Vibrational structures are susceptible to catastrophic failure or structural damage when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy to address this challenge is using dampers to suppress the effect of these disturbances. This leads to the question of how to find optimal damper viscosities and positions for a given vibrational structure....
In this talk, we will consider a linear gyroscopic mechanical systems of the form
\begin{equation}\displaystyle M \ddot x(t) + G\dot x(t) + K x(t) = 0,
\end{equation}
where the mass matrix $M\in\mathbb{R}^{n\times n}$ and the stiffness matrix $K\in\mathbb{R}^{n\times n}$ are symmetric positive definite matrices, while the gyroscopic matrix $G \in\mathbb{R}^{n\times n}$ is skew-symmetric,...
In this talk, we will discuss the perturbation of a Hermitian matrix pair (H, M), where H is non-singular and M is a positive definite matrix. The corresponding perturbed pair (\widetilde{H}, \widetilde{M}) = (H + \delta H, M + \delta M) is assumed to satisfy the conditions that \widetilde{H} remains non-singular and \widetilde{M} remains positive definite. We derive an upper bound for the...
