In this paper, the postbuckling problem and free linear nonlinear vibration surrounding configuration are accurately analyzed. The placement of translating beams that undergo significant overall buckling deformations in high-speed region, leading to strongly vibration, is studied. Using Galerkin method, we found partial differential equation reduced an ordinary with cubic quadratic terms, which...

Singh, Shubham, MS, Purdue University, August 2016. Applications of the Homotopy Analysis Method to Optimal Control Problems. Major Professor: Michael J. Grant. Traditionally, trajectory optimization for aerospace applications has been performed using either direct or indirect methods. Indirect methods produce highly accurate solutions but suffer from a small convergence region, requiring initi...

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

Abstract: This article is devoted to consider homotopy analysis method (HAM) for discontinued problems arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a nonlinear differential-difference model is considered as an alternative approach to describing discontinued problems. This procedure is powerful tool for solving large amount of problems. Using this method, it is p...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

In this paper, we consider fractional reaction-diffusion equations with linear and nonlinear fractional reaction terms in a semi-infinite domain. Using q-Homotopy Analysis Method, solutions to these equations are obtained in the form of general recurrence relations. Closed form solutions in the form of the Mittag-Leffler function are perfectly obtained in the case with linear fractional reactio...

In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate solutions of electrostatically actuated micro-beam. To illustrate applicability and accuracy method, a high level was established for by comparing results with numerical solution as well already published literature, such variational approach ...

The present investigation focuses the flow and heat transfer characteristics of the steady three-dimensional Sisko fluid driven by a bidirectional stretching sheet. The modeled partial differential equations are reduced to coupled ordinary differential equations by a suitable transformation. The resulting equations are solved numerically by the shooting method using adaptive Runge Kutta algorit...

In this paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...

Unsteady permeable stretching sheet; Second grade fluid; Stagnation point flow; Heat transfer Abstract This article discusses the stagnation-point flow of second grade fluid over an unsteady stretching surface in the presence of variable free stream. Flow analysis has been carried out with heat transfer analysis. The resulting partial differential equations have been converted into ordinary dif...