Introduction:
Introduction to Dynamic problems in Civil Engineering, Concept of degrees of freedom, D’Alembert’s principle, principleof virtual displacement and energy principles .
Dynamics of Single degree-of-freedom systems:
Mathematical models of Single-degree-of-freedom systems system, Free vibration response of damped and undamped systems including methods for evaluation ofdamping.
Response of Single-degree-of-freedom systems to harmonic loading including support motion, vibration isolation, transmissibility. Numerical methods applied to Single-degree-of-freedom systems – Duhamel integral. Principle of vibration measuring instruments– seismometer and accelerometer.
Dynamics of Multi-degree freedom systems:
Mathematical models of multi-degree-of-freedom systems, Shear building concept, free vibration of undamped multi-degree-offreedom systems – Natural frequencies and mode shapes – Orthogonality of modes.
Response of Shear buildings for harmonic loading without damping using normal mode approach. Response of Shear buildings for forced vibration for harmonic loading with damping using normal mode approach.
Approximate methods:
Rayleigh’s method, Dunkarley’s method, Stodola’s method.
Dynamics of Continuous systems:
Flexural vibration of beams with different end conditions. Stiffness matrix, mass matrix (lumped and consistent).