Showing papers in "Applied and Computational Mechanics in 2021"

Theoretical Study of Convective Heat Transfer in Ternary Nanofluid Flowing past a Stretching Sheet

Abstract: A new theoretical tri-hybrid nanofluid model for enhancing the heat transfer is presented in this article. This model explains the method to obtain a better heat conductor than the hybrid nanofluid. The tri-hybrid nanofluid is formed by suspending three types of nanoparticles with different physical and chemical bonds into a base fluid. In this study, the nanoparticles TiO2, Al2O3 and SiO2 are suspended into water thus forming the combination TiO2-SiO2-Al2O3-H2O. This combination helps in decomposing harmful substances, environmental purification and other appliances that requires cooling. The properties of tri-hybrid nanofluid such as Density, Viscosity, Thermal Conductivity, Electrical Conductivity and Specific Heat capacitance are defined mathematically in this article. The system of equations that governs the flow and temperature of the fluid are converted to ordinary differential equations and are solved using RKF-45 method. The results are discussed through graphs and it is observed that the tri-hybrid nanofluid has a better thermal conductivity than the hybrid nanofluid.

Free Vibration Analysis of FG Porous Sandwich Plates under Various Boundary Conditions

Abstract: In the present work, free vibration analysis of the square sandwich plate with functionally graded (FG) porous face sheets and isotropic homogenous core is performed under various boundary conditions For this purpose, the material properties of the sandwich plate are supposed to vary continuously through the thickness direction according to the volume fraction of constituents defined with the modified rule of the mixture including porosity volume fraction with four different types of porosity distribution over the cross-section Furthermore, a hyperbolic shear displacement theory is used in the kinematic relation of the FG porous sandwich plate, and the equations of motion are derived utilizing Hamilton’s principle Analytical solutions are achieved for free vibration analysis of square sandwich plates with FG porous face sheets under various boundary conditions, ie combinations of clamped (C), simply supported (SS), and free (F) edges are presented Several parametrical studies are conducted to examine the effects of porosity volume fraction, type of porosity distribution model, lay-up scheme, side to thickness ratio, and boundary conditions on the free vibration of the FG sandwich plates Finally, it is concluded that the investigated parameters have significant effects on the free vibration of the FG sandwich plates and the negative effects of porosity may be reduced by adopting suitable values for said parameters, considerably

Comparative Study of Mixed Convective MHD Cu-Water Nanofluid Flow over a Cone and Wedge using Modified Buongiorno’s Model in Presence of Thermal Radiation and Chemical Reaction via Cattaneo-Christov Double Diffusion Model

Abstract: The steady Cu-water nanofluid flow in presence of magnetic field is investigated numerically under the effects of mixed convection, thermal radiation and chemical reaction. For investigating the nanofluid flow, the flow over two different geometries, cone and wedge have been considered. The Tiwari and Das nanofluid model is implemented together with Buongiorno nanofluid model. Thermal and concentration diffusion are studied using the Cattaneo-Christov double diffusion model. At the boundary of the surface, no slip and zero mass flux condition are implemented to control the nanoparticle volume fraction at surface. Constitutive laws of flow are obtained in form of ordinary differential equations by the use of similarity transformation. The modeled flow problem is solved numerically by the Runge-Kutta-Fehlberg method and shooting scheme. Variation in flow properties due to parameters involved is presented graphically and through tabular values. The effect of thermal radiation and thermal relaxation parameter is to increase heat transfer. The temperature of nanofluid and drag force at surface increases due to enhanced magnetic field. The nanoparticles are found to be concentrated near the surface of cone and wedge but concentration decreases with chemical reaction parameter and Schmidt number as fluid moves towards far field.

