PSI - Issue 71

Faisal Hussain et al. / Procedia Structural Integrity 71 (2025) 248–255

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The existence of nonlinear exertion is indicated by substantial change at higher frequencies as shown in Fig.9, 10 and 11. The existence of significant oscillations at high frequencies indicates that the behavior is not solely dependent on the frequency. Nevertheless, other elements, such as the nonlinear nature of the structural elements or the presence of additional forces, had a significant impact. The data indicates that the frequencies are particularly responsive to oscillations occurring at the fastened joint interface. Conversely, an intimate peak could indicate a system with less damping, while a wider, more level peak could suggest a structure with increased damping. Harmonic spikes might vary based on the extent of the shift in non-dimensional inherent frequency levels. This analysis assists in developing and optimization of fastened connection structures by preventing unintended failures or vibrations. The variation in the equivalent linearized stiffness, which is determined, using curve fitting, is depicted in Fig. 12 and Fig. 13 for mode 3 and mode 5, respectively. The slope equations in Fig.12 and Fig.13 provide the values of coefficient cubic stiffness 9.829 x 10 4 and 10.565 x 10 4 which was utilized for calculating the cubic stiffness non linearity. The figures mentioned above were used to visually represent the differences between the estimated linear stiffness and the real non-linear stiffness of the joint. The results of the calculated cubic stiffness coefficient K 4 for modes 3 and 5 are presented in Table 3.

Acceleration (g)

Acceleration (g)

Frequency (Hz)

Frequency (Hz)

Fig. 10. Frequency Variation in mode 3

Fig. 11. Frequency Variation in mode 5

Equivalent Stiffness

Equivalent Stiffness

Response amplitude in radian

Response amplitude in radian

Fig. 12. Variation of Stiffness (Mode 3)

Fig. 13. Variation of Stiffness (Mode 5)

Table 3. Cubic Stiffness Coefficient value of K 4

Mode

Estimated Stiffness Coefficient ( K c )

K 4 = (4/3) K c

Exact Value of K 4 (N-m/rad 3 )

Percentage Error in Estimation of K 4

Second Third Fourth

10.582 x10 4 9.829 x10 4 10.501 x10 4 10.565 x10 4

1.4110 x10 5 1.3105 x10 5 1.4002 x10 5 1.4086 x10 5

5.740 % -1.487 % 5.013 %

1.33 x 10 5

Fifth 5.580 % The results suggest that, despite inaccuracies in determining the frequency, the estimation of the stiffness cubic coefficient stays extremely accurate. This directs that the mathematical framework model is capable of withstanding and recovering from inaccuracies in the resolution of FFT. The ability of the structures to stiffen due to minor modifications is examined by comparing the stiffness levels with and without disturbances. This data is crucial for understanding the extent of adaptability of the beam bolted framework to variations in its characteristics. The reaction varies with decreasing frequency, which is caused by joint non-linearity. Non-linearities have the capacity