Hybrid design and optimization of a tuned dynamic vibration absorber for washing machine drum systems using Den Hartog equal-peak theory and genetic algorithms

Excessive vibration in horizontal-axis washing machines, primarily caused by unbalanced rotating masses during high-speed spinning, leads to structural noise, reduced component life, and transmission of forces to the supporting floor. This study presents a comprehensive approach for vibration reduction through the design and optimization of a Tuned Dynamic Vibration Absorber (TDVA). A detailed mathematical model of the washing machine drum system was developed by incorporating the effects of inclined suspension springs and dampers, equivalent vertical stiffness, and the unbalanced mass eccentricity excitation. Den Hartog’s equal-peak tuning principle was employed to obtain absorber stiffness and frequency ratios. To enhance tuning accuracy under real damping conditions, a Genetic Algorithm (GA) was implemented to optimize the absorber mass by minimizing the frequency response amplitude of the primary system. The GA achieved rapid convergence, identifying an optimal absorber mass of approximately 0.654 kg, which was shown to significantly reduce the resonant peak. A compact cantilever-based absorber prototype was designed with a tunable tip mass to achieve the optimized stiffness-mass combination. Experimental investigations were performed on an actual washing machine to validate the model predictions. Results demonstrate that the optimized TDVA achieves up to 46–50% reduction in vibration amplitude near the natural frequency, outperforming classical designs and non-optimized absorbers. The study confirms that the hybrid Den Hartog analytical tuning with evolutionary Genetic Algorithm based optimization produces a highly effective and practical vibration mitigation solution for household washing machines. This integrated modeling, optimization and experimental framework provides a robust guideline for future appliance vibration control design.