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Smart structures with integrated piezoelectric elements play a pivotal role in mitigating vibrations across diverse applications, by safeguarding against structural damage and performance degradation. This study delves into the active control of vibrations in beams, particularly in fluid-immersed environments where hydrodynamic forces induce complex beam oscillations. The dynamic behavior of geometrically nonlinear, simply supported beams integrated with piezoelectric elements was examined. The position of the piezoelectric patch was optimized through the GA algorithm to minimize the settling time. The optimal location for the piezoelectric patch was determined in the middle of the beam. The investigation encompasses harmonic excitation forces spanning frequencies from 10Formula: see textHz to 200Formula: see textHz. Our study evaluates the system’s response under two critical conditions: one with the presence of external hydrodynamic forces and the other without. To achieve effective vibration control, we employ both Proportional-Derivative (PD) and Sliding Mode Controllers (SMC), optimizing their parameters for minimum settling time as an objective function. The results underscore the remarkable superiority of the SMC, reducing settling times by an impressive 50% when compared to the PD controller. Additionally, the SMC demonstrates the ability to significantly reduce control efforts, as evidenced by actuator voltage. In the context of forced vibrations, the SMC maintains its superior performance, especially at lower frequencies. However, at higher frequencies, the emergence of chattering affects the SMC’s performance, although it remains more effective than the PD controller in low-frequency scenarios. This study sheds light on the effectiveness of piezoelectric-based control strategies for smart beams, offering valuable insights into their performance under various vibration conditions. These findings hold significant promise for practical applications where vibration control is critical.
Dehkordi et al. (Thu,) studied this question.