A new state-space method for exponentially damped linear systems

Wu, Xinhai; He, Huan; Chen, Guoping

doi:10.1016/j.compstruc.2018.10.004

Cited by 19 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As complementary original aspect, the differentiation properties of the N exponential functions in the Prony series are leveraged to reformulate the dynamic model in an enlarged state space, including N additional viscoelastic variables. The essential and valuable consequence is that the free and forced damped dynamics turns out to be described by a coupled system of ordinary differential equations providing a straightforward state-space representation suitable for the characterization and the study of non-viscously damped systems, as also shown in [46] and, more recently, in [47]. Interestingly, the proposed mathematical formulation describing the viscoelastic behavior of internal resonators finds a strong similarity with the so-called indicial function theory adopted in aerodynamics.…”

Section: Introductionmentioning

confidence: 93%

Wave propagation in viscoelastic metamaterials via added-state formulation

Arena

Bacigalupo

Lepidi

2022

International Journal of Mechanical Sciences

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 93%

Wave propagation in viscoelastic metamaterials via added-state formulation

Arena

Bacigalupo

Lepidi

2022

International Journal of Mechanical Sciences

View full text Add to dashboard Cite

“…Whether the calculation of the response or the vibration control of a system both need the precise damping model to represent the materials and the structures of a system (Lee, 2020a). Dynamic analysis needs a suitable damping model (Lee, 2020b; Wu et al, 2019). Several researchers (Bandstra, 1983; Papoulia and Kelly, 1997; Palmeri and Muscolino, 2011) may use different damping models such as the ideal hysteretic model (Crandall, 1970), fractional derivatives model (Gaul et al, 1991) and frequency-dependent model (Naylor, 1970) in different engineering fields.…”

Section: Introductionmentioning

confidence: 99%

“…Some materials exhibit non-viscous damping behavior such as polymer materials and composite materials structures (Liu, 2018). The use of the polymer materials and composite materials in engineering is much greater than before (Wu et al, 2019). The composite damping materials are used in some engineering fields such as navigation (Mouritz et al, 2001), vehicle transport (Fan et al, 2009), aerospace (Ghiringhelli et al, 2013), and electronics industries (Rao, 2003; Zhou et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Characteristics of passive vibration control for exponential non-viscous damping system: Vibration isolator and absorber

Shen

Zhou

Lee

2022

Journal of Vibration and Control

View full text Add to dashboard Cite

Materials or structures made of polymers or composites often exhibit non-viscous damping behavior. The non-viscous damping forces that depend on the history velocity can be expressed by the exponential non-viscous damping model. Some polymer or composite materials can be used as damping materials for kinetic energy absorption in the dynamic systems. Vibration isolator and absorber are usually considered for shock absorption. In this study, transfer ratios of vibration isolator and absorber with exponential non-viscous damping system are derived by using the Laplace transform. The dimensionless amplitude of vibration absorber with exponential non-viscous damping is derived too. Compared to viscous damping system, transfer ratio and dimensionless amplitude of exponential non-viscous damping system are influenced by the ratio of the relaxation parameter and natural frequency or the frequency of the external load. With the non-viscous damping material used in vibration control, the ratio is therefore a non-negligible factor which should be considered in analysis.

show abstract

“…However, literature shows the importance of building a unified simple model to better represent the thermal system dynamics [12]. The state-space method was a subject of development for both linear and non-linear systems [13][14][15][16][17][18]. Furthermore, in thermal dynamics, the method gets interesting for its flexibility and ease-of-implementation in control and optimization models.…”

Section: Introductionmentioning

confidence: 99%

A Substitutive Coefficients Network for the Modelling of Thermal Systems: A Mono-Zone Building Case Study

et al. 2021

View full text Add to dashboard Cite

A modelling approach based on the Substitutive Coefficients Network (SCN) is developed to predict the thermal behavior of a system in the dynamic state-space, without requiring knowledge of the thermal mass. The method can apply either to large- (building, combined solar systems, geothermal energy, and thermodynamic installations) or to small-scale systems (heat exchangers, electronic devices cooling systems, and Li-ion batteries). This current method is based on a dimensionless formulation of the simplified dynamic thermal balance model, using relaxation time as a key parameter to establish the model. The introduction of relaxation time reduces the parameters set as guidance coefficients. The parameters are finally expressed by a combination of global heat transfer coefficients related to each layer and/or sub-layer of the system. Advantages of the method are reliability, “non-destructibility”, i.e., it allows a reliable prediction of the thermal behavior which experimentally is inaccessible, and reducibility of the parameters size estimate. Additionally, the method is inexpensive in terms of computation memory. It is also easy to implement in practical numerical schemes. In this paper, the method leads to a simplified mathematical model that predicts the thermal behavior of a mono-zone eco-cottage building installed at Lorraine University (in Longwy, France) as a case study. Thermal performance of the building is estimated under the hourly weather conditions onsite, as obtained from the Meteonorm software. The thermal dynamics within hourly Typical Meteorological Year 2 (TMY2) Meteonorm data disturbances and the internal heating input state in the winter period were simulated with a simplified numerical discretization method. Results provide a general dynamic state of the different sub-components of the system, with limited design of the model parameters.

show abstract

A new state-space method for exponentially damped linear systems

Cited by 19 publications

References 25 publications

Wave propagation in viscoelastic metamaterials via added-state formulation

Wave propagation in viscoelastic metamaterials via added-state formulation

Characteristics of passive vibration control for exponential non-viscous damping system: Vibration isolator and absorber

A Substitutive Coefficients Network for the Modelling of Thermal Systems: A Mono-Zone Building Case Study

Contact Info

Product

Resources

About