The Rigid Finite Element Method

Wittbrodt, Edmund; Szczotka, Marek; Maczyński, Andrzej; Wojciech, Stanisław

doi:10.1007/978-3-642-29886-8_8

Cited by 9 publications

(19 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth noticing that the number of the RFE elements is (n+1) whereas the SDE elements is n. Theoretically, the higher the number of RFE elements is, the more precise the simulation will be in comparison with the analytical method but at the expense of computational time. A rough estimation has shown that the relative error is 1.14% and 0.41% at first resonant frequency [63] with respect to the analytical method solution when the number of RFE is 4 (n=3) and 6 (n=5), respectively. Within our proposed model, we have chosen two cases where n=3 (3 SDEs) and n=5 (5 SDEs) to investigate the accuracy of our model.…”

Section: The Global Bond Graph Model Of the Actuatormentioning

confidence: 99%

“…In addition, evidence of the large displacement of the trilayer actuator used in this study and shown in figure 13 suggests that a nonlinear model should be developed to describe the mechanical system. Several beam modeling methods exist, such as, for a small displacement: the Euler-Bernoulli beam theory [60], the Timoshenko beam theory, and the Rayleigh-Ritz beam theory [61], and for a large displacement such as the Galerkin finite element method to solve second order nonlinear differential equations [62], as well as the RFEM [63]. RFEM allows us to take into account the nonlinear dynamic mechanical behavior of the actuator easily, and to account for inertia [39,64,65].…”

Section: Electro-mechanical Couplingmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Nguyen

Dobashi

Soyer

et al. 2018

Smart Mater. Struct.

View full text Add to dashboard Cite

Trilayer conducting polymer (CP) actuators are potential alternatives to piezoelectric and electrostatic actuators due to their large strain, and recently demonstrated operation at hundreds of Hertz. However, these actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state, when operated over their full strain range, making it more challenging to accurately predict their mechanical behavior. In this paper, an analytical multiphysics model of the CP actuators is proposed to predict their nonlinear dynamic mechanical behavior. To demonstrate the accuracy of the model, a trilayer actuator composed of a solid polymer electrolyte sandwiched between two poly(3,4-ethylenedioxythiophene) (PEDOT) electrodes was fabricated and characterized. This system consists of an electrical subsystem represented by an RC equivalent circuit, an electro-mechanical coupling matrix, and a mechanical subsystem described by using a rigid finite element method. The electrical conductivity and the volumetric capacitance, an empirical strain-to-charge ratio, and Young's modulus of the actuator as a function of the PEDOT electrode charge state were also implemented into the model, using measured values. The proposed model was represented using a bond graph formalism. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the nonlinear dynamic electrical and mechanical response of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution including dissipated, stored, and transferred energy. These are the key parameters for designing, optimizing, and controlling the actuation behavior of a trilayer actuator.

show abstract

Section: The Global Bond Graph Model Of the Actuatormentioning

confidence: 99%

Section: Electro-mechanical Couplingmentioning

confidence: 99%

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Nguyen

Dobashi

Soyer

et al. 2018

Smart Mater. Struct.

View full text Add to dashboard Cite

show abstract

“…4 A discrete model of the system (Fig. 5) is created using the rigid finite element method [3,6], where the continuous structure (Fig. 4) is divided into 152 rigid finite elements (RFE) as well as 156 spring-damping elements (SDE).…”

Section: Numerical Calculations and Resultsmentioning

confidence: 99%

“…It includes: rotary inertia, shear deformation, the gyroscopic effect as well as internal and external damping. By applying the rigid finite element method [3,6], one can obtain the following equations for the rotor:…”

Section: Model Of Discontinuous Speed-varying Rotormentioning

confidence: 99%

Hybrid Reduced Model of Rotor

Hein¹,

Orlikowski²

2013

Archive of Mechanical Engineering

View full text Add to dashboard Cite

In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

show abstract

“…In the analysis of spatial systems rfes have six degrees of freedom in the classical formulation, or three degrees of freedom in the modification limited to bending and torsional vibrations. Monograph [27], published in 2006 by an international publisher, is the recapitulation of this stage of the development of the RFEM.…”

Section: In Memory Of Professor Jan Kruszewski-majewski (1929-2012)mentioning

confidence: 99%