ADM Solution for Cu/CuO –Water Viscoplastic Nanofluid Transient Slip Flow from a Porous Stretching Sheet with Entropy Generation, Convective Wall Temperature and Radiative Effects

Abstract: A mathematical modelis presented for entropy generation in transient hydromagnetic flow of an electroconductive magnetic Casson (non-Newtonian) nanofluid over a porous stretching sheet in a permeable medium. The Cattaneo-Christov heat flux model is employed to simulate non-Fourier (thermal relaxation) effects. A Rosseland flux model is implemented to model radiative heat transfer. The Darcy model is employed for the porous media bulk drag effect. Momentum slip is also included to simulate non-adherence of the nanofluid at the wall. The transformed, dimensionless governing equations and boundary conditions (featuring velocity slip and convective temperature) characterizing the flow are solved with the Adomian Decomposition Method (ADM). Bejan’s entropy minimization generation method is employed. Cu-water and CuO-water nanofluids are considered. Extensive visualization of velocity, temperature and entropy generation number profiles is presented for variation in magnetic field parameter, unsteadiness parameter, Casson parameter, nanofluid volume fraction, permeability parameter, suction/injection parameter, radiative parameter, Biot number, relaxation time parameter, velocity slip parameter, Brinkman number (dissipation parameter), temperature ratio and Prandtl number. The evolution of skin friction and local Nusselt number (wall heat transfer rate) are also studied. The ADM computations are validated with simpler models from the literature. The solutions show that with elevation in volume fraction of nanoparticle and Brinkman number, the entropy generation magnitudes are increased. An increase in Darcy number also increases the skin friction and local Nusselt number. Increasing magnetic field, volume fraction, unsteadiness, thermal radiation, velocity slip, Casson parameters, Darcy and Biot numbers are all observed to boost temperatures. However, temperatures are reduced with increasing non-Fourier (thermal relaxation) parameter. Greater flow acceleration is achieved for CuO-water nanofluid compared with Cu-water nanofluid although the contrary response is computed in temperature distributions. The simulations are relevant to the high temperature manufacturing fluid dynamics of magnetic nanoliquids, smart coating systems etc.

A Variational Principle for a Nonlinear Oscillator Arising in the Microelectromechanical System

Abstract: A nonlinear oscillator arising in the microelectromechanical system is complex and it is difficult to obtain a variational principle. This paper begins with a wrong variational formulation and uses the semi-inverse method to obtain a genuine variational principle. Additionally, this paper gives simple formula for the fast frequency estimation of the nonlinear oscillator. Only simple calculation is needed to have a relatively high accuracy results when compared with the other methods.

Heat Transport Exploration of Free Convection Flow inside Enclosure Having Vertical Wavy Walls

Abstract: This paper expresses a numerical study of flow features and heat transport inside enclosure. Governing equations will be discretized by finite-element process with a collected variable arrangement. The assumptions of the Grashof number (103 - 106), aspect ratio (1.0 – 2.0), wave ratio (0.0 - 0.40) concerning a fluid with Pr = 0.71. Streamlines and isotherm lines are utilized to show the corresponding flow and thermal field inside a cavity. Global and local distributions Nusselt numbers are displayed for the before configuration. Finally, velocity and temperature profiles are displayed for some selected positions inside an enclosure for a better perception of the flow and thermal field.

MHD Oldroyd-B Fluid with Slip Condition in view of Local and Nonlocal Kernels

Abstract: We examine the velocity field of an incompressible Oldroyd-B fluid over a horizontal plate of continual length in a permeable medium with magnetohydrodynamics effect. Firstly, the results for the dimensionless classical model (governing equation) have been studied analytically then the study is extended for different fractional operators. The relations to determine the velocity fields of this problem are found by Laplace transformation and different numerical inversion algorithms. The impact of physical parameters on velocity profiles is analyzed graphically for integer and non-integer models. Non-integer operators are used to analyzing the impact of fractional parameters on the fluid curves of the fluid.

Influence of Thermophysical Features on MHD Squeezed Flow of Dissipative Casson Fluid with Chemical and Radiative Effects

Abstract: Theoretical investigation of variable mass diffusivity, thermal conductivity, and viscosity on unsteady squeezed flow of dissipative Casson fluid is presented. Physically, for any effective heat and mass transfer process, a proper account of thermophysical properties in such a system is required to attain the desired production output. The magnetized free convective flow of unsteady Casson fluid encompassing Joule dissipation, radiation, and chemical reactive influence is induced as a result of squeezing property. The governing model assisting the magnetized flow is formulated and transformed via an appropriate similarity transformation. The resulting set of ordinary differential equations is solved numerically using Chebyshev based Collocation Approach (CCA). However, variable viscosity, thermal conductivity, and mass diffusivity effects are seen to diminish the fluid flow velocities, temperature, and concentration respectively along with the lower plate. Heat and mass transfer coefficient, skin friction downsized to an increasing value of variable thermal and mass diffusivity parameters while variable viscosity pronounces the skin friction coefficient. Furthermore, the present analysis is applicable in polymer processing, such as injection molding, extrusion, thermoforming among others.

