This article presents a comprehensive numerical analysis of the dynamic behaviour of a concrete beam with spatially varying elastic moduli. The primary objective of the study is to evaluate and compare the vibrational characteristics of a conventional concrete composite beam with those of modified composites incorporating Recycled Concrete Aggregate (RCA) as a partial or full replacement for natural aggregate. The motivation for using RCA stems from sustainability goals and the growing interest in environmentally friendly construction materials. The dynamic response of the beam was examined under three different types of mechanical excitation: sinusoidal (harmonic), impulse, and stochastic (random) loading. Each case provided insight into how changes in material stiffness affect the vibrational performance of the structure. Furthermore, a time-dependent damage model was implemented to simulate progressive material degradation by reducing the elastic modulus over time. This allowed for the observation of damage evolution and its impact on the dynamic characteristics of the beam. Frequency Response Functions (FRFs) were computed for each scenario to identify shifts in resonance frequencies and changes in amplitude response.