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Über dieses Buch

This book focuses on the qualitative theory in structural mechanics, an area that remains underdeveloped. The qualitative theory mainly deals with the static deformation and vibrational modes of linear elastic structures, and cover subjects such as qualitative properties and the existence of solutions.

Qualitative properties belong to one type of structure, are at the system level and of clear regularity, and often result from analytical derivation and logical reasoning. As for the existence of solutions, it addresses a fundamental issue in structural mechanics, and has far-reaching implications for engineering applications.

A better understanding of qualitative properties can assist in both numerical computation and experimental studies. It also promotes the development of better dynamic designs for structures. At the same time, a sound grasp of the existence of solutions and related subjects can aid in quantitative analysis, and help researchers establish the theoretical background essential to their work.

This book is among the few that is dedicated exclusively to the qualitative theory in structural mechanics and systematically introduces the important and challenging area to a wide audience, including graduate students in engineering.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Overview

Abstract
This chapter gives an introduction to the qualitative theory in Structural Mechanics, providing a brief history of its development, describing the content and methods of the study, and explaining the significance of the theory in research and application. In addition, this chapter presents main results of qualitative theory in Structural Mechanics covered in the book, which makes it easier for readers to select portions of the book for further study based on their personal need and interest.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 2. Oscillatory Matrices and Kernels as Well as Properties of Eigenpairs

Abstract
The theory of oscillatory matrices and kernels forms the mathematical foundation for the study of qualitative properties of natural frequencies and mode shapes of bars and beams. This chapter provides an introduction to the theory. The content is drawn largely from the monograph, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, written by creators of the theory, Gantmacher and Krein; but Sect. 2.11 and most of Sect. 2.10 are the original work by authors of this book as well as their collaborators Zijun Zheng and Pu Chen.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 3. Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Strings and Bars

Abstract
In this chapter, we will study qualitative properties of natural frequencies and mode shapes of discrete models of second-order continuous systems, such as strings in lateral vibration, bars in longitudinal vibration, and shafts in torsional vibration. We will also discuss qualitative properties of static deformation associated with some of these discrete systems.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 4. Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Beams

Abstract
The focus of the first six sections of this chapter is on qualitative properties of the finite difference model or the related physical model of a beam. We will set up the governing equations of motion and boundary conditions associated with the finite difference system; derive various modal qualitative properties of the discrete model under different boundary constraints, by applying the theory of oscillatory matrices and the concept of conjugate beams; and establish qualitative properties in static deformation of the finite difference system of a well-constrained beam.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 5. Qualitative Properties of Vibration and Static Deformation of the Sturm–Liouville System

Abstract
Chapters 3 and 4 were devoted to qualitative properties in vibration and static deformation of discrete systems, while the focus of this chapter is shifted to similar topics related to Sturm–Liouville systems. We will primarily discuss the qualitative properties of a bar with distributed parameters and in longitudinal vibration.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 6. Qualitative Properties of Vibration and Static Deformation Associated with Continuous Systems of Beams

Abstract
In this chapter, we prove the Green’s function of a well-constrained beam to be an oscillatory kernel by verifying that the beam has the oscillatory properties in static deformation.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 7. Qualitative Properties of Vibration and Static Deformation of Repetitive Structures

Abstract
The focus of this chapter is qualitative properties of vibrational modes, static deformation, vibration control, etc. of repetitive structures. Types of repetitive structures covered here include structures with mirror symmetry (abbreviated as symmetric structures in subsequent discussion), rotationally periodic structures (also referred to as cyclic periodic or cyclic symmetric structures in the literature), linearly periodic structures (called linear periodic structures by some authors), chain structures (also known as linking or linked structures), and axisymmetric structures.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Chapter 8. Theory on the Existence of Solutions in Structural Mechanics

Abstract
This chapter is devoted to the more fundamental subjects, such as the existence of solutions of static deformation and vibrational modes in the linear theory of Structural Mechanics and the validity of linear theoretical models of structures.
Dajun Wang, Qishen Wang, Beichang (Bert) He

Backmatter

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