A Fractal Rheological Model for SiC Paste using a Fractal Derivative

Abstract: The rheological property plays an important role in a free-form extrusion 3D printing process, no rheological model was available in open literature that could effectively take into account effects of both the non-Newtonian viscosity and the concentration of nano/micro particles in a paste. Here a fractal law for non-Newtonian fluids is suggested using a fractal derivative, the law can predict correctly the boundary effect of a viscous flow, and can model effectively the nonlinear velocity distribution across the section. A systematic derivation of a fractal rheological model is suggested using the basic laws in the fluid mechanics, which can provide a deep insight into the two-scale fractal interpretation of non-Newtonian fluids. An experiment was carefully designed to verify the model and to elucidate the relationship between the shear rate and viscosity of the SiC paste. 15wt.%, 25wt.%, 35wt.% and 45wt.% SiC pastes were prepared by using mixing, stirring and ball milling processes. The rheology of the paste can be controlled primarily through the SiC concentration, which affects the fractal order. The fractal model sheds a bright light on a simple but accurate approach to non-Newtonian fluids.

Analysis of Dual Solutions of Unsteady Micropolar Hybrid Nanofluid Flow over a Stretching/Shrinking Sheet

Abstract: An unsteady boundary layer flow of a micropolar hybrid nanofluid over a stretching/shrinking sheet is analyzed. The nonlinear ordinary differential equations of the problem have been solved using the efficient implicit Runge–Kutta–Butcher method along with Nachtsheim–Swigert iteration technique. For a certain set of parameters, numerical results expose dual solutions with the change of the velocity ratio parameter. The dual solutions are presented in a wide range of the physical parameters. Using a lot of numerical data, the critical values of the velocity ratio parameter, local friction factor, local couple-stress and local Nusselt number for the existence of dual solutions are expressed as a function of the physical parameters. These expressions might be useful for the development of new technology or for the future experimental investigation.

A Novel Fractional-Order System: Chaos, Hyperchaos and Applications to Linear Control

Abstract: Chaos and hyperchaos are generated from a new fractional-order system. Local stability of the system’s three equilibria is analyzed when the fractional parameter belongs to (0,2]. According to Hopf bifurcation theory in fractional-order systems, approximations to the periodic solutions around the system’s three equilibria are explored. Lyapunov exponents, Lyapunov spectrum and bifurcation diagrams are computed and chaotic (hyperchaotic) attractors are depicted. Furthermore, a linear control technique (LFGC) based on Lyapunov stability theory is implemented to derive the hyperchaotic states of the proposed system to its three equilibrium points. Numerical results are used to validate the theoretical results.

Role of Magnetic field on the Dynamical Analysis of Second Grade Fluid: An Optimal Solution subject to Non-integer Differentiable Operators

Abstract: The dynamical analysis of MHD second grade fluid based on their physical properties has stronger resistance capabilities, low-frequency responses, lower energy consumption, and higher sensitivities; due to these facts externally applied magnetic field always takes the forms of diamagnetic, ferromagnetic and paramagnetic. The mathematical modeling based on the fractional treatment of governing equation subject to the temperature distribution, concentration, and velocity field is developed within a porous surfaced plate. Fractional differential operators with and without non-locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. The fractionalized analytical solutions have been traced out separately through Atangana-Baleanu and Caputo-Fabrizio fractional differential operators. Our results suggest that the velocity profile decrease by increasing the value of the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.

