Nonlinear Longitudinal Vibrations in Accreting One-dimensional Nanostructures
Abstract A governing partial differential equation that describes an accreting nanochain containing an attachment of infinite atoms was considered in this paper. We transformed the space variable u(t,r) → v(τ,x) (for a governing PDE formulated in previous research studies) and introduced a function of linear growth. The boundary conditions were also transformed into the new variables, the left end of the accreting chain was free u(t, r=0)=0 while the right end was fixed. The method of lines was also employed to numerically analyze the governing partial differential equation. We detailed the differential transformation for the change of variables used in obtaining the transformed partial differential equation. We also considered what happens with the introduction of the viscous damping term, (δ). The governing partial differential equation was formulated. Numerical simulations for both cases, was then carried out.