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Higher Polytechnic University College
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Grao en Enxeñaría Mecánica
  Theory of Vibration
Topic Sub-topic
Chapter 0. The following topics develop the contents set up in the verification memory. Dynamic equations. Modelling. Vibration of systems of 1 and N degrees of freedom. Buffer. Vibration of continuous systems
Chapter 1. Introduction to structural dynamics:dynamic equations and modeling. Basic concepts. Classification of vibrations. Modelling systems: stiffness, inertia, and damping elements. Mathematical models of Single Degree Of Freedom (SDOF) systems. Application of Newton's laws. Application of the principle of virtual displacements. Hamilton principle. Application of the Lagrange equations.
Chapter 2. Free vibration of SDOF system. Damping. Free vibration of undamped SDOF systems. Free vibration of viscous damped SDOF systems. Other types of damping.
Chapter 3. Response of SDOF to harmonic excitation. Damping. Response of undamped SDOF to harmonic excitation. Response of viscous damped SDOF to harmonic excitation. Complex frequency response. Vibration isolation. Force Transmissibility. Base motion. Response of SDOF due to unbalance in rotating machines.
Chapter 4. Analytical methods of solution. Response of SDOF to a general dynamic excitation Response of SDOF to special forms of excitation. Ideal step input, rectangular pulse and ramp loadings. Short-duration impulse. Unit impulse response. Classification of methods. Duhamel Integral Method.
Chapter 5. Numerical methods of solution. Response of SDOF to a general excitation. Numerical evaluation of the integral of convolution. Method of linear forces. Step by step methods. The average acceleration method. Methods of Newmark family.
Chapter 6. Continuous systems. Mathematical models of Multiple Degrees Of Freedom (MDOF) systems Continuous systems. Discrete systems: application of Newton's laws, application of the Lagrange equations. Equations of motion.
Chapter 7. Free vibration response of MDOF systems Natural frequencies and modes of vibration of MDOF systems. Free vibration response of MDOF systems. Rigid body modes of vibration. Some properties of the natural frequencies and natural modes. Scaling or normalizing. Orthogonality. Expansion theorem. Free vibration response of MDOF systems. Mode-superposition method.
Chapter 8. Forced vibration response of MDOF systems. Mode-superposition method response of undamped MDOF systems. Truncation. Damped MDOF systems. Orthogonal, modal, classic or proportional damping. Rayleigh damping. Non-proportional damping.
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