MHD Non-Newtonian Fluid Flow past a Stretching Sheet under the Influence of Non-linear Radiation and Viscous Dissipation

Abstract: This work reports the heat and mass transfer of the 2- D MHD flow of the Casson and Williamson motions under the impression of non-linear radiation, viscous dissipation, and thermo-diffusion and Dufour impacts. The flow is examined through an extending zone along with inconsistent thickness. The partial differential equations are extremely nonlinear and lessen to ODEs throughout of the appropriate similarity transformation. The system of nonlinear and coupled ODEs is handled applying a numerical approach with shooting procedure. Numerical solutions for momentum and energy descriptions are deliberated through graphs and tabular form for the impacts of magnetic parameter, Soret and Dufour variables, momentum power index variable, Schmidt number, wall thickness variable, without dimensions velocity slip, heat jump and mass jump variable. Outcomes illustrate that the momentum, temperature, and concentration transfer of the laminar boundary layers of equally non-Newtonian liquid motions are non-consistent. A comparison made with the existing literature which shows an good agreement and confidence of the present outcomes. It shows that Casson parameter restricted the skin friction, local heat and mass transfer while l enhanced the skin friction, local heat and mass transfer. Velocity slip constant decreases the skin friction, local heat and mass transfer and a similar observation for thermal slip constant while an opposite phenomena for the solutal slip constant.

Free Vibration Analysis of Functionally Graded Porous Nano-plates with Different Shapes Resting on Elastic Foundation

Abstract: This paper proposes a finite element method (FEM) based on a nonlocal theory for analyzing the free vibration of the functionally graded porous (FGP) nano-plate with different shapes lying on the elastic foundation (EF). The FGP materials with two-parameter are the power-law index (k) and the porosity volume fraction (ξ) in two cases of even and uneven porosity. The EF includes Winkler stiffness (k1) and Pasternak stiffness (k2). Some numerical results in our work are compared with other published to verify accuracy and reliability. Moreover, the influence of geometric parameters, materials on the free vibration of the FGP nano-plates resting on the EF is comprehensively investigated.

Effects of Non-Linear Thermal Radiation and Chemical Reaction on Time Dependent Flow of Williamson Nanofluid With Combine Electrical MHD and Activation Energy

Abstract: The current article will present the impact of the heat and mass transfer of combine electrical MHD flow of time dependent Williamson fluid with nanoparticles by the incorporating the influences of non-linear thermal radiation and the chemical reaction through wedge shape geometry. The fluid flows past a porous stretching wedge with convected Nield boundary conditions. The several (geometrical and physical) conditions have been included to provide more practicable results. The effects of activation energy further discussed. Due to relevant similarity transformation, set of partial differential equations which is non-linear and complicated is converted into simplest system of ordinary differential equations. To obtain the desired solution, famous numerical technique (shooting) used with the help of bvp4c MATLAB coding. The variation physical quantities namely velocity, temperature, concentration of nanoparticles, local Sherwood number, coefficient of skin friction and local Nusselt number have been observed under the influence of emerging parameters. The elaborated discussion presented with graphical and tabular illustrations.

The Rank Upgrading Technique for a Harmonic Restoring Force of Nonlinear Oscillators

Abstract: An enhanced analytical technique for nonlinear oscillators having a harmonic restoring force is proposed. The approach is passed on the change of the auxiliary operator by another suitable one leads to obtain a periodic solution. The fundamental idea of the new approach is based on obtaining an alternative equation free of the harmonic restoring forces. This method is a modification of the homotopy perturbation method. The approach allows not only an actual periodic solution but also the frequency of the problem as a function of the amplitude of oscillation. Three nonlinear oscillators including restoring force, the simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon equation are offered to clarify the effectiveness and usefulness of the proposed technique. This approach allows an effective mathematical approach to noise and uncertain properties of nonlinear vibrations arising in physics and engineering.

Unsteady MHD Mixed Convection Flow of Water over a Sphere with Mass Transfer

Abstract: This paper examines the unsteady magnetohydrodynamic (MHD) mixed convection flow over a sphere combined with variable fluid properties. An implicit finite difference scheme, together with the quasi-linearization, is used to find non-similar solutions for the governing equations. The vanishing skin friction is prevented or at least delayed by enhancing the mixed convection in both the cases of steady and unsteady fluid flow. Both skin friction and heat transfer coefficients are found to be increasing with an increase in time or MHD parameter.

