Principles of vibration

Free vibration of single degree of freedom systems translational vibrations - undamped rotational vibrations - undamped viscous damping Lagrange's equations homework problems forced vibration of single degree-of-freedom systems seismic excitation direct force excitation transfer functions viscous damping complex representations damped seismic motion rotating imbalance identification of damping and natural frequency other types of damping accelerometers and seismometers homework problems non-sinusoidal excitations Fourier series analysis forced response via the convolution integral shock response homework problems vibrations involving more than one degree of freedom free response - undamped system forced response vibration absorbers without damping real behaviour of a vibration absorber zeros in a forced response putting problems into normal form orthogonality of system eigenvectors more on normal forms linear damping comparison of damped eigensolutions forced response of damped systems symmetry of mass and stiffness matrices repeated frequencies and zero frequencies influence coefficients problems distributed systems free vibration of a bar (rod, string, etc.) free vibration of a beam continuous systems - forced vibration orthogonality of eigenfunctions approximate solutions methods lumped approximations Rayleigh's quotient Rayleigh-Ritz method: discrete systems Rayleigh-Ritz Method: continuous problems assumed modes method seat of the pants engineering getting approximate results limiting cases verifying your analyses random vibrations and modal analysis signal descriptions Fourier transform analysis spectral analyses noise sensors and actuators nonlinear effects four continuous systems lumped spring constants Assorted material constants elementary matrix relations vibration texts.