Dynamic Analysis of a Uniform Microbeam Resting on a Nonlinear Foundation Considering Its Curvature Subjected to a Mechanical Impact and Electromagnetic Actuation.

This study proposes an investigation into the nonlinear vibration of a simply supported, flexible, uniform microbeam associated with its curvature considering the mechanical impact, the electromagnetic actuation, the nonlinear Winkler-Pasternak foundation, and the longitudinal magnetic field. The governing differential equations and the boundary conditions are modeled within the framework of a Euler-Bernoulli beam considering an element of the length of the beam at rest and using the second-order approximation of the deflected beam and the Galerkin-Bubnov procedure. In this work, we present a novel characterization of the microbeam and a novel method to solve the nonlinear vibration of the microactuator.

Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler-Pasternak Foundation.

This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler-Pasternak foundation near the primary resonance. Two Euler-Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton's principle, Eringen's nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin-Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients.

Dynamics of SEIR epidemic model by optimal auxiliary functions method.

The aim of the present work is to establish an approximate analytical solution for the nonlinear Susceptible, Exposed, Infected, Recovered (SEIR) model applied to novel coronavirus COVID-19. The mathematical model depending of five nonlinear differential equations, is studied and approximate solutions are obtained using Optimal Auxiliary Functions Method (OAFM). Our technique ensures a fast convergence of the solutions after only one iteration.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown.

Analytic approximate solution for Falkner-Skan equation.

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions.