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## Über dieses Buch

This book introduces the theory of structural dynamics, with focus on civil engineering structures. It presents modern methods of analysis and techniques adaptable to computer programming clearly and easily. The book is ideal as a text for advanced undergraduates or graduate students taking a first course in structural dynamics. It is arranged in such a way that it can be used for a one- or two-semester course, or span the undergraduate and graduate levels. In addition, this book serves the practicing engineer as a primary reference. This book is organized by the type of structural modeling. The author simplifies the subject by presenting a single degree-of-freedom system in the first chapters and then moves to systems with many degrees-of-freedom in the following chapters. Many worked examples/problems are presented to explain the text, and a few computer programs are presented to help better understand the concepts. The book is useful to the research scholars and professional engineers, besides senior undergraduate and postgraduate students.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
Majority of today’s structures is subjected to load which varies with time. In fact, with the possible exception of dead load, no structural load can really be considered as static. However, in many cases the variation of the force is slow enough, which allows the structures to be treated as static. For highrise buildings subjected to wind and earthquake, offshore platforms surrounded by waves, aeroplanes flying through storms, vehicles moving on the road, reciprocating engines, rotors placed on the floor and many other categories of loading, the dynamic effect associated with the load must be accounted for in the proper evaluation of safety, performance and reliability of these systems.

### Chapter 2. Free Vibration of Single Degree of Freedom System

Abstract
The simplest physical system is one having single degree of freedom. Almost all practical systems are much more complex than this simple model. However, for obtaining an approximate idea about vibration characteristics, some of the systems are at times reduced to that of a single degree of freedom, such as the water tower of Fig. 2.1.

### Chapter 3. Forced Vibration of Single Degree of Freedom System

Abstract
In the previous chapter, solutions have been obtained for the differential equation of free vibration of single degree of freedom system (SDF) and also, determination of free vibration characteristics of SDF systems by energy methods. In this chapter, attention is directed towards the study of forced vibration of SDF systems and some of its applications. The chapter is begun with the study of harmonic loading. Towards the end of the chapter, the earthquake response analysis of structures has been dealt with.

### Chapter 4. Numerical Methods in Structural Dynamics: Applied to SDF Systems

Abstract
The analysis of SDF systems requires the solution of the differential equation. For simple cases of forcing functions, the solution of the equation can be obtained in closed bound form. However, the dynamic loading obtained from the records for many practical cases is not easily mathematically amenable and as such numerical procedures are to be applied for obtaining the solution.

### Chapter 5. Vibration of Two Degrees of Freedom System

Abstract
Up to the last chapter, we have dealt with systems having only single degree of freedom. We gradually pass on to the more advanced topics. We embark on this chapter on systems, which are referred to as two degrees of freedom system. As has already been explained, if a system requires two independent coordinates to describe the motion, it is said to have two degrees of freedom

### Chapter 6. Free Vibration of Multiple Degrees of Freedom System

Abstract
After getting a taste of two degrees of freedom system, we now proceed to a more general treatment of the problem. In the previous chapter, it is revealed that the two degrees of freedom system are more involved in computation than the single degree of freedom system. When more number of masses are considered, the mathematical formulation becomes much more complicated.

### Chapter 7. Forced Vibration Analysis of Multiple Degrees of Freedom System

Abstract
Most of the structures represented as multiple degrees of freedom system are subjected to dynamic loads, for which they are to be analysed.

### Chapter 8. Free Vibration Analysis of Continuous Systems

Abstract
Structures analysed so far have been treated as discrete systems. Structures have been idealised, and for convenience of computation, simplifying assumptions have been introduced and as such results obtained can only be treated as approximate.

### Chapter 9. Forced Vibration of Continuous Systems

Abstract
In the previous chapter, we have considered the free vibration analysis of continuous systems. We pass on to the forced vibration analysis of continuous systems in this chapter. Though we start with axial vibration problem, the major emphasis will be placed on flexural vibrations of beams

### Chapter 10. Dynamic Direct Stiffness Method

Abstract
The procedure presented in Chap. 8 for the determination of free vibration characteristics of the structural member, by considering it as a system having distributed mass, requires the evaluation of constants which are dependent on the boundary conditions.

### Chapter 11. Vibration of Ship and Aircraft as a Beam

Abstract
Aircrafts and ships are complex structures. They have curved surfaces with various forms of intricate stiffening arrangements. For simplification of the analysis, they are sometimes treated as a beam having varying rigidity. This no doubt facilitates the analysis to a great extent, both for static and dynamic cases, but it introduces certain special problems, particularly in vibration analysis.

### Chapter 12. Finite Element Method in Vibration Analysis

Abstract
In the finite element method, the continuum is divided into a finite number of meshes by imaginary lines. For one-dimensional continuum, two adjacent elements placed side-by-side will meet at a point. Two dimensional continuum will have adjacent elements meeting at a common edge. Strictly speaking, the continuity requirement along the edge should be satisfied, but for the sake of simplicity, it is assumed that the elements are connected only at the nodal points and the continuum has to be continuous through those points. Total structure obtained as an assembly of elements is then analysed.

### Chapter 13. Finite Difference Method for the Vibration Analysis of Beams and Plates

Abstract
The finite difference technique is another versatile numerical method for the solution of vibration problems. The method has been explained in Chap. 4 with respect to the time function. It is applied here with respect to spatial variables. The differential equation is the starting point of the method. The continuum is divided into the form of a mesh, and the unknowns in the problem are those at the nodes.

### Chapter 14. Nonlinear Vibration

Abstract
In all the preceding chapters, we have discussed different linear systems. All the differential equations that have been formed and dealt with so far, whether a single equation in the case of SDF system or a set of coupled equations in the case of MDF system, are linear. But there are certain vibration phenomena, which cannot be predicted by the linear theory. The vibration of a string, the belt friction drive, the shimming of automobile wheels and the inclusion of nonlinear damping are some of the examples of nonlinear vibration .

### Chapter 15. Random Vibrations

Abstract
During the last three decades, a great deal of activity has taken place in studying the loads acting on the structure in a realistic manner and the necessary response thereof. The analytical methods during this period have made tremendous strides, and a need has been felt to account for the load in its truer perspective. The dynamic loads which have been considered in all the previous chapters have fixed or definite values of amplitude, frequency, period and phase. But for many cases, such as wave forces on offshore structures, earthquake effects on buildings, bridges and dams, air pressure on aeroplanes and vibration of ships in rough seas, there is an uncertainty involved with the exactness of the loading parameters. These uncertainties are related to the random time functions.

### Chapter 16. Computer Programs in Vibration Analysis

Abstract
Based on the chapters dealt with, it is revealed that the linear vibration analysis of a structure will involve one or more of the following types: free vibration analysis, forced vibration analysis and random vibration analysis. The free vibration analysis is essentially an eigenvalue problem. If the problem is to be solved on the basis of matrix operations, then the mass matrix and the stiffness matrix of the structure are to be formed.