**Abstract**

There are a few kinds of structures that are created to fill in as a system, for example, springs, torsion bars, and axles, among others. They are structures, since they comprise of one single body, with no movement joints, however, with degrees of freedom, allowed by the mechanical compliance of the body. This aspect is extremely difficult to represent in durability assessment, since these structures-mechanisms are highly sensitive to dynamic effect of the system and the traditional method to predict fatigue (load history) is static and does not consider how the structure responds dynamically to the loading. In this chapter, we will study the fatigue behavior of two generic components, a classical structure and a structure-mechanism, using three different methods of calculation: load history (static), transient modal superposition (dynamic), and frequency domain modal superposition (dynamic). The objective is to demonstrate the differences between each calculation methodology due to the different ways each considers the dynamic effect.

**Keywords:** fatigue, structure, mechanism, deflection, dynamic, static, modal, superposition, transient, frequency, domain

## **1. Introduction**

A mechanism is a system of multiple bodies assembled by one or many joints, with the objective to change a given input set of forces and moments to a desired output set of forces and moments. In a traditional mechanism, joints or kinematic pairs interface these bodies, giving relative movement between them. The combination between all bodies and joints produces the degrees of freedom of the component.

However, it is possible to design mechanisms with the desired degrees of freedom, without relying on joints and kinematic pairs. Compliant structures can produce relative movement depending on its design shape and the elastic characteristic of the material it consisted, by high mechanical strains.

A high mechanical strain implies that the absolute deflection of a body is "huge" when contrasted with its original form (without any deflection). Although there is no standard to characterize what is "huge," it is very much acknowledged and broadly received as strains higher than 5% [1].

However, even with "huge" strains, the material of the structure must always be inside the elastic region; otherwise, the mechanical work can cause failure. This can be achieved by tuning the design accordingly to the material used. For example, rubbers in simple prismatic rectangles can achieve "huge" deflections in axial directions, while steel must be in a different shape as a coil spring.

The utilization of components dependent on mechanical strain rather than kinematic sets is basic in the industry. Torsion axles, coil springs, leaf springs, and stabilizer bars are a few models broadly embraced in business applications, for example, trains, planes, and vehicles.

Due to its larger compliance and, therefore, natural degrees of freedom, the mechanism-structures respond differently to dynamic inputs, usually presenting lower natural modes. This characteristic has an important influence in fatigue performance when the loading input is dynamic.

To measure this influence, we will study in this chapter the fatigue performance using three different approaches: static load history, transient modal superposition, and frequency domain modal superposition.
