Qualitative Theory in Structural Mechanics: Qualitative Properties and Existence of Solutions

Description

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. Front Matter ....Pages i-x Overview (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 1-32 Oscillatory Matrices and Kernels as Well as Properties of Eigenpairs (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 33-85 Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Strings and Bars (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 87-118 Qualitative Properties of Vibration and Static Deformation Associated with Discrete Systems of Beams (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 119-181 Qualitative Properties of Vibration and Static Deformation of the Sturm–Liouville System (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 183-213 Qualitative Properties of Vibration and Static Deformation Associated with Continuous Systems of Beams (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 215-269 Qualitative Properties of Vibration and Static Deformation of Repetitive Structures (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 271-325 Theory on the Existence of Solutions in Structural Mechanics (Dajun Wang, Qishen Wang, Beichang (Bert) He)....Pages 327-389 Back Matter ....Pages 391-395