Dr. Louay S. Yousuf is a lecturer professor in the Department of Mechanical Engineering, San Diego State University, USA. He received his Ph.D. from the University of Baghdad, Iraq, and was a postdoctoral fellow at the Mechanical Engineering Department, University of Auburn, USA, before joining San Diego State University. His research interests include nonlinear dynamics, composite materials, finite element methods, mechanical vibrations, mechanisms, and robotics.
Chaos theory is an interdisciplinary area of scientific study and a branch of engineering focused on the law of dynamic systems. Even very accurate measurements of the current state of a chaotic system become useless indicators of where the system will be. Many approaches to nonlinear dynamics such as the Fast Fourier Transform (FFT), phase-plane diagram, Poincaré map, bifurcation diagram, and Lyapunov exponent are used to detect and suppress the chaotic motion at different degrees of freedom. Chaos can help scientists explore the sudden transition from periodic motion to non-periodic motion at any dynamical system. There is a relationship between the finite element method and chaos analysis in which the dynamic quantity is increased with the increase of mesh generation. The refinement of element size in mesh generation affects the chaotic phenomenon Chaos theory has a wide variety of applications in engineering, such as robotics, and in medical fields, such as human gait locomotion. The dynamic description of the long-term behavior of any dynamical quantity is hard or impossible to predict. The three factors that affect chaos analysis are time delay, embedding dimensions, and the distribution of that dynamical quantity against time. Periodic, non-periodic motions, and chaos are used to describe the level of nonlinear dynamics. The vibrational signal of chaos might be continuous, discontinuous, solitons, and fractals. This book contains the method of chaos to detect the level of chaotic motion such as entropy, Lyapunov exponent, Poincare map, and phase-plane diagram.
Go to the bookIn this chapter, the derivation of analytic formulation of bending deflection has been done using the theory of classical laminate plate. The method of Navier and Levy solutions are used in the calculation. The composite laminate plate is exposed to out-off plane temperatures and combined loading. The temperature gradient of thermal shock is varied between 60C∘ and −15C∘. The combined loading are the bending moment (Mo) in the y-direction and in-plane force (Nxx) in the x-direction. The in-plane force (Nxx) has a great effect on the bending deflection value within a 95.842%, but the bending moment (Mo) has a small effect on the bending deflection value in the rate of 4.101%. The results are compared and verified for central normal deflection.
Part of the book: Structural Integrity and Failure
Nonlinear response of the follower motion is simulated at different cam speeds, different coefficient of restitution, and different internal distance of the follower guide from inside. The nonlinear response of the follower is employed to investigate the chaotic phenomenon in cam follower system in the presence of follower offset. The numerical results are done using SolidWorks software. The chaos phenomenon is detected using Poincare’ maps with phase-plane portraits, the largest Lyapunov exponent parameter, and bifurcation diagram. The largest Lyapunov exponent has a maximum values when the follower offsets to the right, while the largest Lyapunov exponent has a minimum values when the follower offsets to the left. The chaotic phenomenon in cam follower system when the follower offsets to the left is more than the chaotic phenomenon when the follower offsets to the right.
Part of the book: Functional Calculus
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-follower mechanism.
Part of the book: Chaos Monitoring in Dynamic Systems