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The main objective of this study focuses on using, for the first time, the Cole–Cole semilogarithmic fractal plot to study the fractal rheological behavior of magnetorheological elastomer materials using the fractional Zener model. Experimental data and theoretical results show that the Cole–Cole semilogarithmic fractal plot predicts the Zener mathematical model’s material parameters. This paper elucidates the benefits of using Cole–Cole semilogarithmic fractal plots to accurately predict material rheological properties of composite elastomer reinforced with nano or microiron particles observed during experimental tests. [ABSTRACT FROM AUTHOR]

The main goal of this work is to focus on using He's two-scale fractal dimension transform, the Caputo–Fabrizio fractional-order derivative, and the harmonic balance and the homotopy methods are applied for deriving the approximate solution of the fractal, damped cubic–quintic Duffing's equation when the fractional derivative order of the inertia term is not twice of that of the damping term. Numerical results obtained from the derived expressions and the numerical integration solution show good agreement, especially at small values of the nonlinear parameters. Furthermore, when the fractal order of the damping term decreases, the damping oscillation frequency values increase with a decrease in the system wavelength values, which indicates a slower decay in the system oscillation amplitudes. Our solution procedures elucidate the applicability of He's two-scale fractal dimension transform for solving nonlinear dynamic systems with inertia and damping fractal terms. [ABSTRACT FROM AUTHOR]

This paper advances fundamental knowledge of how environmental conditions and physical phenomena at different scales can be included in the differential equation that models the flight dynamics of dipteran insects. The insect's anatomical capability of modifying their mass inertia and flapping-wing damping properties during flight are included by modeling inertia and damping forces with fractal derivatives. An expression for calculating fractal dimension linked to the temporal distribution of non-geometric quantities related to atmospheric processes such as turbulence flow is introduced using, for the first time ever, the two-scale fractal dimension definition and adopting the flow energy spectrum of eddies that occur at large and small scales. The applicability of the derived expression is illustrated with the prediction of the fractal dimension observed in turbulent flows. Then, the two-scale fractal dimension transform is used to re-write the dipteran flight equation of motion in equivalent form to derive its approximate solution using harmonic balance and homotopy perturbation methods. Numerical predictions computed from the derived approximate solutions allow to elucidate how insects and animals could adapt to flight under different environmental conditions. [ABSTRACT FROM AUTHOR]

This paper elucidates how the two-scale fractal dimension transform, and a transformation method can be applied to replace the Warner–Gent equation that models the fractal dynamic response of porous viscohyperelastic materials with an equivalent power-form equation. Furthermore, this research work elucidates the advantages of modeling viscohyperlastic materials using the fractal Warner–Gent's model since the values of the fractal dimension parameter unveil how the global molecular structure of viscohyperelastic materials varies as a function of the vibration frequency wavelength. Compared to the original one, the accuracy attained from the Warner–Gent power-form equivalent equation is examined by plotting the frequency–amplitude and time–amplitude curves obtained from the corresponding numerical integration solutions. It is found that both numerical integration solutions agree well since the root-mean-square-error (RMSE) values remain small. [ABSTRACT FROM AUTHOR]

This paper investigates the applicability of the ancient Chinese algorithm jointly with the two-scale fractal dimension transform to find the frequency–amplitude relationship of fractal equations of motion with and without damping terms. Analytical results show that for a fractal equation of motion without damping terms, the oscillation amplitudes do not exhibit decaying effects. However, when damping terms are included, the fractal parameter tends to shift the decaying oscillation amplitudes that decrease faster with time for fractal values less than one. This paper provides an efficient tool for finding the amplitude–frequency relationship of damped fractal oscillators. To illustrate the solution process, the steady-state solution of the fractal equation of motion that arises in plasma physics is derived. The proposed approach elucidates the applicability of He's formulation jointly with the two-scale fractal calculus to find the frequency–amplitude of fractal systems with and without damping terms. [ABSTRACT FROM AUTHOR]

