.... The first one specifies the amount of the integer and the noninteger gradient of strain in the strain energy relation, and the second one controls the order of the strain derivatives in the conformable energy relation. The obtained governing (nonlinear) equation has been solved by the Galerkin method...

... in this study, providing a theoretical framework to study insertion and deformation of needles. Galerkin method and iteration cycle analysis are applied in solving a series of deformation control equations to obtain the needle deflection. The parameters used in the mechanics-based model are obtained from...

... multiwavelet are first presented. These properties together with the Galerkin method are then utilized to reduce the nonlinear DGRLW equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. 23 07 2009 03 04...

... filter by operating one in the softening domain and the other in the hardening domain. 24 04 2010 30 10 2010 12 04 2011 12 04 2011 band-pass filters beams (structures) distributed parameter filters filtration Galerkin method There is a continuous trend to realize...

... and the substrate using a nonlinear foundation of springs and dampers. The system partial differential equation is converted into coupled nonlinear ordinary differential equations using the Galerkin method. A numerical solution is obtained by treating all nonlinear terms as external forces. We use the model...

... equations Galerkin method integro-differential equations nonlinear equations numerical analysis 15 09 2009 18 08 2010 28 10 2010 28 10 2010 Remark 8. The DAE system approximates the original dynamic system and not just a specific solution. Beyond direct numerical solution...

... of motion for the structure and the modal equations of motion for the first, second, and third sloshing modes are derived by using Galerkin’s method, taking into account the nonlinearity of the sloshing. Then, van der Pol’s method is employed to determine the frequency response curves. It is found...

... the basis includes an joint vector. In this case there are one eigenmode of the reference linear system and one Milman–Chu joint vector. 05 09 2006 23 01 2007 nonlinear dynamical systems Galerkin method eigenvalues and eigenfunctions vibrations springs (mechanical) damping...