An interaction model between flexible structures and piezoelements useful in multi-body modelling

Abstract

In this paper, a general procedure for the synthesis of a reduced dynamic model for the description of exible structures coupled with piezoelectric sensors and actuators is shown. The authors built an interaction modelling procedure, useful in mechanical system simulation (MSS) software, using a theoretical and nite element modelling (FEM) approach. By modifying and developing an existing modal synthesis method, which is used by most commercial software, a new mode component synthesis methodology was developed. This new procedure allows the simulation of any system containing exible parts coupled with piezoelectric materials, in linear and non-linear behaviour, under any mechanical and electrical boundary condition both in the frequency and time domain. This is not possible by either the theoretical-analytical or the FEM approach without the involvement of heavy, lengthy computational loads.

Development of selection methodologies and procedures of the modal set for the generation of flexible body models for multi-body simulation

“…The exible deformations, expressed in the body-xed coordinate system, are estimated through a displacement function u which is obtained through the product of space dependent functions and time dependent functions. The space dependent functions are the modal eigenvector represented by the modal matrices, and the time dependent functions are the generalized or modal coordinates [1,10,11]. Therefore, the following equation is used u(c, t)ˆU(c) ¢ q(t) ( 1 ) in which c is the point mass vector position, U is the shape function expressed in terms of displacement and rotation and q is the vector of the generalized coordinates.…”