This paper focuses on predicting the shape, duration, and peak magnitude of the displacement, velocity, and acceleration curves while dropping weight over a viscoelastic fractal cushioning packaging system. Furthermore, to capture high-frequency harmonic components observed during the impact time span, the approximate frequency–amplitude expression of the governing equation of motion will be obtained via an ancient Chinese algorithm and He's formulation by assuming initial trial solutions based on Jacobi elliptic functions. Numerical simulations confirmed the ability of the Jacobi elliptic functions to capture high-frequency harmonics observed during the cushioning packaging system dynamic response with a root mean square error (RMSE) value that does not exceed 0.0218, which is an indication of the great accuracy attained from our derived solution when compared to the exact numerical one. Furthermore, our derived approximate solution predicts that when a weight is dropped over the cushioning packaging, the cushion material with smaller porosity will absorb the produced kinetic energy faster. [ABSTRACT FROM AUTHOR]

This paper introduces a novel methodology to determine the frequency-amplitude relationship of fractal-order viscoelastic polymer materials using the two-scale fractal dimension transform, the equivalent power-form representation of the conservative restoring forces, and a simple coordinate transformation to eliminate viscoelastic effects. Then, the ancient Chinese algorithm Ying Bu Zu Shu and He's formulation are used for obtaining the frequency-amplitude relationship. Simulation results obtained from the derived expressions exhibit good agreement when compared to numerical integration solutions. This article elucidates how the molecular structure of polymer chains influences the relaxation oscillations as a function of the fractal parameter values. [ABSTRACT FROM AUTHOR]

This paper uses the two-scale fractal dimension transform and He's formula derived from the ancient Chinese algorithm Ying Bu Zu Shu to find the approximate frequency–amplitude expression of the fractal and forced anharmonic oscillator that can be used to study the nonlinear oscillations produced by the plasma physics fractal structures. The results show how the electron frequency and wavelength change as a function of the plasma physics fractal structure. In fact, if the value of the fractal parameter is decreased, the wavelength increases, and consequently, the system frequency decreases. The introduced solution procedure sheds a bright light on the easy-to-follow steps to obtain an accurate steady-state analytical solution of fractal anharmonic nonlinear oscillators. [ABSTRACT FROM AUTHOR]

In this paper, the analytical solution that describes the evolution in time of the fractal damped Duffing equation subjected to external forces of elliptic type is derived using He's two-scale fractal transform and the elliptic balance method (EBM). This solution predicts the evolution in time of the Duffing equation and unveils qualitative and quantitative system behavior when the values of the fractal parameter varies, and how these affect the frequency, the wavelength, and the oscillation amplitude from the start of the motion. Comparison of the amplitude–time response curves over the selected time-interval with those obtained from numerical simulations confirms the accuracy of the derived analytical solution. [ABSTRACT FROM AUTHOR]

In this paper, the approximate frequency-amplitude response of the fractal equation that describes the non-Gaussian polymer chains' motion is derived using a two-scale dimension transform and the ancient Chinese algorithm Ying Bu Zu Shu. Theoretical predictions show that the oscillation amplitude of the polymer chains varies since the response curves shift to the left ( α < 1 ) and to the right ( α > 1 ) from those curves plotted for a fractal parameter value α = 1 . This system response suggests that the magnitude of the molecular chain stretching is modified during motion due to the polymer fractal molecular structure, which indicates the mobility and flexibility of the polymer molecules that unveil possible molecular structure defects and intermolecular cohesion. [ABSTRACT FROM AUTHOR]

This paper aims to study the dynamic response of the fractal Fangzhu's forced device to elucidate how the harvester device's surface fractal patterned influences water molecules' motion due to the increase or reduction of the wave velocity. It is also investigated under which conditions the oscillation amplitude favors the complete water removal from Fangzhu fractal surface device. Based on the approximate fractal frequency–amplitude relation derived using an ancient Chinese algorithm, and by varying the value of the fractal dimension parameter linked to the material surface morphology, it was found that the Fangzhu water harvester device can efficiently capture microscopic water droplets if the surface morphology is such that the fractal dimension α is less than one. This condition can be used to develop superhydrophobic surfaces mimicking fractal patterned surface structures. [ABSTRACT FROM AUTHOR]

In this paper, the ancient Chinese algorithm is applied to derive fractal microgravity forced oscillator's frequency–amplitude response curves using the two-scale fractal transform derivative. Depending on the fractal parameter values, it is shown that the system restoring forces exhibit hardening or softening behavior. Furthermore, the proposed solution approach is simple, efficient, and accurate for obtaining the approximate steady-state solution of a fractal microgravity nonlinear oscillator with a purely nonlinear power-form restoring force. [ABSTRACT FROM AUTHOR]

