SIMULATION AND ASSESSMENT OF THE EXPERIMENTAL PARAMETERS OF FRACTIONAL-ORDER FOR THIN PLATE VIBRATION DYNAMICS EQUATION

Fractional vibration dynamics in rectangular thin plates use fractional derivatives to represent material memory and hereditary effects, introducing notable mathematical complexity. This study assesses the experimental parameters and the variation of time-fractional orders to simulate vibration behavior over time. A computational framework developed in Maple is applied to analyze how changes in the fractional order affect vibration frequencies, alongside variations in Young’s modulus—a key indicator of material stiffness governing stress–strain relationships. The simulations show that both parameters strongly influence the plate’s dynamic response. Increasing the fractional order modifies damping and resonance patterns, while higher values of Young’s modulus raise natural frequencies and alter vibrational modes. The results provide valuable insight into how fractional dynamics interact with elastic properties, supporting improved analysis and design of advanced materials and structures exposed to vibration. This approach enhances the modeling of vibration-sensitive engineering systems by accurately capturing complex mechanical behavior.