Preface

Chaotic phenomenon has been and continues to be an essential component in the nonlinear vibration of dynamical systems at different degrees of freedom. The nonlinear response of vibration is employed to describe the movement of the dynamical system. This book discusses the chaotic phenomenon in cam-follower systems, rolling bearings, high-rise buildings, and vehicle track interaction. The experimental data included supports the numerical simulation results. The Lyapunov exponent parameter is used to quantify the level of chaos in nonlinear dynamics systems. Moreover, the Fast Fourier Transform (FFT), bifurcation diagram, Poincaré map, and phase-plane diagram are used in nonlinear dynamics behaviors. SolidWorks, MEMS, and ANSYS programs are used to detect the nonlinear response of dynamical systems in different applications of sciences.

> **Louay S. Yousuf** Mechanical Engineering Department, San Diego State University, San Diego, California, USA

**Chapter 1**

*Louay S. Yousuf*

follower mechanism.

**1. Introduction**

**1**

**Abstract**

Effect of Different Material

Properties on the Nonlinear

Dynamics Phenomenon of

Cam-Follower Mechanism

The effect of different material properties for both radial cam and translated roller

follower on the nonlinear dynamics phenomenon is investigated at different cam speeds. The equations of the dynamic motion of the follower movement are derived based on the conception of mechanical vibration theory. In this chapter, we investigate the nonlinear dynamics behavior by detecting it using phase-plane diagram and Poincare' map at different material properties and different cam speeds of the cam. The follower is moved with three degrees of freedom inside its guides and the cam is spinning about a fixed pivot. The nonlinear response of the follower is calculated using SolidWorks program at different cam speeds, different guides' clearances, and different material properties. The nylon, acrylic, and aluminum greasy and steel dry and greasy material properties are examined for nonlinear dynamics behavior of cam-

**Keywords:** phase-plane diagram, Poincare' map, radial cam, translated follower,

The radial cam and translated roller follower mechanism can be found in windshield wiper of the car in which the oscillating motion of the wiper is controlled by the rotary motion of the cam. This kind of cam has been selected based on the irregular profile in which it has two noses and two flanks. At high speeds of the cam, the follower will jump off the cam and introduce chaotic motion at the locations of the tip of the noses. The application of the proposed mechanism is in controlling the opening and closing of valves in internal combustion engine. Nonlinear dynamics phenomenon has happened in the presence of the follower guide's clearance. The mathematical model of transient impact, separation, and contact is described by Yang et al. using an oblique impact in cam-follower system [1]. They explained that at low speed for the

different material properties, nonlinear dynamics, non-periodic motion
