Prediction of Beyond Design and Residual Performances of Viscoelastic Dampers by a Simplified Fractional Derivative Model

When subjected to excessive shear deformation, viscoelastic (VE) dampers may inevitably suffer from damages, due to their VE material layers with limited thickness. Under the circumstance, their stiffness and energy dissipation capabilities may deteriorate but not totally vanish. To estimate the seismic performances of viscoelastically damped structures, the beyond design and residual performances of damaged VE dampers are crucial to protect structures from severe failure during the following main shock or aftershocks. On the other hand, for new viscoelastically damped structures under the normal design earthquakes, neglecting the residual performance of damaged VE dampers may result in nonconservative design. Thus, this study aims to provide approaches to analytically characterize the beyond design and residual performances of damaged full-scale VE dampers. Based on the simplified fractional derivative model, the analytical predictions have been compared with the experimental results. The proposed model works well for the design performance of the intact full-scale VE dampers. Particularly, it can also reproduce the beyond design and residual performances of damaged full-scale VE dampers, if due consideration is taken of the effects of excitation frequencies, ambient temperatures, temperature rises, softening, and hardening.

Download Full-text

Thermomechanical Fractional Derivative Model of Viscoelastic Isolators

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.952.219 ◽

2014 ◽

Vol 952 ◽

pp. 219-222

Author(s):

Zhen Li Zhang ◽

Chao Shang ◽

Wei Hua Shi

Keyword(s):

Fractional Derivative ◽

Engineering Application ◽

Coupling Model ◽

Measured Data ◽

Thermomechanical Coupling ◽

Damping Characteristics ◽

Fractional Derivative Model ◽

Proposed Model ◽

Vibration Process ◽

Difference Form

In vibration process, viscoelastic isolators’ temperature will rise due to energy dissipation, especially when the isolators have high damping characteristics. First, for the arbitrary loadings, the thermomechanical coupling model and the corresponding difference form are established based on the five-parameter fractional derivative model. Then, for the steady-state harmonic inputs, which is very common in engineering application, the derived model is significantly simplified by Fourier transformation. Finally, the proposed model is verified by experiments and shows a reasonable agreement with measured data.

Download Full-text

Stochastic dynamic response and reliability assessment of controlled structures with fractional derivative model of viscoelastic dampers

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2015.11.016 ◽

2016 ◽

Vol 72-73 ◽

pp. 865-896 ◽

Cited By ~ 35

Author(s):

Jun Xu ◽

Jie Li

Keyword(s):

Dynamic Response ◽

Fractional Derivative ◽

Reliability Assessment ◽

Stochastic Dynamic ◽

Viscoelastic Dampers ◽

Fractional Derivative Model ◽

Controlled Structures

Download Full-text

Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Earthquake Engineering and Engineering Vibration ◽

10.1007/s11803-002-0070-5 ◽

2002 ◽

Vol 1 (2) ◽

pp. 251-260 ◽

Cited By ~ 24

Author(s):

Tsu-sheng Chang ◽

Mahendra P. Singh

Keyword(s):

Fractional Derivative ◽

Seismic Analysis ◽

Viscoelastic Dampers ◽

Fractional Derivative Model

Download Full-text

A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-013-0006-y ◽

2013 ◽

Vol 16 (1) ◽

Cited By ~ 35

Author(s):

Wen Chen ◽

Jianjun Zhang ◽

Jinyang Zhang

Keyword(s):

Fractional Derivative ◽

Measurement Data ◽

Chloride Ions ◽

Chloride Diffusion ◽

Influence Coefficient ◽

Variable Order ◽

Binding Behavior ◽

Fractional Derivative Model ◽

Proposed Model ◽

Variable Function

AbstractThis study proposes a new variable-order fractional diffusion equation model to describe the coupled chloride diffusion-binding processes in reinforced concrete, in which the order of fractional derivative term is a variable function instead of a constant in the standard fractional model. The concentration influence coefficient k is introduced to capture the effect of concentration dependency on chloride transport due to the chloride binding behavior. The two parameters in the proposed model can be determined directly by a statistical analysis of measurement data. Four test cases illustrate that the proposed variable-order fractional derivative model agrees significantly better with experimental data than the most commonly used traditional model governed by the classical Fick’s second law, especially when a large concentration coefficient k is involved. That proposed model is also verified by accurately predicting chloride concentration profiles in a period of 200 days.

Download Full-text

Computational and experimental studies of the strength of full-scale samples of pipes with defects "metal loss" and "dent with groove"

SCIENCE & TECHNOLOGIES OIL AND OIL PRODUCTS PIPELINE TRANSPORTATION ◽

10.28999/2541-9595-2020-10-3-226-233 ◽

2020 ◽

Vol 10 (3) ◽

pp. 226-233

Author(s):

Dmitry A. Neganov ◽

◽

Victor M. Varshitsky ◽

Andrey A. Belkin ◽

◽

...

Keyword(s):

Internal Pressure ◽

Experimental Studies ◽

Full Scale ◽

The Other ◽

Metal Loss ◽

Calculation Methods ◽

Reliable Operation ◽

Sufficient Stability ◽

Comparative Results ◽

The Moment

The article contains the comparative results of the experimental and calculated research of the strength of a pipeline with such defects as “metal loss” and “dent with groove”. Two coils with diameter of 820 mm and the thickness of 9 mm of 19G steel were used for full-scale pipe sample production. One of the coils was intentionally damaged by machining, which resulted in “metal loss” defect, the other one was dented (by press machine) and got groove mark (by chisel). The testing of pipe samples was performed by applying static internal pressure to the moment of collapse. The calculation of deterioration pressure was carried out with the use of national and foreign methodical approaches. The calculated values of collapsing pressure for the pipe with loss of metal mainly coincided with the calculation experiment results based on Russian method and ASME B31G. In case of pipe with dent and groove the calculated value of collapsing pressure demonstrated greater coincidence with Russian method and to a lesser extent with API 579/ASME FFS-1. In whole, all calculation methods demonstrate sufficient stability of results, which provides reliable operation of pipelines with defects.

Download Full-text

Caputo Fractional Derivative and Quantum-Like Coherence

Entropy ◽

10.3390/e23020211 ◽

2021 ◽

Vol 23 (2) ◽

pp. 211

Author(s):

Garland Culbreth ◽

Mauro Bologna ◽

Bruce J. West ◽

Paolo Grigolini

Keyword(s):

Diffusion Equation ◽

Fractional Derivative ◽

Anomalous Diffusion ◽

Caputo Fractional Derivative ◽

Quantum Coherence ◽

Time Derivative ◽

The Other ◽

Diffusion Equations ◽

Self Organization ◽

Ordinary Time

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

Download Full-text