.... 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...

... at one cross section. The Galerkin method is used to discretize the nonlinear differential equations of the needle and subsequently, these equations can be computed by performing a linearization using an iterative method. Fig. 7 Depiction of the mechanics-based needle insertion model and methods...

... 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. band-pass filters beams (structures) distributed parameter filters filtration Galerkin method There is a continuous trend to realize efficient and effective bandpass filters with near-optimal...

... 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 Initial value fractional differential/integrodifferential equations have been studied in many areas of science and engineering including viscoelasticity ( 1 2 ), control ( 3 4 5 ), fluid mechanics...

... 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...

... structures, though demonstrably nonlinear, manifest kinematics that are well described using eigenmodes of a corresponding system where the joints are replaced by linear springs. 05 09 2006 23 01 2007 nonlinear dynamical systems Galerkin method eigenvalues and eigenfunctions vibrations...