Akademik Veri Yönetim Sistemi
Thin-Walled Structures, cilt.226, 2026 (SCI-Expanded, Scopus)
This paper presents a Laplace-domain Complementary Functions Method (CFM) for the forced vibration of functionally graded nanobeams within Eringen's nonlocal elasticity, providing a unified formulation for the Timoshenko and Euler–Bernoulli beam models (TBT/EBT). Power-law gradation is incorporated through closed-form section properties, and boundary conditions for simply supported, cantilever, and clamped–pinned beams are enforced directly in the transform domain. Five transient load shapes are treated consistently. A central contribution is the first derivation and reporting of the canonical Laplace-domain state equations for nonlocal graded nanobeams, which are derived for the first time and solved using the CFM. Parametric results show that higher gradation enlarges the response (rotation more sensitive than deflection), and greater slenderness raises amplitudes and lengthens the period. TBT exceeds EBT at moderate thickness but converges for slender beams, while nonlocal effects depend on load shape by amplifying sustained steps and damping sharp pulses. The formulation is further extended to Kelvin damping via elastic–viscoelastic correspondence in the Laplace domain, introducing a damping coefficient without changing the canonical state structure; increasing damping coefficient attenuates amplitudes and accelerates transient decay in all cases.