In this paper, the steady-state solution of Duffing-type oscillators with fractal-order derivative is obtained. First, the two-scale fractal-order derivative transform is used to write the fractal differential equation of motion as an ordinary differential non-homogenous equation of motion. Then the ancient Chinese algorithm and He's formulation are used to find the approximate frequency-amplitude response curve. The results show that the steady-state response diagrams exhibit hardening or softening behavior depending on the fractal parameter value. [ABSTRACT FROM AUTHOR]

In this work, the fractal cubic–quintic Duffing's equation analytical solution is obtained using the two-scale transform and elliptic functions. Then, the analytical solution is used to study wave propagation in a fractal medium. Since the value of the fractal parameter adjusts the pulse frequency and wavelength propagation velocity, depending upon the fractal medium physical properties, it is found that the information contained in the pulse can be carried out faster over long distances without distortion or loss of intensities. This paper offers a new light on the applicability of the two-scale transform of fractal theory to comprehend natural phenomena. [ABSTRACT FROM AUTHOR]

This paper aims to derive the equivalent power-form representation for the Toda oscillator, which describes the intensity fluctuations of Nd:YAG lasers. A two-scale dimension transform is introduced to study the transient fractal response of Toda oscillator. Numerical simulations indicate that for increasing values of the fractal exponent α , the frequency of the Toda oscillator increases. [ABSTRACT FROM AUTHOR]

In this paper, an equivalent power-form transformation method with a weighted function is applied for solving the one-dimensional fractal Bratu's boundary value equation. Numerical integration solutions obtained from the equivalent Bratu's equation as well as those from its approximate Taylor's series solution reveal that the proposed methodology yields highly accurate solutions. Therefore, it is believed that by applying the power-form transformation, various fractal differential equations in which two scales are needed because of the physical laws involved in modeling the observed phenomena, can be solved by treating the nonlinear terms as equivalent power-form terms. [ABSTRACT FROM AUTHOR]

In this work, the Duffing's type analytical frequency–amplitude relationship for nonlinear oscillators is derived by using Hés formulation and Jacobi elliptic functions. Comparison of the numerical results obtained from the derived analytical expression using Jacobi elliptic functions with respect to the exact ones is performed by considering weak and strong Duffing's nonlinear oscillators. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the creation of a hybrid magnetorheological elastomer that combines nano- and microparticles. The mixture contained 45 wt.% fillers, with combinations of either 0% nanoparticles and 100% microparticles or 25% nanoparticles and 75% microparticles. TGA and FTIR testing confirmed the materials' thermal and chemical stability, while an SEM analysis determined the particles' size and morphology. XRD results were used to determine the crystal size of both nano- and microparticles. The addition of reinforcing particles, particularly nanoparticles, enhanced the stiffness of the composite materials studied, but their overall strength was only minimally affected. The computed interaction parameter relative to the volume fraction was consistent with the previous literature. Furthermore, the study observed a magnetic response increment in composite materials reinforced with nanoparticles above 30 Hz. The isotropic material containing only microparticles had a lower storage modulus than the isotropic sample with nanoparticles without a magnetic field. However, when a magnetic field was applied, the material with only microparticles exhibited a higher storage modulus than the samples with nanoparticles. [ABSTRACT FROM AUTHOR]

In this paper, we derive an analytical solution of the damped cubic–quintic Duffing oscillator which is based on a rational elliptic form used to obtain exact and approximate solutions of undamped oscillators. We examine different set of system parameter values to assess the accuracy of our derived solution. It is shown that theoretical predictions compares well with the numerical integration solutions obtained by a fourth order Runge–Kutta method. This demonstrates the applicability of rational elliptic forms to solve damped oscillators with higher nonlinear terms. [ABSTRACT FROM AUTHOR]

In this paper we propose a new approach to replace nonlinear ordinary differential equations by approximate cubic-quintic Duffing oscillators in which its coefficients depend on the initial amplitude of oscillation. It is shown that this procedure leads to angular frequency values with relative errors that are lower than those found by previously developed approximate solutions. [ABSTRACT FROM AUTHOR]

