This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects of nonconservative stability problems, analysis of singularities of boundaries for the stability domains, stability analysis of multiparameter linear periodic systems, and optimization of structures under stability constraints. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems.A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed. Among these problems, the authors consider systems of rotating bodies, tubes conveying fluid, elastic columns under the action of periodic and follower forces, optimization problems for conservative systems, etc. The methods presented are constructive and easy to implement in computer programs.This book is addressed to graduate students, academics, researchers, and practitioners in aerospace, naval, civil, and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics.
Fundamentals of Stability Theory; Bifurcation Analysis of Eigenvalues; Stability Boundary of a General System Depending on Parameters; Bifurcation Analysis of Roots and Stability of a Characteristic Polynomial Depending on Parameters; Vibrations and Stability of a Conservative System Depending on Parameters; Stability of a Linear Hamiltonian System Depending on Parameters; Stability of Linear Gyroscopic Systems Depending on Parameters; Mechanical Effects Related to Bifurcation of Eigenvalues and Singularities of the Stability Boundary; Stability of Periodic Systems Depending on Parameters; Stability Boundary of a General Periodic System Depending on Parameters; Instability Domains of Oscillatory Systems with Small Parametric Excitation and Damping; Stability Domains of Nonconservative Systems Under Small Parametric Excitation.