Topic
Multiple-scale analysis
About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.
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TL;DR: In this paper, a nonlinear model for coupled 3D displacements of the doubly-clamp microbeams based on the modified couple stress theory is presented, where the microbeam is assumed to deflect in axial and lateral directions and the nonlinearities caused by the midplane stretching are considered.
45 citations
TL;DR: In this paper, the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions is studied.
Abstract: In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Karman strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.
45 citations
TL;DR: In this paper, an approximate analytical solution for the transverse vibrations of a beam during axial deployment is derived, which relies on removing the time dependency from the boundary conditions, and transferring it to the differential equation.
45 citations
TL;DR: In this article, a full visco-elastic non-linear beam with cubic nonlinearities is considered, and the governing equations of motion of the system for large amplitude vibrations are derived.
44 citations
TL;DR: In this paper, the effect of time delay in active suppression of nonlinear vibrations applied to a nonlinear saturation-based controller is investigated. But, the results of the analysis showed that all predictions from analytical solutions were in good agreement with the numerical simulation.
44 citations