In this work, we use the rule of mixtures to develop an equivalent material model in which the total strain energy density is split into the isotropic part related to the matrix component and the anisotropic energy contribution related to the fiber effects. For the isotropic energy part, we select the amended non-Gaussian strain energy density model, while the energy fiber effects are added by considering the equivalent anisotropic volumetric fraction contribution, as well as the isotropized representation form of the eight-chain energy model that accounts for the material anisotropic effects. Furthermore, our proposed material model uses a phenomenological non-monotonous softening function that predicts stress softening effects and has an energy term, derived from the pseudo-elasticity theory, that accounts for residual strain deformations. The model's theoretical predictions are compared with experimental data collected from human vaginal tissues, mice skin, poly(glycolide-co-caprolactone) (PGC25 3-0) and polypropylene suture materials and tracheal and brain human tissues. In all cases examined here, our equivalent material model closely follows stress-softening and residual strain effects exhibited by experimental data. [ABSTRACT FROM AUTHOR]

A nonlinear transformation approach based on a cubication method is developed to obtain the equivalent representation form of conservative two-degree-of-freedom nonlinear oscillators. It is shown that this procedure leads to equivalent nonlinear equations that describe well the numerical integration solutions of the original equations of motion. [ABSTRACT FROM AUTHOR]

We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM) that is based on the homotopy perturbation method (HPM) and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM). At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves. [ABSTRACT FROM AUTHOR]

In this paper we have modified an existing material model introduced by Cantournet and co-workers to take into account softening and residual strain effects observed in polymeric materials reinforced with carbon nanotubes when subjected to loading and unloading cycles. In order to assess the accuracy of the modified material model, we have compared theoretical predictions with uniaxial extension experimental data obtained from reinforced polymeric material samples. It is shown that the proposed model follows experimental data well as its maximum errors attained are lower than 2.67%, 3.66%, 7.11% and 6.20% for brominated isobutylene and paramethylstyrene copolymer reinforced with multiwall carbon nanotubes (BIMSM-MWCNT), reinforced natural rubber (NR-MWCNT), polybutadiene-carbon black (PB-CB), and PC/ABS reinforced with single-wall carbon nanotubes (SWCNT), respectively. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we derive the exact solution of the cubic-quintic Duffing oscillator based on the use of Jacobi elliptic functions. We also showed that the exact angular frequency of this cubic-quintic Duffing equation is given in terms of the complete elliptic integral of the first kind. [Copyright &y& Elsevier]

We use a nonlinear transformation method to develop equivalent equations of motion of nonlinear homogeneous oscillatory systems with linear and nonlinear odd damping terms. We illustrate the applicability of our approach by using the equations of motion that arise in many engineering problems and compare their amplitude-time curves with those obtained by the numerical integration solutions of the original equations of motion. [ABSTRACT FROM AUTHOR]

This work focuses on the formulation of a constitutive equation to predict Mullins and residual strain effects of buna-N, silicone, and neoprene rubber strings subjected to small transverse vibrations. The nonmonotone behavior exhibited by experimental data is captured by the proposed material model through the inclusion of a phenomenological non-monotonous softening function that depends on the strain intensity between loading and unloading cycles. It is shown that theoretical predictions compare well with uniaxial experimental data collected from transverse vibration tests. [ABSTRACT FROM AUTHOR]

This work focuses on the experimental characterization of suture material samples of Mono Plus, Monosyn, polyglycolic acid, polydioxanone 2-0, polydioxanone 4-0, poly(glycolide-co-epsilon-caprolactone), nylon, and polypropylene when subjected to cyclic loading and unloading conditions. It is found that all tested suture materials exhibit stress-softening and residual strain effects related to the microstructural material damage upon deformation from the natural, undistorted state of the virgin suture material. To predict experimental observations, a new constitutive material model that takes into account stress-softening and residual strain effects is developed. The basis of this model is the inclusion of a phenomenological nonmonotonous softening function that depends on the strain intensity between loading and unloading cycles. The theory is illustrated by modifying the non-Gaussian average stretch, full-network model to capture stress-softening and residual strains by using pseudoelasticity concepts. It is shown that results obtained from theoretical simulations compare well with suture material experimental data. [ABSTRACT FROM AUTHOR]

The enhanced cubication method is applied to develop approximate solutions for the most common nonlinear oscillators found in the literature. It is shown that this procedure leads to amplitude-time response curves and angular frequency values with maximum relative errors lower than those found by previously developed approximate solutions. [ABSTRACT FROM AUTHOR]

The aim of this paper focuses on applying a nonlinearization method to transform forced, damped nonlinear equations of motion of oscillatory systems into the well-known forced, damped Duffing equation. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the amplitude-time, the phase portraits, and the continuous wavelet transform diagrams of the cubic-quintic Duffing equation, the generalized pendulum equation, the power-form elastic term oscillator, the Duffing equation with linear and cubic damped terms, and the pendulum equation with a cubic damped term. [ABSTRACT FROM AUTHOR]

