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Analysis of a nonlinear tuned mass damper by using the multi-scale method

Liu Junfeng, Yao Ji, Huang Kun, Zhang Qing, Ze Li

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 3

463--477

EN

A tuned mass damper is a kind of vibration damping device which has been widely used in tall buildings, machinery, bridges, aerospace engineering and other fields. In practical engineering applications, due to large deformation caused by large displacement, errors in engineering constructions and the existence of limit devices, the structure and tuned mass dampers inevitably produce some nonlinear characteristics, but these nonlinearities are often ignored. The results of this study confirm that the nonlinearity of the structure and the mass damper should be considered in the process of optimal frequency design, otherwise there will be a large deviation between the design optimal frequency of the mass damper and the actual optimal frequency. In this paper, nonlinear characteristics of the tuned mass damper and the main structure are considered. The first-order differential equations are obtained by using the complex average method, and the nonlinear equations of the tuned mass damper system are derived by using the multi-scale method. On this basis, the parameters are determined. The numerical results show that the error of the approximate solution method is small in the given example. The nonlinear tuned mass damper with nonlinear design exhibits a better control performance.

2

A crystal plasticity finite element-based approach to model the constitutive behavior of multi-phase steels

Liu Hongguang, Shin Yung C.

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 2

707--720

EN

Steels are the most commonly used multi-phase materials in the industry, and their mechanical behaviors depend on the microstructure, composition, and phase fractions. Generally, the material behaviors need to be measured by experiments like a tensile test or split Hopkinson bar test, which is very time-consuming and expensive. Once the heat treatment and phase fractions are changed, it needs to be tested again, and, to avoid this, a better method is required to obtain the material behavior quickly and easily. In this study, a novel multi-scale approach is described to predict the material behaviors of multi-phase steels based on the phase fractions. A crystal plasticity finite element method is used to obtain the material behavior of each phase at a micro-scale with elevated strain rates, which is validated with experimental data or theoretical models at static or quasi-static conditions. Then a homogenization procedure with the rule of mixture method, which is based on the phase fractions measured from the microstructure characterization, is used to get the macro-scale constitutive behavior, and it is then implemented into the commercial software Abaqus/Standard to simulate the process of tensile test and compared with the experimental data. Good agreements are obtained between simulation and experimental results.

3

Investigation of crack resistance in epoxy/boron nitride nanotube nanocomposites based on multi-scale methodInvestigation of crack resistance in epoxy/boron nitride nanotube nanocomposites based on multi-scale method

Hemmatian Hossein, Zamani Mohammad Reza, Jam Jafar Eskandari

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 1

207--219

EN

Boron nitride nanotubes (BNNTs) possess superior mechanical, thermal and electrical properties and are also suitable for biocomposites. These properties make them a favorable reinforcement for nanocomposites. Since experimental studies on nanocomposites are timeconsuming, costly, and require accurate implementation, finite element analysis is used for nanocomposite modeling. In this work, a representative volume element (RVE) of epoxy/BNNT nanocomposites based on multi-scale modeling is considered. The bonds of BNNT are modeled by 3D beam elements. Also non-linear spring elements are employed to simulate the van der Waals bonds between the nanotube and matrix based on the Lennard- -Jones potential. Young’s and shear modulus of BNNTs are in ranges of 1.039-1.041 TPa and 0.44-0.52 TPa, respectively. Three fracture modes (opening, shearing, and tearing) have been simulated and stress intensity factors have been determined for a pure matrix and nanocomposite by J integral. Numerical results indicate that by incorporation of BNNT in the epoxy matrix, stress intensity factors of three modes decrease. Also, by increasing the chirality of BNNT, crack resistance of shearing and tearing modes are enhanced, and stress intensity factor of opening mode reduced. BNNTs bridge the crack surface and prevent crack propagation.