The primary objective of this course is to enable you to build and solve mathematical models of vibrating systems. The emphasis is on linear systems subject to sinusoidal or periodic excitations. The course requires a math background in Fourier series, solving ordinary differential equations (ODEs) and basic linear algebra (including eigenvalue problems).
Building Vibration Models – Assumptions and approximations; Practical case study – deriving the equations of motion; highlight need for single degree-of-freedom (SDOF) models SDOF Models – Free vibration without and with damping; viscous and other damping types; Forced vibration – harmonic force, rotating unbalance/base excitation, vibration isolation; periodic forcing and concept of frequency response function (FRF); General Excitation – Impulse response, Step and pulse type forces, shock response spectrum Multi degree-of-freedom (MDOF) Models – Deriving equations of motion for complex models; Concept of mode shapes and associated mathematical properties; Use of modal superposition to obtain forced vibration response; Concept of proportional or Rayleigh damping; More on FRFs and their uses; Vibration absorber application Continuous system Models – Equations of motion for transverse vibration of strings, torsional vibration of shafts, axial and beam bending vibrations; forced vibration of continuous systems using modal Superposition; Approximation methods – Rayleigh-Ritz and Galerkin based solutions.
1. W. T. Thomson, M. D. Dahleh and C. Padmanabhan, 2008, Theory of Vibration with Applications, Pearson Education India: New Delhi.
2. L. Meirovitch, 2001, Elements of Vibration Analysis, Tata McGraw-Hill: New Delhi.
3. S. S. Rao, 2003, Mechanical Vibrations, 4th Edition, and Pearson India: New Delhi.
1. B. Balachandran, E. B. Magrab, 2009, Fundamentals of Vibrations} Cengage Engineering: New Delhi.
2. V. Ramamurti, 2012, Mechanical Vibration Practice and Noise Control, Narosa: New Delhi.