Differential quadrature discrete time transfer matrix method for vibration mechanics. (May 2019)

• Record Type: Journal Article
• Authors: Rui, Xue; Wang, Guoping; He, Bin
• Is Part Of: Advances in mechanical engineering. Volume 11:Number 5(2019)
• Publication Date: 2019-05
• Subjects: Vibration -- transient response -- time integration -- transfer matrix -- differential quadrature -- Riccati transformation; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/1687814019849980
• Languages: English
• ISSNs: 1687-8132

Abstract

Transfer matrix method is a practical technology for vibration analysis of engineering mechanics. In this article, a new version of mixed differential quadrature discrete time transfer matrix method is presented for simulating vibrations. First, ordinary differential equations of the substructure or the element of a mechanical system are determined by classical mechanics rules or the finite element method. These ordinary differential equations can be transformed to a set of algebraic equations at some discrete time points by the application of a differential quadrature method. After extending the state vector of the transfer matrix method, new transfer equations and transfer matrices of the substructures (or elements) of a mechanical system are developed finally. Riccati transformation is used to improve the computational convergence of the method. Several numerical examples show that the proposed method can be regarded as an efficient tool for transient response analysis of vibration systems.