Vibration Problems in EngineeringThe Fifth Edition of this classic work retains the most useful portions of Timoshenko's book on vibration theory and introduces powerful, modern computational techniques. The normal mode method is emphasized for linear multi-degree and infinite-degree-of-freedom systems and numerical methods dominate the approach to nonlinear systems. A new chapter on the finite-element method serves to show how any continuous system can be discretized for the purpose of simplifying the analysis. Includes revised problems, examples of applications and computer programs. |
Contents
SYSTEMS WITH NONLINEAR CHARACTERISTICS | 139 |
SYSTEMS WITH TWO DEGREES OF FREEDOM | 217 |
SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM | 275 |
CONTINUA WITH INFINITE DEGREES OF FREEDOM | 363 |
FINITEELEMENT METHOD FOR DISCRETIZED | 511 |
Common terms and phrases
a₁ acceleration action equations amplitude angular frequency applied approximation assume beam becomes C₁ C₂ calculate coefficients constant corresponding cos w₁t cross section curve damping ratio deflection degrees of freedom Determine displacement coordinates Duhamel integral eigenvalue eigenvectors elastic energy equations of motion Example expression figure flexural flexural rigidity forcing function free vibrations given by Eq harmonic inertia initial conditions integral iteration k₁ k₂ load m₁ m₂ mass matrix maximum method mode shapes modes of vibration moment of inertia nodal nonlinear normal coordinates normal-mode obtain one-degree system prismatic bar Prob problem Q₁ r₁ ratio represents rigid-body rotation shaft shown in Fig simple harmonic motion sin Qt solution spring spring constant static steady-state response system in Fig t₁ torsional translation u₁ u₂ undamped v₁ values vector viscous damping w₁ w₁t w₂t X₁