normal stresses in the form medium were calculated for different values of the physical, mechanical, and microstructural characteristics of the materials. Numerical calculations were performed for the case of experimental values of foam characteristics (Anderson et al., 1994) and for those obtained using the numerical modelling method (Mikulich, 2023). Numerical analysis of the distribution of normal stresses in the medium is carried out for the case of foams, the characteristics of which are given in Table 1. Here, the value for the first and last lines corresponds to foams WF300 and WF110 accordingly. These values are derived from Anderson et al. (1994) based on experimental investigations. The values of mechanical, physical, and microstructural characteristics for other foam were obtained using simulation numerical modelling based on the approach proposed in Mikulich, 2023. 0.3518 (+0.051%) The results of numerical calculations of normalized normal stresses ̅̅̅̅ in a foam medium with different values of mechanical, physics, and microstructure characteristics are presented in Fig. 1. Numerical results were performed for layers distant from the boundary of load application at distances  =2 ℓ ,  =6 ℓ ,  =10 ℓ and  =14 ℓ , accordingly. Here, ℓ is the scale parameter of the medium within the couple stress elasticity, √ (Mikulich et al., 2021). The values of the scale parameter ℓ are given in Table 1. The percentage deviation of the theoretically calculated value ℓ from the experimentally determined value l b is written in brackets. Calculations were performed for the case of external load in the form of an elastic impulse steady applied along the boundary surface medium. The maximum intensity of external impulse load is . The calculations were performed for the case of impulse duration ¯ where ¯ , here ¯ is the time parameter, √ ( ) is the speed of the expansion wave, is is character size. Table 1. The characteristics of foams. Sample number G , MPa l b , mm N 2  , kg/m 3 E, MPa ℓ, mm I (WF300) 285 216 146 0.8 0.04 380 290 220 110 637 521 382 216 0.8172 (+2.1%) 0.6487 (+1.36%) 0.4943 (+0.87%) II 0.64 0.49 0.35 0.026 0.017 III IV (WF110) 75 0.01