Dynamics of nonlocal stress-driven Rayleigh Beam

Abstract

This paper presents a novel investigation of the dynamic behavior of Rayleigh nanobeams using a nonlocal stress-driven differential elasticity model, extending the foundational work of Barretta. Unlike previous studies that exclusively employed the Euler-Bernoulli beam theory and neglected rotary inertia, this work is the first to incorporate the rotary inertia term within the stress-driven nonlocal framework, providing a more accurate and comprehensive analysis of nanoscale beam dynamics. The equilibrium equations are derived using a variational approach and solved analytically via the Laplace transform technique, yielding closed-form expressions for the natural frequencies of nanobeams under various boundary conditions, including simply supported, clamped, and cantilevered configurations. The results demonstrate that nonlocal stress effects significantly increase the natural frequencies, particularly in higher vibrational modes, where sensitivity to size-dependent interactions is most pronounced. These findings highlight the inadequacy of classical elasticity models and the necessity of accounting for nonlocal and rotary inertia in dynamic analyses. The proposed model shows excellent agreement with existing literature, validating its robustness and offering valuable insights for designing and optimizing nanoscale devices such as MEMS, NEMS, and nanocomposites. This study sets a new benchmark in nonlocal elasticity by addressing rotary inertia, paving the way for more refined studies of nanoscale dynamics.

Keywords

• Nonlocal elasticity
• Stress-driven model
• Rayleigh nanobeams
• Variational method
• Laplace transform
• Nanoscale dynamics