A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams

Sarker, Pratik; Chakravarty, Uttam K.

doi:10.1016/j.matcom.2019.10.011

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…One of the most popular strategies is the method of lines (MOL). This strategy is a semi-discrete method, which discretizes the spatial variables by keeping the time parameter [39,40]. Then, the space partial derivatives were algebraically approximated by finite differences using the dss routines and the resulting system is integrated as a function of time with the stiff integrator, ode 15 s, in MATLAB code.…”

Section: Numerical Simulation Of Mathematical Modelmentioning

confidence: 99%

Novel Insights into Activated Carbon Derived from Municipal Solid Waste for CO2 Uptake: Synthesis, Adsorption Isotherms and Scale-up

Karimi

Zafanelli

Almeida

et al. 2020

Journal of Environmental Chemical Engineering

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Recently, developing bio-based carbon materials due to the surface chemistry and a large spectrum of pore structures have received much attention. In the present work, a series of activated carbon (AC) adsorbents were synthesized from the compost derived by the mechanical/biological treatment of municipal solid wastes and evaluated regarding their CO 2 uptake. The AC samples were characterized by sulfuric acid and calcination by N 2 at 400 and 800°C. Then, the CO 2 uptake capacities were evaluated by dynamic breakthrough experiments in a temperature range of 40-100°C and pressures up to 3 bar. The presented data were properly described by Langmuir model and it was revealed that the CMSW-S-800 sample, treated with sulfuric acid and activated at 800°C, has the highest CO 2 uptake capacity with an amount adsorbed around 2.6 mol/kg at 40°C. In the next step, a mathematical model has been developed to match the experimental dynamic breakthrough data and design a pressure swing adsorption (PSA) cyclic process to evaluate the capacity and potential of the best AC sample for CO 2 adsorption. The results arising from this work showed a possible route for the application of the compost as a source of activated carbon for the sorption of greenhouse gases.

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Section: Numerical Simulation Of Mathematical Modelmentioning

confidence: 99%

Novel Insights into Activated Carbon Derived from Municipal Solid Waste for CO2 Uptake: Synthesis, Adsorption Isotherms and Scale-up

Karimi

Zafanelli

Almeida

et al. 2020

Journal of Environmental Chemical Engineering

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show abstract

“…Also, many recent studies found in the literature utilized this method as a numerical tool for solving many applied engineering problems. For example, a fourth order, forced beam vibration problem subjected to axial tension was investigated using the MOL in [18].…”

Section: Introductionmentioning

confidence: 99%

Investigations of Couette Flow Unsteady Radiative Convective Heat Transfer in a Vertical Channel Using the Generalized Method of Lines (MOL)

Sowayan

2022

International Journal of Applied Mechanics and Engineering

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This study describes a very efficient and fast numerical solution method for the non-steady free convection flow with radiation of a viscous fluid between two infinite vertical parallel walls. The method of lines (MOL) is used together with the Runge-Kutta ODE Matlab solver to investigate this problem numerically. The presence of radiation adds more stiffness and numerical complexity to the problem. A complete derivation in dimensionless form of the governing equations for momentum and energy is also included. A constant heat flux condition is applied at the left wall and a transient numerical solution is obtained for different values of the radiation parameter (R). The results are presented for dimensionless velocity, dimensionless temperature and Nusselt number for different values of the Prandtl number (Pr), Grashof number (Gr), and the radiation parameter (R). As expected, the results show that the convection heat transfer is high when the Nusselt number is high and the radiation parameter is low. It is also shown that the solution method used is simple and efficient and could be easily adopted to solve more complex problems.

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“…Using the results of the above research, the choice of reinforcement is effective in analyzing the various engineering structures. Bending, buckling, and vibration of bars (Niu et al, 2020;Radhakrishnan et al, 2020), beams (Mohammadimehr and Mehrabi, 2018;Sarker and Chakravarty, 2020;Zhao et al, 2020), plates (Avramov, 2016;Kumar Gupta and Sharma, 2012;Yuan et al, 2020), and shells (Kang, 2015;Zhang et al, 2018) are usually considered an important problem in solid mechanics and, the published articles focused on these topics and investigated different parameters in this field. Jafari-Talookolaei et al (2018) worked on free and forced vibration of a microscale Timoshenko beam subjected to a moving microparticle based on the modified couple stress theory (MCST).…”

Section: Introductionmentioning

confidence: 99%

Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

Mohammadimehr

Mehrabi

Mousavinejad

2020

Journal of Vibration and Control

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This article discusses about vibration analysis of single-/three-layered microsandwich Timoshenko beams with porous core and graphene platelet–reinforced composite face sheets under magnetic field and elastic foundation based on the modified strain gradient theory. It is assumed that the material properties of matrix and reinforcement vary in thickness directions. Hamilton’s principle based on the energy approach is used to obtain the governing equations of motions. The equations of motions are solved using a numerical differential quadrature method for various boundary conditions. The obtained results of this study are compared with other previous research studies, and there is a good agreement between them. Moreover, the effects of different parameters such as length-to-thickness ratio, magnetic field, various distributions of graphene platelets and porous beams, and volume fractions of graphene platelets are studied on the dimensionless natural frequencies. In fact, the main idea of this work is combination of structure reinforcement with magnetic field and graphene platelets on the sandwich porous beams at microscale, and the effects of these parameters are developed on the dimensionless natural frequencies of the microbeam. The results of the present study demonstrate that applying magnetic field and increasing its intensity lead to enhance the natural frequency. Also, it is showed that graphene platelet reinforcement with one percent of weight fraction has an effective effect on the increasing dimensionless natural frequencies of the microporous beam. Thus, it can be predicted that graphene platelets can be used instead of nanotubes because they do not have the problem of nanotube accumulation and they are more economical than nanotubes.

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A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams

Cited by 7 publications

References 24 publications

Novel Insights into Activated Carbon Derived from Municipal Solid Waste for CO2 Uptake: Synthesis, Adsorption Isotherms and Scale-up

Novel Insights into Activated Carbon Derived from Municipal Solid Waste for CO2 Uptake: Synthesis, Adsorption Isotherms and Scale-up

Investigations of Couette Flow Unsteady Radiative Convective Heat Transfer in a Vertical Channel Using the Generalized Method of Lines (MOL)

Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

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