Dynamic response of a viscously damped two adjacent degree of freedom system linked by inerter subjected to base harmonic excitation

The study investigates the dynamic response of a viscously damped two adjacent single degree-of-freedom (2-ASDOF) system coupled by a connection that includes an inerter element. The dynamical model of a pair of simple oscillators coupled with various connection elements is synthetic but also representative to describe different classes of structures (i.e. contiguous buildings, adjacent walls and frames and so on). The specific kind of connection fundamentally alters the dynamic behavior of the entire system. Coupling elements typically studied are springs, dampers, linear or non-linear, passive, semi-active or active, e.g. [1,2]. The inerter is a novel device able to generate a resisting force, proportional to the relative acceleration of its terminals, equivalent to a force produced with an apparent (inertial) mass two orders of magnitude greater than its own physical (gravitational) mass [3]. In this study, a non-conservative connection, realized with a spring-inerter-viscous damper elements, adjusted in parallel, is considered as linking scheme for the 2-ASDOF system. In order to perform modal analysis, the first order state-space representation is adopted and the modal equations for the viscously damped system are derived. By solving the eigenvalue problem, the attention is focused on how modal parameters, i.e. the natural frequencies, the modal damping ratios and modes are affected by the connection. The system is then subject to harmonic base excitation and frequency response functions are depicted showing the influence of the link (through spring stiffness, inertance and damping coefficient) on the dynamic response. From the analysis with the different linking schemes, it emerges that the specific kind of connection influences the system dynamic characteristics

Identification of Nonlinear Normal Modes of Engineering Structures under Broadband Forcing

The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.Comment: Journal pape

Latent force models for sound: Learning modal synthesis parameters and excitation functions from audio recordings

Latent force models are a Bayesian learning technique that combine physical knowledge with dimensionality reduction - sets of coupled differential equations are modelled via shared dependence on a low-dimensional latent space. Analogously, modal sound synthesis is a technique that links physical knowledge about the vibration of objects to acoustic phenomena that can be observed in data. We apply latent force modelling to sinusoidal models of audio recordings, simultaneously inferring modal synthesis parameters (stiffness and damping) and the excitation or contact force required to reproduce the behaviour of the observed vibrational modes. Exposing this latent excitation function to the user constitutes a controllable synthesis method that runs in real time and enables sound morphing through interpolation of learnt parameters