Classical vibration design uses modes and transfer functions generated with the superposition principle to allow the verification of design objectives. If redesign is needed, one optimizes mass and stiffness in order to modify the transfer until the specification is met. Integrating damping and non-linearities in the optimization of detailed industrial models is however still considered a major difficulty, even though the physical mechanisms are well known. Approaches to handle viscoelastic damping and time domain modal damping are thus discussed. Distributed non-linearities, such as contact and friction, are becoming accessible to transient simulation, but lead to responses where modes are no longer defined. It is however illustrated that operational deflection shapes, associated with a singular value decomposition of the response, give similar information. Finally, a fundamental aspect of non-linear vibration simulation is the volume of output and the associated numerical cost. Model reduction is a key ingredient of practical approaches and a perspective on related issues is given.
