Abstract:Many authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency-and temperaturedependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very co… Show more
“…This strategy is originally described here for nonlinear strain measure, but was inspired in Mesquita and Coda (2002), Mesquita and Coda (2003) and Mesquita and Coda (2007) where linear viscoelastic models are proposed. As far as the authors knowledge goes it is different from all nonlinear viscoelastic formulations present in literature, see for example, Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000), Petiteau et al (2013), Marko et al (2006) and Clough and Penzien (1985).…”
Section: Latin American Journal Of Solids and Structures 13 (2016) 96mentioning
confidence: 86%
“…Moreover, the dampers used in such devices can be represented by viscous constitutive models that, associated with their stiffness, result in viscoelastic models similar to the Kelvin/Voigt one. The treatment of these linear and nonlinear viscoelastic formulations is usually done by more or less complicated traditional convolution techniques or decaying functions as explained by Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000) and Petiteau et al (2013) used or not in vibration control (Marko et al (2006) and Clough and Penzien (1985)). There are no significant differences regarding the traditional rheological viscoelastic approach of materials in all consulted bibliography.…”
This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique
“…This strategy is originally described here for nonlinear strain measure, but was inspired in Mesquita and Coda (2002), Mesquita and Coda (2003) and Mesquita and Coda (2007) where linear viscoelastic models are proposed. As far as the authors knowledge goes it is different from all nonlinear viscoelastic formulations present in literature, see for example, Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000), Petiteau et al (2013), Marko et al (2006) and Clough and Penzien (1985).…”
Section: Latin American Journal Of Solids and Structures 13 (2016) 96mentioning
confidence: 86%
“…Moreover, the dampers used in such devices can be represented by viscous constitutive models that, associated with their stiffness, result in viscoelastic models similar to the Kelvin/Voigt one. The treatment of these linear and nonlinear viscoelastic formulations is usually done by more or less complicated traditional convolution techniques or decaying functions as explained by Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000) and Petiteau et al (2013) used or not in vibration control (Marko et al (2006) and Clough and Penzien (1985)). There are no significant differences regarding the traditional rheological viscoelastic approach of materials in all consulted bibliography.…”
This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique
“…The temperatures at points A and C of the specimen were measured by using thermocouples and its signal was acquired and processed by a signal analyzer Agilent 34970. Also, in all tests, a vertical displacement, To compare the simulations obtained previously with the acquired experimental results, the static displacement of the viscoelastic material was computed based on the tangent stiffness matrix concept (de Lima et al, 2015a). Also, it is assumed that only the viscoelastic cores are deformed during the application of the static displacements by the screws.…”
The good damping performance and inherent stability of viscoelastic materials in relatively broad frequency bands, besides cost effectiveness, offers many possibilities for practical engineering applications. However, for viscoelastic dampers subjected to dynamic loadings superimposed on static preloads, especially when good isolation characteristics are required at high frequencies, traditional design guidelines can lead to poor designs due to the rapidly increasing rate of temperature change inside the material. This paper is devoted to the numerical and experimental investigation in the degradation of the stiffness and capacity of a viscoelastic material induced by the thermal runaway phase, when it is subjected to dynamic and static loads simultaneously. After the theoretical background, the obtained results in terms of the temperature evolutions at different points within the volume of the material and the hysteresis loops for various static preloads are compared and the main features of the proposed study are highlighted.
“…In the quest for analyzing and synthesizing viscoelastically damped structures, one of the primary tasks is to model the rheological behavior of viscoelastic materials. However, this is also a challenge work due to the high dependency on viscoelastic materials of operational and environmental factors such as vibration frequency, external temperature, pre-loads, etc [2].…”
This paper proposes fractional sliding control designs for single-degree-of-freedom fractional oscillators respectively of the Kelvin-Voigt type, the modified Kelvin-Voigt type and Düffing type, whose dynamical behaviors are described by second-order differential equations involving fractional derivatives. Firstly, the differential equations of motion are transformed into non-commensurate fractional state equations by introducing state variables with physical significance. Secondly, fractional sliding manifolds are constructed and stability of the corresponding sliding dynamics is addressed via the infinite state approach and Lyapunov stability theory. Thirdly, sliding control laws and adaptive sliding laws are designed for fractional oscillators respectively in cases that the bound of the external exciting force is known or unknown. Finally, numerical simulations are carried out to validate the above control designs.
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