Ανάλυση και Σχεδιασμός Συστήματος Απορρόφησης Κραδασμών με Αρνητικά Στοιχεία Δυσκαμψίας

Abstract

The purpose of this Ph.D. thesis is to design a vibration absorbing mechanism that overcomes the disadvantages of previously known ones. This is done by capturing the idea of the KDamper. This mechanism overcomes the drawbacks of the most widely used systems so far and enables the achievement of extremely satisfactory results in terms of absorption. As will be seen from the applications of this construction, its implementation can be done in a simple way and this greatly increases the areas in which it can be applied.This doctoral dissertation is divided into five chaptersapart from Chapter 1 that is the introduction.Chapter 2 gives an overview of conventional vibration absorbers, mainly Tuned Mass Damper and Inerter. The steps for the optimal design of the KDamper are then described and the two basic parameters κand μare determined. Finally, the three attributes that arise for KDamper and its comparative advantage over TMD are described.Chapter 3 attempts to implement the KDamper through the use of a non-linear negative spring. The linear model is first presented, the parameters of KDamper are selected and then it is first simulated in Matlab. The response curves for displacement and velocity are presented analytically under the application of an initial displacement, and the curves of the stiffness are given both as a function of time and as a function of displacement.Chapter 4 presents the Disc Springs (Belleville) theory. Their basic properties, their equations for Force and stiffness and the different configurations with which they can be used are presented. The above-mentioned KDamper example is implemented using these springs. Initially, their parameters are calculated for two different material cases (steel and ABS) and then it is simulated in Matlab and the response curves of each systemare obtained.In Chapter 5 a computational simulation of disc springs (Belleville) is performed in a finite element program. Initially, a spring that simulates a positive stiffness is introduced. After analyzing the particularities present in this case and all the necessary steps in that direction, it is simulated a negative stiffness disc spring.Chapter 6 presents a complete example of KDamper design. After making all the necessary calculations for the linear model, the parameters of all the elements that make up the construction are calculated. Initially, disc springs simulating negative stiffness are designed, while the inner spring is designed with both disc and spiral springs. Finally, spiral springs are designed to simulate external positive stiffness. All stiffness elements are entered separately in a finite element program, while the overall model is presented in the end.Finally, Chapter 7 presents some ideas for future research in the specific scientific field.