To investigate nonlinear bending of the functionally graded (FGM) plates with complex shape and resting on elastic foundation a variational-structural method (RFM) is proposed. Mathematical statement boundary value problems plate carried out in framework classical geometrically theory. solve sequence linear obtained as result linearization original system equations by successive loadings Newton...

As is well-known, the classical PID control plays a dominating role in various loops of industrial processes. However, theory that can explain rationale why linear successfully deal with ubiquitous uncertain nonlinear dynamical systems and method provide explicit design formulae for parameters are still lacking. This paper continuation authors recent endeavor towards establishing theoretical fo...

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...

In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The Visco-Pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied t...

Primarily, two models are commonly used to describe rocking of rigid bodies; the Housner model, and the Winkler foundation model. The first deals with the motion of a rigid block rocking about its base corners on a rigid foundation. The second deals with the motion of a rigid block rocking and bouncing on a flexible foundation of distributed linear springs and dashpots (Winkler foundation). The...

APPROACH: Buckling driven delamination is difficult to control in experiments. Thus, the present study relies on numerical simulations using geometrically nonlinear finite element analysis as well as the softening foundation model, which is an adaptation of Winkler elastic foundation. Delamination fracture is modeled by a cohesive crack model. Dimensionless variables are used to cover the entir...

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

Due to long-term unpredictability of nonlinear system, based on the analysis of the bridge structure nonlinear characteristics and chaotic time series kolmogorov entropy extraction algorithm, calculate kolmogorov entropy of responding information time series to obtain the most predictable points of complex structure system state, so providing the theoretical support for predictable confidence i...

The nonlinear physical model such as the cubic nonlinear Schrodinger equation has been applied in many branches of physics. In this paper, the )) ( exp(    expansion method is applied to evaluate new exact travelling wave solutions of the complex Schrodinger equation with cubic nonlinearity. Various solutions of the cubic nonlinear Schrodinger equation using this method provide us the firm m...

Nonlinear beam resting on linear elastic foundation and subjected to harmonic excitation is investigated. The beam is simply supported at both ends. Both linear and nonlinear analyses are carried out. Hamilton’s principle is utilized in deriv ing the governing equations. Well known forced duffing oscillator equation is obtained. The equation is analyzed numerically using Runk-Kutta technique. T...