We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion. [ABSTRACT FROM AUTHOR]

We study the dynamical response of an asymmetric forced, damped Helmholtz-Duffing oscillator by using Jacobi elliptic functions, the method of elliptic balance, and Fourier series. By assuming that the modulus of the elliptic functions is slowly varying as a function of time and by considering the primary resonance response of the Helmholtz-Duffing oscillator, we derived an approximate solution that provides the time-dependent amplitude-frequency response curves. The accuracy of the derived approximate solution is evaluated by studying the evolution of the response curves of an asymmetric Duffing oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes. [ABSTRACT FROM AUTHOR]

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we derive a class of analytical solution of the damped Helmholtz–Duffing oscillator that is based on a recently developed exact solution for the undamped case. Our solution procedure indicates that this solution holds for specific system parametric choice values. [Copyright &y& Elsevier]

Abstract: New analytical approximate solutions based on Jacobi elliptic functions are formulated to compute the angular frequency value of a nonlinear singular oscillator. It is shown that when our derived analytical angular frequency solutions are compared to the exact angular frequency value, the third-order elliptic balance solution provides the best estimate to the exact value since the percentage error value is about 0.0059% which is 216 times lower than the best estimate percentage error value reported in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, the exact solution of the quadratic mixed-parity Helmholtz–Duffing oscillator is derived by using Jacobi elliptic functions. It is also shown that the exact period of oscillation is given as a function of the complete elliptic integral of the first kind. At the end of the paper, we examine the stability of the system and determine the regions for which periodic and unbounded motions take place. [Copyright &y& Elsevier]

The cubication and the equivalent nonlinearization methods are used to replace the original Duffing-harmonic oscillator by an approximate Duffing equation in which the coefficients for the linear and cubic terms depend on the initial oscillation amplitude. It is shown that this procedure leads to angular frequency values with a maximum relative error of 0.055%. This value is 21% lower than the relative errors attained by previously developed approximate solutions. [ABSTRACT FROM AUTHOR]

Abstract: A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order rational elliptic form solutions to obtain approximate solutions of two nonlinear oscillators. At the end of the paper, we compare the numerical integration values of the angular frequencies with approximate solution results, based on the proposed rational elliptic balance method. [ABSTRACT FROM AUTHOR]

The application of the elliptic balance method to the solution of undamped, two degree of freedom homogeneous nonlinear systems is described. This method uses Jacobian elliptic functions in the balance and is based on the concept of averaging with respect to complete elliptic integrals of the first kind. To assess the accuracy of the approximate solution thus obtained, we consider the motion of a linear vibration absorber attached to a rigid body that is supported symmetrically by incompressible, homogeneous and isotropic hyperelastic shear blocks. It is shown that the amplitude–time response of the model system is well predicted by the elliptic balance method solution even for relatively large parameter values. [Copyright &y& Elsevier]

We investigate the dynamical response of a beam-column system with hinged ends subjected to an axial pulsating force of elliptic type. It is shown that the resulting equation is of the formd2y1/dτ2+y1[d1+d2cn2(τ,k2)]=0,which is the well-known Lame´ equation . In this paper, we obtain the general exact solution of this equation that reveals stable behavior of the beam-column system if the assigned initial conditions are of the form y1(0)=y10 and y˙1(0)=0. It is also found that at a certain value of the modulus of the elliptic force, the lateral vibrational frequency is independent of the material properties of the beam-column system. [Copyright &y& Elsevier]

In this work, a transient three-dimensional finite element model (FEM) of the laser micro spot welding (LMSW) process was established considering three heat source approaches: static heat source model (SHSM), dynamic heat source model (DHSM), and double dynamic heat source model (DDHSM). Each model was computed according to the aspect ratio of spot width to depth and the absorptance of the material. The numerical simulation computed the conduction-to-keyhole transition using an AISI 302 stainless steel alloy. Our results showed that the DDHSM results were based on the experiments reported in the literature. The conduction-to-keyhole transition for the SHSM and DHSM was observed to depend on the average laser power, having a constant keyhole aperture at 75 ms exposure time and 220 W average laser power. Additionally, the DDHSM configuration gave a conduction-to-keyhole transition with a similar constant aperture at 75 and 50 ms of exposure time for 200 and 220 W average laser power, respectively. The percentage errors for the DDHSM were 8%, 15%, 17%, and 20% for the penetration depth, top, middle, and bottom width, respectively. [ABSTRACT FROM AUTHOR]

