Longitudinal wave propagation analysis of a bar according to modified strain gradient elasticity theory
Abstract
This paper employs the modified strain gradient elasticity theory to investigate microbars' size-dependent longitudinal wave propagation analysis. It presents the governing equation of motion of the modified strain gradient bar, which is derived using Hamilton's principle. The problem of longitudinal wave propagation in microbars is solved, and the effect of the size-dependent bar model is identified and assessed. Also, a new model is proposed for use in wave propagation problems, which appears when the sign of the higher-order term is changed. It is concluded that the modified strain gradient elasticity bar shows size-dependent and stiffer mechanical behavior compared with the classical one. Also, the new model predicts physically acceptable frequencies and phase velocities compared with the above models.
Fields of Study & Subjects
Nonlocal and gradient elasticity in micro/nano structures
Composite Structure Analysis and Optimization
Thermoelastic and Magnetoelastic Phenomena
Publication details
- Journal / source
- U Porto Journal of Engineering
- Publisher
- University of Porto
- Volume
- 12
- Issue
- 1
- Pages
- 132–143
- Publication date
- 8 May 2026
- Language
- EN