Gradient-Based Optimization of Wave Propagation in Dual Directional Porous Functionally Graded Beams

This study presents a gradient-driven optimization framework to enhance the dynamic performance of bi-directional porous functionally graded (FG) beams. Material properties are tailored along both the thickness (z) and width (y) directions using power-law distributions, with porosity modeled via uniform and non-uniform approaches.Using Touratier’s higher-order shear deformation theory (HSDT), the formulation captures nonlinear shear stresses and dynamic behaviors more accurately than classical beam theories. A gradient-based optimization strategy is applied to optimize power-law indices, porosity factors, and geometric parameters to maximize natural frequencies and minimize structural weight.The analytic solution results from the literature used to computes bending stiffness and mass matrices. The optimization employs the Quasi-Newton BFGS algorithm , avoiding explicit Hessian computation while ensuring fast convergence.The optimized designs aim for a 25% increase in natural frequencies and 15-20% 1 weight reduction compared to conventional FG beams. The proposed framework highlights the effectiveness of dual-directional grading and controlled porosity in balancing stiffness-to-weight trade-offs. The optimized design can be applied in aerospace, civil infrastructure, and mechanical systems.