Optimization of vibration and sound insulation in GPLRC honeycomb structures based on circle chaos mapping and Levy flight-enhanced YDSE with constraints

Utilizing the first-order shear deformation theory (FSDT) and Hamilton's principle, dynamic equations for tunable Poisson's ratio metamaterial honeycomb sandwich panels have been derived. These panels include petal-shaped, star-shaped, and butterfly-shaped designs. The acoustic response of these panels when subjected to plane harmonic sound waves has been formulated, treating them as fluid-structure interaction systems. To enhance the structural vibration and sound propagation attributes, traditional metallic aluminum has been replaced with graphene platelet-reinforced composites (GPLRC). Through computational analysis and finite element simulation data, the natural frequencies and sound transmission loss (STL) characteristics of the panels have been determined. An improved heuristic algorithm called the circle chaos mapping and levy flight enhanced Young's double-slit experiment optimizer (CLYDSE) has been introduced to optimize their vibrational and acoustic properties. This algorithm builds upon Young's double-slit experiment optimizer (YDSE) by incorporating circle chaos mapping for initializing a monochromatic light source and utilizing the levy flight principle for more accurate search results. These enhancements allow the CLYDSE algorithm to avoid local optima and improve convergence velocity. A penalty function method was employed to establish mass and equivalent elastic modulus as optimization constraints, aiming to achieve superior specific stiffness. Finally, structural optimization using the proposed CLYDSE method was conducted to enhance the vibrational and acoustic performance of the three types of honeycomb sandwich panels. The results validate the effectiveness of the theoretical model in predicting vibration and acoustic response, as well as the improved performance of the CLYDSE algorithm in terms of convergence velocity and optimization accuracy. This demonstrates the algorithm's efficacy in refining the acoustic and vibrational qualities of these advanced honeycomb structures.