Composite materials, valued for their high strength-to-weight ratios, are critical in fields like aerospace, automotive, and construction, where structural integrity and low weight enhance performance. As these materials increasingly face dynamic loads, such as random vibrations from operational environments, understanding their vibrational response becomes essential to ensure durability and reliability. While numerous studies have explored composite behavior under random vibrations, there remains a significant gap in research focusing on the vibrational analysis of fiber-reinforced composites with nanoparticle inclusions. This chapter addresses this need by investigating the vibrational response of fiber-reinforced composites containing alumina nanoparticles, employing Power Spectral Density (PSD) analysis, a frequency-domain approach traditionally used in signal processing but novel in this context. Our parametric study examines varying fiber contents (35%, 45%, and 50%) with a fixed nanoparticle reinforcement of 20%, aiming to identify the optimal fiber-matrix configuration for superior dynamic performance. By evaluating the interplay between fibers and nanoparticles, this research provides insights into optimizing composite materials in dynamic applications, contributing to the design of lightweight, durable materials that meet the rigorous demands of advanced industries.