Reducing the effect of unwanted vibrations is an important topic in many engineering applications. In this paper we describe some recent developments in the area of passive vibration mitigation. This is based on a new device called the inerter which can be exploited in a range of different contexts. In this paper we consider two recent examples; (i) where a flywheel inerter is combined with a hysteretic damper, and (ii) in which a pivoted bar inerter is developed for a machining application. In both cases, experimental test results show that the devices can outperform existing methods.

The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system with the Mathieu equation, the problem of dynamic stability was solved. By examining the influence of internal and external damping and damping in the beam supports, their influence on the regions of stability and instability of the solution to the Mathieu equation was determined.