In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler–Bernoulli beam model, the governing nonlinear PDE of the beam’s transverse vibration and also its associated boundary conditions ...

This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed ...

We study the dynamics of a two-degrees-of-freedom (two-DOF) nonlinear oscillator representing a quarter-car model excited by a road roughness profile. Modeling the road profile by means of a harmonic function, we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the ...

One subject of spatial epidemiology is spatial variation in disease risk or incidence. The spread of epidemics can result in strong spatial patterns of such risk or incidence: for example, pathogen dispersal might be highly localized, vectors or reservoirs for pathogens might be spatially restricted, or susceptible hosts might be clumped. Here, spatial pattern of an epidemic model ...

The behavior of systems of coupled nonlinear oscillators and, connected with it, the synchronization phenomena are of significant interest in many areas of science. One of the most important problems in this field is the stability of the synchronous state. The most often applied tool which allows one to quantify this stability is the largest Transversal Lyapunov Exponent (TLE) and, ...

We examine the regenerative cutting process by using a single degree of freedom nonsmooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test analysis for chaos detection. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. For the investigated ...

In this paper, we apply an improved version of the multiple scales perturbation method to a system of weakly nonlinear, regularly perturbed ordinary difference equations. Such systems arise as a result of the discretization of a system of nonlinear differential equations, or as a result in the stability analysis of nonlinear oscillations. In our procedure, asymptotic approximations ...

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2-cycles, grazing and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from ...

Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect, i.e., interaction of optical waves with nonlinear medium with polarizability χ (3) is the basic phenomenon needed to explain, for example, the process of light transmission in fibers and optical couplers. In this paper, we analyze the two Kerr oscillators coupler and we ...

In this paper, nonlinear resonances in a coupled shaker-beam-top mass system are investigated both numerically and experimentally. The imperfect, vertical beam carries the top mass and is axially excited by the shaker at its base. The weight of the top mass is below the beam’s static buckling load. A semi-analytical model is derived for the coupled system. In this model, ...

In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling ...

A new adaptive synchronization scheme by pragmatical asymptotically stability theorem is proposed in this paper. Based on this theorem and nonlinear control theory, a new adaptive synchronization scheme to design controllers can be obtained and especially the constraints for minimum values of feedback gain K in controllers can be derived. This new strategy shows that the constraint ...

A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be dynamically varied. The string is assumed to have distributed mass and elasticity that permits axial deformations. The rigid body is attached to ...

In this paper, the concept of invariance factors for second order difference equations to obtain first integrals or invariants will be presented. It will be shown that all invariance factors have to satisfy a functional equation. Van Horssen (J. Indones. Math. Soc. 13:1–15, 2007) developed a perturbation method for a single first order difference equation based on invariance ...