Dynamic stiffness of nonlocal damped nano-beams on elastic foundation

Free and forced bending vibration of damped nonlocal nano-beams resting on an elastic foundation is investigated. Two types damping models, namely, strain-rate-dependent viscous velocity-dependent are considered. A frequency-dependent dynamic finite element method developed to obtain the response. Frequency-adaptive complex-valued shape functions used for derivation stiffness matrix. It shown that there six unique coefficients which define general These obtained exactly in closed-form illustrated numerically as frequency. proved matrix reduces well known special cases under different conditions. The mass matrices beam also using conventional method. numerical algorithm extract eigenvalues from with a transcendental case when system undamped suggested. Results compared. application approach through response analysis double-walled carbon nanotube pinned-pinned cantilever configurations. Explicit expressions both have been role crucial parameters such as, factors, parameter