Discrete dynamics analysis for nonlinear collocated multivariable mass-damper-spring intelligent mechanical vibration systems

A new time-discretization method for the development of nonlinear collocated multivariable mass-damper-spring (MDS) intelligent mechanical vibration systems is proposed. It is based on the Runge-Kutta series expansion method and zero-order hold assumption. In this paper, we show that the mathematical structure of the new discretization scheme is explored and characterized in order to represent the discrete dynamics properties for nonlinear collocated multivariable MDS intelligent mechanical vibration systems. In particular, the decent effects of the time-discretization method on key properties of nonlinear multivariable MDS mechanical vibration systems, such as discrete zero dynamics and asymptotic stability, are examined. The resulting time-discretization provides discrete dynamics behavior for nonlinear MDS mechanical vibration systems, which enabling the application of existing controller design techniques. The ideas presented here generalize well-known results from the linear case to nonlinear plants

Discrete dynamics analysis for nonlinear collocated multivariable mass-damper-spring intelligent mechanical vibration systems

A new time-discretization method for the development of nonlinear collocated multivariable mass-damper-spring (MDS) intelligent mechanical vibration systems is proposed. It is based on the Runge-Kutta series expansion method and zero-order hold assumption. In this paper, we show that the mathematical structure of the new discretization scheme is explored and characterized in order to represent the discrete dynamics properties for nonlinear collocated multivariable MDS intelligent mechanical vibration systems. In particular, the decent effects of the time-discretization method on key properties of nonlinear multivariable MDS mechanical vibration systems, such as discrete zero dynamics and asymptotic stability, are examined. The resulting time-discretization provides discrete dynamics behavior for nonlinear MDS mechanical vibration systems, which enabling the application of existing controller design techniques. The ideas presented here generalize well-known results from the linear case to nonlinear plants

The solution of vibroacoustic linear systems as a finite sum of transmission paths

© 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Linear systems are frequently encountered in low, mid and high vibroacoustics modelling of mechanical built-up structures. It has recently been proved that the solution to those systems can be always factorized as an infinite (weighted) Neumann series summation, which accounts for signal transmission through paths connecting system elements. The key to path expansion relies on the concept of direct transmissibility. In this work, we explore some additional theoretical aspects of transmissibility-based transmission path analysis (TPA), which is known to constitute a valuable tool to remedy noise and vibration problems. In particular, we show that it is also possible to expand the solution of a matrix linear system as a finite summation of transmission paths. Furthermore, our goal is to provide mathematical and physical insight into such path factorization. As regards the former, we exploit the relationship between graph theory and matrix algebra to interpret the terms appearing in the series expansion as combinations of open and closed paths in a graph. In what concerns the second, two benchmark examples are addressed that benefit from the graph theory outcomes. The first one consists of a mass-damping-stiffness system representative of vibroacoustic modelling at low frequencies. A relation is established between the relative weights of the paths, the global system resonances and the resonances of complementary systems, which contain elements not belonging to the paths. The second example involves a statistical energy analysis (SEA) model made of connected plates. The meaning of the relative weights of open paths in the finite expansion for energy transmission between SEA subsystems is analyzed and compared to the results of infinite SEA path factorization.Peer ReviewedPostprint (author's final draft

On transmission Zeros of piezoelectric structures

The evaluation of transmission zeros is of great importance for the control engineering applications. The structures equipped with piezoelectric patches are complex to model and usually require finite element approaches supplemented by model reduction. This study rigorously investigates the influence of mesh size, model reduction, boundary conditions (free and clamped), and sensor/actuator configuration (collocated and non-collocated) on the evaluation of transmission zeros of the piezoelectric structures. The numerical illustrations are presented for a thin rectangular plate equipped with a single pair of piezoelectric voltage sensor/ voltage actuator. Through the examples considered in this study, a link is presented between the static response (or static deflected shape) and the transmission zeros of the piezoelectric structures. This interesting observation forms the basis of: (i) a local mesh refinement strategy for computationally efficient estimation of the transmission zeros and (ii) a physical interpretation of the pole-zero pattern in the case of piezoelectric structures. The physical interpretation developed in this study helps in qualitatively explaining the pole-zero patterns observed for different configurations. It is also shown that this understanding of the relation between the static deformed shape and the transmission zeros can be used by the practitioners to modify the pole-zero pattern through a careful selection of the orientation and the size of the piezoelectric patches