The research presents a full semi-analytical framework that engineers need to assess lattice-core sandwich panels that have elastic edge constraints for the development of lightweight structures that require exceptional dynamic capabilities in high-performance sports applications. The sandwich plate core uses an anisogrid lattice design, which provides a better weight-to-stiffness ratio, together with superior vibration management capabilities than standard core designs. The face sheets are assumed to be functionally graded materials whose effective mechanical properties vary continuously across the thickness according to a power-law distribution pattern, which enables designers to create specific stiffness and mass patterns that achieve optimal dynamic performance. The first-order shear deformation theory establishes the structural kinematics because it includes transverse shear deformation effects, which apply to moderately thick sandwich plates used in sports equipment like rackets and boards and protective panels. The system implements elastic edge restraints through distributed connective springs, which enable complete energy potential representation of multiple boundary flexibility conditions. The displacement fields are approximated through a hybrid expansion that uses trigonometric series and Jacobi orthogonal polynomials to achieve fast convergence with high accuracy while meeting the requirements of geometric compatibility. The Lagrangian energy function creates its value through the total contributions of strain energy, kinetic energy, and spring potential energy, which establishes the foundation for deriving the equations of motion from the Lagrangian’s stationary point. The proposed formulation delivers an efficient analytical solution method to study the vibration behavior of advanced lattice-core sandwich plates, which helps engineers create better dynamic performance sports structures for future development.
Zhang et al. (Wed,) studied this question.