Featured Application: This article provides proper fitting parameters, for a wide variety of metallic alloys, to apply the derived mathematical expression (which allows to determine the scanning speed value needed, with respect to laser power) to produce highly dense components through selective laser melting. In this work, a previously developed mathematical model to predict bulk density of SLMed (produced via Selective Laser Melting) component is enhanced by taking laser power, scanning speed, hatch spacing, powder's thermal conductivity and specific heat capacity as independent variables. Experimental data and manufacturing conditions for the selective laser melting (SLM) of metallic materials (which include aluminum, steel, titanium, copper, tungsten and nickel alloys) are adapted from the literature and used to evaluate the validity of the proposed enhanced model. A strong relation between dependent and independent dimensionless products is observed throughout the studied materials. The proposed enhanced mathematical model shows to be highly accurate since the computed root-mean-square-error values (RMSE) does not exceed 5 × 10−7. Furthermore, an analytical expression for the prediction of bulk density of SLMed components was developed. From this, an expression for determining the needed scanning speed, with respect to laser power, to achieve highly dense components produced via SLM, is derived. [ABSTRACT FROM AUTHOR]

Featured Application: Mathematical tool for tuning Selective Laser Melting process parameters for achieving highly dense components. In this work, dimensional analysis is used to develop a general mathematical model to predict bulk density of SLMed components taking volumetric energy density, scanning speed, powder's thermal conductivity, specific heat capacity, and average grain diameter as independent variables. Strong relation between dependent and independent dimensionless products is observed. Inconel 718 samples were additively manufactured and a particular expression, in the form of a power-law polynomial, for its bulk density, in the working domain of the independent dimensionless product, was obtained. It is found that with longer laser exposure time, and lower scanning speed, better densification is attained. Likewise, volumetric energy density has a positive influence on bulk density. The negative effect of laser power in bulk density is attributed to improper process conditions leading to powder particle sublimation and ejection. A maximum error percentage between experimental and predicted bulk density of 3.7119% is achieved, which corroborates the accuracy of our proposed model. A general expression for determining the scanning speed, with respect to laser power, needed to achieve highly dense components, was derived. The model's applicability was further validated considering SLMed samples produced by AlSi10Mg and Ti6Al4V alloys. This article elucidates how to tune relevant manufacturing parameters to produce highly dense SLM parts using mathematical expressions derived from Buckingham's π- theorem. [ABSTRACT FROM AUTHOR]

This article aims to investigate the solution of the fractional Troesch's equation that models the mechanism of current generation in porous electrodes by numerical integration of its equivalent power-form representation and by deriving its approximate Taylor series solution. Simulation results compare to experimental data demonstrate that the overpotential distribution and efficiency within a porous electrode, from the bottom to the top of the bed is predicted by using Troesch's fractal overpotential diffusion equation, when the fractal parameter values are α ≥ 1.2618 for a porous electrode that follows the Hausdorff dimension, or α ≥ 1.236 for El Naschie's fractal space-time. • An equation that models the mechanism of current generation in porous electrodes is investigated. • The equivalent representation power-form expression for Troesch's equation is derived • Two scale dimension transform is used to study fractal Troesch's equation. • The Taylor series method is used to solve the equivalent power-form representation of Troesch's equation. [ABSTRACT FROM AUTHOR]

The aim of this article was to investigate the mechanical performance of magnetorheological polyurethane elastomers reinforced with different concentrations of carbonyl iron microparticles (CIPs) in which stress softening, energy dissipation, residual strains, microparticles orientation, and magnetic flux density effects will be considered. Other aspects, such as the determination of the dissipated energy during cyclic loading and unloading, were investigated by considering a pseudo-elastic network model that takes into account residual strains, magnetic field intensity, and the isotropic and anisotropic material behavior. Theoretical predictions confirmed that the material shear modulus becomes sensitive not only for higher concentrations of CIPs added into the elastomer material matrix, but also to the magnetic flux intensity that induces attractive forces between CIPs and to the strong bonds between these and the elastomer matrix. It was also found that the addition of CIPs when embedded into the polymer matrix with a predefined orientation enhances the material shear modulus as well as its capacity to dissipate energy when subjected to magnetic flux density in loading and unloading directions. [ABSTRACT FROM AUTHOR]

