Multi-mass linear systems; flexibility and stiffness matrices, natural frequencies, mode shapes and orthogonal properties, coupled and uncoupled system equations, solutions for damped or undamped response to arbitrary forcing and initial conditions. Linear continuous systems; wave equation problems and lateral beam vibration with classical boundary conditions. Effects of added mass or stiffness on frequencies and modes. Forced and transient response. Transfer matrix methods for lumped parameter systems and continuous systems; application to axial and torsional vibration of rods, shafts and beams with attached mass or stiffness. Non-linear vibration; basic methods for solution. Characteristic non-linear effects. Random vibration; elements of describing random response, Fourier transforms and frequency response functions.
Graduate course in the Mechanical Engineering program administered by the Faculty of Graduate Studies.