A review on stress-driven nonlocal elasticity theory

Abstract: The behavior of materials at the nanoscale cannot be studied by classical theories. Accordingly, new theories have been developed to predict the behavior of materials at the nanoscale; some of them are nonlocal elasticity, strain gradient theory, couple stress theory, and surface effect theory. In most articles, the authors use a differential form of nonlocal elasticity theory. Recently, many authors have used the integral form of this theory and obtained interesting results. Therefore, in the present research, the articles related to the integral form of non-local theory have been examined for small-scale tubes, beams, shells, and plates.

On the Usefulness of Pre-processing Methods in Rotating Machines Faults Classification using Artificial Neural Network

Abstract: This work presents a multi-fault classification system using artificial neural network (ANN) to distinguish between different faults in rotating machines automatically. Rotation frequency and statistical features, including mean, entropy, and kurtosis were considered in the proposed model. The effectiveness of this model lies in using Synthetic Minority Over-sampling Technique (SMOTE) to overcome the problem of imbalance data classes. Furthermore, the Relief feature selection method was used to find the most influencing features and thus improve the performance of the model. Machinery Fault Database (MAFAULDA) was deployed to evaluate the performance of the prediction models, achieving an accuracy of 97.1% which surpasses other literature that used the same database. Results indicate that handling imbalance classes hold a key role in increasing the overall accuracy and generalizability of multi-layer perceptron (MLP) classifier. Furthermore, results showed that considering only statistical features and rotational speed are good enough to get a model with high classification accuracy.

Thermodynamic and Environmental Assessment of Mounting Fin at the Back Surface of Photovoltaic Panels

Abstract: Nowadays, researches on different kinds of renewable energies including photovoltaic technology are developing rapidly. It is proved that the output power of a PV cell is reduced by increasing the temperature. In this paper, mounting aluminum fins at the back surface of the PV module is proposed as a simple and low-cost method to decrease the PV cell temperature. It was found that using aluminum fins caused more than 7°C reduction in the cell temperature. Besides, it was shown that the entropy generation of the PV module with fin, was 3.5% lower than the conventional one. Also, the positive environmental impacts of using fins at the back surface of the PV module were estimated by RETScreen software, so that it, leads to enhance the performance of the PV power plant by more than 25 %, from an environmental viewpoint.

Modeling beam-like planar structures by a one-dimensional continuum: an analytical-numerical method

Abstract: In this paper, beam-like structures, macroscopically behaving as planar Timoshenko beams, are considered. Planar frames, made by periodic assemblies of micro-beams and columns, are taken as examples of these structures and the effectiveness of the equivalent beam model in describing their mechanical behavior, is investigated. The Timoshenko beam (coarse model) is formulated via the direct one-dimensional approach, by considering rigid cross-sections and flexible axis-line, while its constitutive laws is determined through a homogenization procedure. An identification algorithm for evaluation of the constitutive constants is illustrated, based on Finite Element analyses of the cell of the periodic system. The inertial properties of the equivalent model are instead analytically identified under the hypothesis the masses are lumped at the joints. The advantages in using the equivalent model are discussed with reference to the linear static and dynamic responses of some planar frames, taken as case-studies, for which both analytical and numerical tools are used. Numerical results, obtained by the equivalent model, are compared with Finite Element analyses on planar frames (fine models), considering both symmetric and not-symmetric layouts, in order to show to effectiveness of the proposed algorithm. A comparison with analytical results is carried out to validate the limits of applicability of the method.

Unsteady Separated Stagnation Point Flow of Nanofluid past a Moving Flat Surface in the Presence of Buongiorno's Model

Abstract: This paper explores energy and mass transport behavior of unstable separated stagnation point flow of nanofluid over a moving flat surface along with Buongiorno’s model. Characteristic of Brownian diffusion and thermophoresis are considered. Additionally, characteristics of chemical reaction is taken into account. A parametric investigation is performed to investigate the outcome of abundant parameters such as temperature, velocity and concentration. An appropriate equation is converting into a set of ODEs through employing appropriate transformation. The governing equations has been solved numerically by using the classical fourth-order Runge-Kutta integration technique combined with the conventional shooting procedure after adapting it into an initial value problem. Our findings depict that the temperature field θ(ζ) improves for augmenting values of theromophoresis parameter (Nt) with dual solutions of attached flow without inflection and flow with inflection. Also, the difference of Brownian motion parameter (Nb) with two different solutions of attached flow exists with energy profile. It can be found that an energy profile θ(ζ) elevates due to augmenting values of (Nb). It has been perceived that thermal boundary layer thickness elevates due to large amount of Brownian motion parameter (Nb).

