Vibrations of Continuous Systems: Theory and Applications

Front Matter....Pages 1-3
Introduction....Pages 5-8
Continuous systems....Pages 9-11
Some classical, conservative, linear systems....Pages 12-21
Wave solutions....Pages 22-27
Other forms of the equations of motion for linear, finite systems....Pages 28-31
Separation of variables; boundary value problem; eigenvalue problem....Pages 32-43
Forced vibrations....Pages 44-48
Methods to calculate eigenvalues of conservative systems....Pages 49-65
Relations between stability and vibrations of conservative systems (Example: Compressed bar)....Pages 66-68
Equations of motion for (nonlinear) nonconservative systems....Pages 69-76
Damping (linear)....Pages 77-91
Some remarks on the separability of damped systems and non-self-adjoint eigenvalue problems....Pages 92-95
Lyapunov’s definition of stability....Pages 96-101
Kinetic stability of autonomous systems....Pages 102-116
Kinetic stability of non-autonomous systems....Pages 117-134
Nonlinear vibrations of autonomous systems....Pages 135-159
Nonlinear vibrations of nonautonomous systems....Pages 160-182
Asymptotic methods....Pages 183-199
Investigation of bifurcation points....Pages 200-210
Back Matter....Pages 211-219