Dynamic responses of flexible-link mechanisms with passive/active damping treatment

Abstract

This work presents a finite element formulation for non-linear transient dynamic analysis of adaptive beams. The main contribution of this work concerns the development of an original co-rotational sandwich beam element, which allows large displacements and rotations, and takes active/passive damping into account. This element is composed of a viscoelastic core and elastic/piezoelectric laminated faces. The latter are modeled using classical laminate theory, where the electromechanical coupling is considered by modifying the stiffness of the piezoelectric layers. For the core, a four-parameter fractional derivative model is used to characterize its viscoelastic dissipative behavior. Equations of motion are solved using an incremental-iterative method based on the Newmark direct time integration scheme in conjunction with the Grü nwald approximation of fractional derivatives, and the Newton-Raphson algorithm.

A discrete formulation of Kirchhoff rods in large-motion dynamics

“…The nonlinear nature of the analyzed mechanical system implies that many features that are difficult to be tackled (see, e.g., in the context of nonlinear vibrations Battisti et al (2017); Chróścielewski et al (2019); Deü et al (2008); Lazarus et al (2012); Thomas et al (2016), nonlinear motions Boyer et al (2002); Boyer and Primault (2004) as well as in dynamic stability of mechanical systems D'Annibale (2013, 2017); Luongo et al (2016Luongo et al ( , 2015; Spagnuolo and Andreaus (2019)). Therefore, having a formulation which is as simple as possible is always an opportunity to pursue.…”

Two-Dimensional Finite Element in General Plane Motion Used in the Analysis of Multi-Body Systems

“…All the bodies are considered to be rigid as is the angular velocity and angular acceleration of the local reference system. In this way, the fields of velocity and acceleration are known for each point of each constitutive element of the MBS [12][13][14][15][16][17][18].…”

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

“…We can mention that the method of Lagrange's equations was, in these works, practically the only method to approach this type of problems. Although, theoretically, analytical mechanics offers many equivalent formulations, the familiarity of researchers and the ease of obtaining equations for systems with a large number of degrees of freedom have made Lagrange's method preferred in studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”