This paper focuses on investigating the residual stress values associated with a part fabricated by Selective Laser Melting technology (SLM) when this is subjected further to forces on single point incremental forming (SPIF) operation of variable wall angle. The residual stresses induced by the SLM manufacturing process on the fabricated AlSi10Mg metallic sheets, as well as those produced during their forming SPIF operation were determined by X-ray diffraction (XRD) measurements. Significant residual stress levels of variation, positive or negative, along the metallic sample were observed because of the bending effects induced by the SPIF processes. It is also shown how the wall thickness varies along the additive manufactured SPIFed part as well as the morphology of the melting pools as a function of the deformation depth. [ABSTRACT FROM AUTHOR]

Dimensional analysis through the Buckingham Pi theorem was confirmed as an efficient mathematical tool to model the otherwise non-linear high order ultrasonic micro-injection molding process (UMIM). Several combinations of processing conditions were evaluated to obtain experimental measurements and validate the derived equations. UMIM processing parameters, output variable energy consumption, and final specimen's Young modulus were arranged in dimensionless groups and formulated as functional relationships, which lead to dimensionless equations that predict output variables as a function of the user-specified processing parameters and known material properties. [ABSTRACT FROM AUTHOR]

In this study, a piezoelectric harvesting device was developed using polyvinylidene fluoride (PVDF) nanofibers reinforced with either BaTiO3 nanoparticles or graphene powder. BaTiO3 nanoparticles were synthesized through the sol-gel method with an average size of approximately 32 nm. The PVDF nanofibers, along with the nanoparticle composites in an acetone-N,N-dimethylformamide mixture, were produced using a centrifugal Forcespinning™ machine, resulting in a heterogeneous arrangement of fiber meshes, with an average diameter of 1.6 μm. Experimental tests revealed that the electrical performance of the fabricated harvester reached a maximum value of 35.8 Voc, demonstrating the potential of BaTiO3/ PVDF-based piezoelectric devices for designing wearable applications such as body-sensing and energy-harvesting devices. [ABSTRACT FROM AUTHOR]

Additive manufacturing and nanotechnology have been used as fundamental tools for the production of nanostructured parts with magnetic properties, expanding the range of applications in additive processes through tank photopolymerization. Magnetic cobalt ferrite (CoFe2O4) and barium ferrite (BaFe12O19) nanoparticles (NPs) with an average size distribution value (DTEM) of 12 ± 2.95 nm and 37 ± 12.78 nm, respectively, were generated by the hydroxide precipitation method. The dispersion of the NPs in commercial resins (Anycubic Green and IRIX White resin) was achieved through mechanochemical reactions carried out in an agate mortar for 20 min at room temperature, with limited exposure to light. The resulting product of each reaction was placed in amber vials and stored in a box to avoid light exposure. The photopolymerization process was carried out only at low concentrations (% w/w NPs/resin) since high concentrations did not result in the formation of pieces, due to the high refractive index of ferrites. The Raman spectroscopy of the final pieces showed the presence of magnetic NPs without any apparent chemical changes. The electron paramagnetic resonance (EPR) results of the pieces demonstrated that their magnetic properties were maintained and not altered during the photopolymerization. Although significant differences were observed in the dispersion process of the NPs in each piece, we determined that the photopolymerization did not affect the structure and superparamagnetic behavior of ferrite NPs during processing, successfully transferring the magnetic properties to the final 3D-printed piece. [ABSTRACT FROM AUTHOR]

Surgical meshes, in particular those used to repair hernias, have been in use since 1891. Since then, research in the area has expanded, given the vast number of post-surgery complications such as infection, fibrosis, adhesions, mesh rejection, and hernia recurrence. Researchers have focused on the analysis and implementation of a wide range of materials: meshes with different fiber size and porosity, a variety of manufacturing methods, and certainly a variety of surgical and implantation procedures. Currently, surface modification methods and development of nanofiber based systems are actively being explored as areas of opportunity to retain material strength and increase biocompatibility of available meshes. This review summarizes the history of surgical meshes and presents an overview of commercial surgical meshes, their properties, manufacturing methods, and observed biological response, as well as the requirements for an ideal surgical mesh and potential manufacturing methods. [ABSTRACT FROM AUTHOR]