Tera-Hertz Wave Propagation in Non-classical Beams Using Spectral Finite Element Method

Abstract

Non-classical beams have vast applications in NEMS/MEMS devices where scale effects are predominant, keeping these applications in mind, the present manuscript studies about the wave dispersion behavior of non-classical beam structures. Governing equations and corresponding boundary conditions for the non-classical Euler-Bernoulli & non-classical Timoshenko beam theories are derived to study the wave propagation characteristics. Time domain equations are converted into frequency domain using fast Fourier transform. Spectral finite element method (SFEM) formulation is implemented for non-classical beams to study the dynamic response of these beam structures in frequency domain. Spectrum and dispersion curves are studied with respect to scale coefficients along with the dynamic stiffness variations in the beams. Numerical experiments are conducted to identify the scale effects on dynamic wave propagation behavior of beams with the consideration of asymptotic frequencies of tera-hertz level. Exhaustive results are presented to understand the complete dynamic wave propagation behavior of these non-classical beams. The presented results are very useful in the design of NEMS/MEMS devices where the beam like elements are critical.