Vibration of sdf systems- Free vibration of sdf systems – undamped and damped free vibration-underdamped, overdamped and critically damped systems-estimation of damping by logarithmic decrement. Forced vibration of sdf systems- Harmonically excited sdf systems-rotating unbalance-support harmonic excitation- vibration isolation-sdf system as a vibration measuring instrument- Half power point method for the estimation of damping- Response to periodic excitation – method of Fourier series. Types of damping – viscous, Coulomb, structural and material damping models- Equivalent viscous damping. Response of sdf system to arbitrary excitation (Transient Vibration)- Convolution integral – method of Fourier transforms.
Vibration of two dof systems-Undamped free vibration of the two dof systems -matrix eigenvalue problem – natural frequencies and natural modes – elastic and inertial coupling – coordinate selection to remove coupling- beat phenomenon – response to harmonic excitation- vibration absorbers – orthogonality of natural modes. Vibration of multi dofsystems-Equations of motion – formulation and solution of matrix eigenvalue problem – computational methods for the solution of matrix eigenvalue problem – decoupling of equations of motion by modal analysis.
Vibration of continuous systems
Transverse vibration of a string – axial vibration of a rod – torsional vibration of a shaft – bending vibration of a beam – formulation and solution of differential eigenvalue problem.