Analytical and numerical investigation of flexural vibrations in clamped-free plates supported by inclined beams

This study presents an analytical formulation and numerical evaluation of flexural natural frequencies in clampedfree rectangular plates supported by inclined Euler–Bernoulli beams. Such structural configurations are frequently found in marine, aerospace, and civil engineering applications, particularly in systems such as ship bridge wings and cantilever platforms where vibration control is critical. Plates are modeled with classical Kirchhoff–Love theory, thereby considering a one-term Ritz approximation that satisfies the boundary conditions. Beam supports are modeled via the equivalent vertical stiffness derived from Euler–Bernoulli beam theory, which accounts for inclination effects and cross-sectional properties. The total energy of the system is formulated through energy methods, in which the strain and kinetic energy of the plate are combined with the stiffness contribution from the inclined beams. The natural frequencies are then extracted from the Rayleigh quotient. The model is solved for varying numbers of beams (n=2 to 5) and inclination angles (a=20o to 60o), and the first three flexural natural frequencies are computed. Unit consistency is carefully maintained by converting all the parameters to SI units. The results reveal that increasing the number of beams or reducing the inclination angle leads to increased stiffness levels and higher natural frequencies. The proposed formulation provides a compact and effective way to estimate natural frequencies at preliminary design stages. It can also serve as a benchmark for validating finite element models and guiding structural optimization under vibration constraints.