Fatigue Analysis on Moving Bodies

Within engineering, mechanical sciences were developed to interpret physical phenomena and describe them using mathematical models. These mathematical models represent important tools within the project area, which serve to predict certain behaviors. Particularly mechanical systems subjected to transient loads must be structurally designed in order to avoid failure modes associated with the alternation of mechanical stresses. This chapter will present some examples of mechanical systems that can be subjected to transient loads during their operation and what are the design criteria used to prevent their failures.

This chapter discusses the concepts involved in the Lagrangian formulation to derive the differential equations of motion of mechanical systems. Here it is demonstrated how the equations of motion from scalar quantities such as work and energy can be obtained in contrast to Newton's second lawprevent their failures.

This chapter covers discrete systems composed of lumped masses, springs and dampers. The energy formulation of these elements from the application of the Lagrange equations, obtaining the differential equations of motion, is presented. The resolution of the equations of motion in the time domain by step-by-step methods such as the Taylor series, Newmark, Wilson and Houbolt is presented. 

This chapter covers continuous elastic elements, such as bars, beams, and shafts required by axial and torsional efforts, bending and rotary bending. The formulations of kinetic energy and elastic deformation energy of these elements are presented from the application of the Lagrange’s equations, obtaining the differential equations of motion.

This chapter will describe the procedure for obtaining the differential equations of motion resulting from the discretization of continuous bar elements under tension or torsion and beam elements under bending and rotary bending from the Lagrangian formulation.

In this chapter, the development of models of more complex mechanical systems is developed, which have continuous elastic elements joined by elastic spring and viscous damper elements. As will be observed, these mechanical systems can be easily identified with the suspensions of bicycles, motorcycles and cars, gear trains and rotating machines. 

In this chapter, a brief review of the basic concepts of fatigue failure mechanism in structural elements requested by cyclic loading is presented. Besides, tests to estimate the fatigue resistance curves of materials for different loading conditions, as well as how these curves can be used to design parts are demonstrated.

This chapter aims to apply the concepts of dynamics and fatigue strength analysis to predict the behavior of dynamically requested mechanical systems, and to design the structural elastic elementsthat constitute them. This procedure is applied to systems with torsional cycling loads, such as gear trains, systems with transversal cycling loads, such as vehicle suspension, and systems with rotary bending, such as turbines and pumps.