PSI - Issue 59

Valerii Kobzar et al. / Procedia Structural Integrity 59 (2024) 344–351 Valerii Kobzar and Oleh Derkach / Structural Integrity Procedia 00 (2023) 000 – 000

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1 – beam specimen; 2 – massive plate; 3 – string; 4 – ferromagnetic patch; A/D – analog-to-digital converter; DA – differential amplifier; EM – electromagnet; PWM – pulse-width modulator; PA – power amplifier; PC – personal computer; SG – strain gauge; STM32 – 32-bit microcontroller; UART – universal asynchronous receiver/transmitter; >0< – set to zero operation.

Fig. 4. Block diagram of the experimental setup for investigations of damping properties of cantilever beams.

To obtain a reliable set of values for the damping characteristic, the envelope of the vibrogram of free damped vibrations is represented as a function ε = f ( n ), where n represents the number of cycles. As shown by Boginich et al. (2023) the most effective approach for determining the smooth dependence of the logarithmic decrement of vibrations on the amplitude of cyclic strain is to approximate the envelope of the vibrogram on a semilogarithmic scale. Consequently, the amplitude-dependent logarithmic decrement is determined using the following formula:

d

 

  ln 

f

 



.

dn

The experimental research and processing of the obtained vibrograms of damped vibrations were conducted in an automatic mode. This enabled us to obtain the dependence of the logarithmic decrement of vibrations on the stress amplitude through two approaches. Firstly, by averaging the amplitude over a specific section of the vibrogram with a certain number of cycles. Secondly, by utilizing smoothing splines, which allow the determination of amplitude dependencies of the decrement using a limited number of points, particularly for systems with a large decrement. 4. Results of experimental investigations According to the problem statement, a series of experiments was conducted to investigate the influence of local damage, caused by quasi-static punching, on the natural frequency and damping capability of cantilever beams. The study involved intact and locally damaged specimens made of woven T300 twill-type structure CFRP. The dimensions of the specimens were b × h × L = 20×3×200 mm, consisting of 8 layers. The woven CFRP samples were cut from the plate along the weft (0 deg fiber orientation) and at 45 deg. Local damage was introduced at a distance of 0.2∙ L from the clamped end of the cantilever beam. The local damage in the CFRP was predetermined using the AE technique. The quasi-static punching of the CFRP specimens was performed using a spherical punch (Fig. 1), with a maximum force of 800 N. The lower die had a diameter of 17 mm, and the spherical punch had a diameter of 8 mm. After determining the dissipative properties of the intact samples, the dependence of the dissipative properties of the samples with predetermined local damage was established. For the damaged samples, the punching process with the spherical punch was interrupted after reaching the predetermined by the Eq. (1) number of pulses N . The damage parameters D = 0.06 and 0.013 were established ( N Σ = 2.5∙10 5 ). The effect of local damage on the dissipated energy in the specimens and its dependence on the amplitudes of relative cyclic strain ε = 10 – 4 ...10 – 3 were determined. The results (Fig. 5) showed that for damaged samples made of