Random vibrations of stress-driven nonlocal beams with external damping

TL;DR

This paper models the stochastic vibrations of stress-driven nonlocal beams with external damping, providing analytical solutions for their dynamic response, which is useful for designing small-scale devices like MEMS and NEMS.

Contribution

It introduces a novel stochastic nonlocal beam model with damping, deriving closed-form expressions for response statistics and analyzing size-dependent dynamic behavior.

Findings

Analytical expressions for power spectral density and variances.

Size-dependent effects on stiffness and displacement variance.

Effective modeling of damping and stochastic loadings in small-scale beams.

Abstract

Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding environment. Loadings are modeled by accounting for their random nature. Such a dynamic problem is characterized by a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field. Differential eigenanalyses are performed to evaluate modal time coordinates and mode shapes, providing a complete stochastic description of response solutions. Closed-form expressions of power spectral density, correlation function, stationary and non-stationary variances of displacement fields are analytically detected. Size-dependent dynamic behaviour is assessed in terms of stiffness, variance and power spectral density of displacements. The outcomes can be useful for design and optimization of structural components of modern small-scale devices, such as Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).