Approximate Solutions of Coupled Nonlinear Oscillations: Stability Analysis

Abstract: The current article is concerned with a comprehensive investigation in achieving approximate solutions of coupled nonlinear oscillations with high nonlinearity. These equations are highly nonlinear second-order ordinary differential equations. Via a coupling of the Homotopy perturbation method and Laplace transforms, which is so-called the He-Laplace method, traditional approximate solutions involving the secular terms are accomplished. On the other hand, in order to cancel the secular terms, an expanded frequency technique is adapted to accomplish periodic approximate solutions. Therefore, a nonlinear frequency, for each differential equation, is achieved. Furthermore, for more convenience, these solutions are pictured to indicate their behavior. The multiple time-scales with the aid of the Homotopy concept are utilized to judge the stability criteria. The analyses reveal the resonance as well as the non-resonant cases. Additionally, numerical calculations are carried out, graphically, to address the regions that guaranteed the bounded solutions. It is found that the latter method, is the most powerful mathematical tool in extracting the stability analysis of the considered system.

Analysis of Axisymmetric Vibration of Functionally-Graded Circular Nano-Plate Based on the Integral Form of the Strain Gradient Model

Abstract: In this paper, it is aimed to analyze the linear vibrational behavior of functionally-graded (FG) size-dependent circular nano-plates using the integral form of the non-local strain gradient (NSG) model. The linear axisymmetric vibration of the circular FG nano-plates based on the non-local strain gradient (NSG) model is the focal point of this study. In this regard, the non-local elasticity theory (NET) and strain gradient (SG) models are used in conjunction with Hamilton's principle to obtain the governing equations. Discretization of the obtained governing equations is performed with the help of generalized differential quadrature rule (GDQR) and Galerkin weighted residual method (GWRM). The analysis is focused on the effect of non-local and material parameters, as well as the aspect ratio, heterogeneity index of FG material, different boundary conditions, and frequency number on the overall behavior of nano-plate. On using the Galerkin method, a system of linear differential equations is obtained and solved to determine the natural linear frequencies and mode shapes. The obtained results are then compared with the existing results in the literature. On using the proposed procedure in this paper, the dynamic behavior of nano-plate under different boundary conditions can be well described. In addition, the existing deficiencies in other non-local theories can be eliminated. The results of this investigation can be considered as a turning point in the improvement of theoretical results for achieving a better prediction of vibrational behavior in nanostructures.

Theoretical Investigation of Viscosity and Thermal Conductivity of a Gas along a Non-isothermal Vertical Surface in Porous Environment with Dissipative Heat: Numerical Technique

Abstract: The prime objective of the current investigation is to explore the variation of viscosity and thermal conductivity impacts on MHD convective flow over a moving non-isothermal vertical plate in presence of the viscous-dissipative heat and thermal-radiation. The compatible transformation of similarity are employed to obtain the non-linear ODE with the appropriate boundary conditions from the governing equations and the numerical solution of the boundary value problem so obtained are solved via MATLAB bvp4c solver. Naturally, the fluid viscosity and thermal-conductivity may vary from liquid to metal with temperatures and therefore, the impact of viscosity and thermal-conductivity in this investigation is quite significant. The physical parameters along with several influences on momentum, temperature, and concentration are explicated and portrayed with graphs. In addition, the velocity, temperature and concentration gradients at the surface are evaluated and displayed in tabular form. A decent agreement is found in the present outcomes with previously issued work. Furthermore, it is found that the growth of the thermal-radiation increases the gas temperature. The present study is useful for various industrial applications like metal and polymer extrusion, continuous casting, cooling process, nuclear plant and many more.

