Computational Modelling and Analysis of Effect of Viscoelastic Materials on Damping and Vibrational Behaviors of Composite Structures—An Extensive Review

Elmoghazy, Yasser Hamed; Safaei, Babak; Asmael, Mohammed; Sahmani, Saeid; Zeeshan, Qasim; Qin, Zhaoye

doi:10.1007/s11831-023-10057-4

Cited by 2 publications

(3 citation statements)

References 275 publications

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“…In the case (b) β = α, for the set of model parameters G 2 (20), the FMM (2) is described by the power-law relaxation modulus G M (t, g) (10) and the absolute boundness of the gradient ∇ g G M (t, g) is resolved by the next result proved in Appendix A.2. Theorem 2.…”

Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 93%

“…Theorem 2. Let G 2 , defined by (20), be the set of the fractional Maxwell model admissible parameters with equal parametersα and β. Then, the relaxation modulus G M (t, g) (10) of the model ( 9) is continuous and differentiable with respect to g (8) for any time t ∈ T and sup t∈T ,g∈G 2…”

Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 99%

“…Describing the rheological properties of polymers by the FMM [18,19] is well known. However, the FMM was also applied, for example, for computational modeling and analysis on the damping and vibrational behaviors of viscoelastic composite structures [20], viscoelastic flow in a circular pipe [21], effect of temperature on the dynamic properties of mixed surfactant adsorbed layers at the water/hexane interface [22,23] and constitutive equations of the Mn-Cu damping alloy [24]. Fractional viscoelasticity described by the Maxwell model turned out to model both exponential and non-exponential relaxation phenomena in real materials.…”

Section: Introductionmentioning

confidence: 99%

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Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Stankiewicz

2024

Materials

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Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model. A weighted least-square approximation problem of the relaxation modulus by the fractional Maxwell model is considered when only the time measurements of the relaxation modulus corrupted by additive noises are accessible for identification. This study was dedicated to the determination of the model, optimal in the sense of the integral square weighted model quality index, which does not depend on the particular sampling points applied in the stress relaxation experiment. It is proved that even when the real description of the material relaxation modulus is entirely unknown, the optimal fractional Maxwell model parameters can be recovered from the relaxation modulus measurements recorded for sampling time points selected randomly according to respective randomization. The identified model is a strongly consistent estimate of the desired optimal model. The exponential convergence rate is demonstrated both by the stochastic convergence analysis and by the numerical studies. A simple scheme for the optimal model identification is given. Numerical studies are presented for the materials described by the short relaxation times of the unimodal Gauss-like relaxation spectrum and the long relaxation times of the Baumgaertel, Schausberger and Winter spectrum. These studies have shown that the appropriate randomization introduced in the selection of sampling points guarantees that the sequence of the optimal fractional Maxwell model parameters asymptotically converge to parameters independent of these sampling points. The robustness of the identified model to the measurement disturbances was demonstrated by analytical analysis and numerical studies.

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Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 93%

Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Stankiewicz

2024

Materials

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Vibration Behavior of 3D-Printed Graded Composites: Fabrication and Testing

Khan,

Singh,

Carter

2024

Polymers

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Multi-head 3D printers afford the ability to create composite structures with significant differences in properties compared to those created through traditional molding techniques. In addition to the usage of different viscoelastic polymeric materials, the selective spatial placement of the build materials enables the creation of layered and graded geometries to achieve specific mechanical and/or vibrational characteristics. This paper describes how the mechanical properties of the individual materials can be used to predict the damping and natural frequencies of a 3D-printed graded structure. Such structures can find usage in rotating machinery, beams, etc., where vibrational characteristics must be controlled. The simulation and experimental results are presented and two forms of the storage and loss modulus are considered: fixed and variable. For the latter condition, E′ and E″ are established as functions of temperature and frequency. Modal vibration testing of the graded samples shows a good match between the simulation and experimental trials, thereby supporting the proposed model as a useful tool for prescribing the structure of a printed part with tailored dynamic properties.

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Computational Modelling and Analysis of Effect of Viscoelastic Materials on Damping and Vibrational Behaviors of Composite Structures—An Extensive Review

Cited by 2 publications

References 275 publications

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Vibration Behavior of 3D-Printed Graded Composites: Fabrication and Testing

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