Nonlinear Dynamic Behavior of Hyperbolic Paraboloidal Shells Reinforced by Carbon Nanotubes with Various Distributions

Abstract: The analytical solution of the nonlinear dynamic behavior of CNT-based hyperbolic paraboloidal shallow shells (HYPARSSs) with various distribution shapes is presented. A theoretical model was created for HYPARSSs reinforced with CNTs using the von Karman -type nonlinearity. Then the nonlinear basic equations are reduced to ordinary nonlinear differential equations using Galerkin methods and the correlation for frequency-amplitude relationship is obtained using the Grigolyuk method. In addition, the nonlinear frequency/linear frequency (NL/L) ratio is determined as a function of amplitude. Comparisons with reliable results in the literature were made to test the accuracy of the formulas. Finally, a systematic investigate is performed to control the influences of CNTs in the matrix, CNT distribution types and nonlinearity on the vibration frequency-amplitude relationship.

Precision Shape Control of Ultra-thin Shells with Strain Actuators

Abstract: This paper is part of an effort conducted at Universite libre de Bruxelles (ULB) on behalf of European Space Agency (ESA) to control the shape of thin polymer shell structures with a unimorph layer of strain actuators (Polyvinylidenefluoride-co-trifluoroethylene, PVDF-TrFE), to achieve high quality light-weight foldable reflectors for space observation. The paper discusses the influence of the electrode size on the morphing capability of the system and addresses the difficulty associated with the ill-conditioning when controlling a very large set of electrodes. The final part of the paper describes a technology demonstrator currently under development and presents some simulation results fitting low order optical modes.

Nonlinear Vibration of an Electrostatically Actuated Functionally Graded Microbeam under Longitudinal Magnetic Field

Abstract: In this work, we develop a model of an electrostatically actuated functionally graded (FG) microbeam under a longitudinal magnetic field based on the Euler-Bernoulli beam and nonlocal strain gradient theories to investigate the nonlinear vibration problem. The FG microbeam is placed between two electrodes, a DC voltage applied between the two fixed electrodes causes an electrostatic force to be exerted on the FG microbeam. The FG microbeam is composed of metal and ceramic in which the properties of these materials are assumed to change in the thickness direction according to the simple power-law distribution. The Galerkin method and the Hamiltonian Approach are employed to find the approximate frequency of the FG microbeam. The accuracy of the present solution is verified by comparing the obtained results with the numerical results and the published results in the literature. Effects of the power-law index, the material length scale parameter, the nonlocal parameter, the applied voltage and the magnetic force on the nonlinear vibration behaviour of the FG microbeam are studied and discussed.

Moving Least Squares Method and its Improvement: A Concise Review

Abstract: The concise review systematically summarises the state-of-the-art variants of Moving Least Squares (MLS) method. MLS method is a mathematical tool which could render cogent support in data interpolation, shape construction and formulation of meshfree schemes, particularly due to its flexibility to form complex arithmetic equation. However, the conventional MLS method is suffering to deal with discontinuity of field variables. Varied strategies of overcoming such shortfall are discussed in current work. Although numerous MLS variants were proposed since the introduction of MLS method in numerical/statistical analysis, there is no technical review made on how the methods evolve. The current review is structured according to major strategies on how to improvise MLS method: the modification of weight function, the manipulation of discrete norms, the inclusion of iterative feature for residuals minimising and integration of these strategies for more robust computation. A wide range of advanced MLS variants have been compiled, summarised, and reappraised according to its underlying principle of improvement. In addition, inherent limitation of MLS method and its possible strategy of improvement is discussed too in this article. The current work could render valuable reference to implement and develop advanced MLS schemes, whenever complexity of the specific scientific problems arose.

Parameter Estimation in Population Balance through Bayesian Technique Markov Chain Monte Carlo

Abstract: In this work, the Markov Chain Monte Carlo is applied to estimate parameters that represent mechanisms that describe particles' dynamics in particulate systems from the literature's proposed models. Initially, the reduced sensitivity coefficient is evaluated to verify which parameters could be estimated simultaneously. The technique is then applied to estimate the models' parameters in different numerical scenarios to determine the rates that influence population dynamics. After the analyzes are performed, the estimates show good precision, accuracy, and a good fit between the measured and estimated state variables. The results show that the Markov chain Monte Carlo can determine the rates of population balance phenomenon.