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 Archive of Applied MechanicsJournal Prestige (SJR): 0.79 Citation Impact (citeScore): 2Number of Followers: 4      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0939-1533 - ISSN (Online) 1432-0681 Published by Springer-Verlag  [2469 journals]
• Surface wave speed of functionally gradient piezoelectric semiconductors

Abstract: In this paper, a shear surface wave propagating along the surface of a functionally graded piezoelectric semiconductor half-space (FGPS), the material parameters of that are assumed to be exponentially increased along the thickness direction, is investigated. Firstly, a governing equation of FGPS with the existence of biasing electric field along the wave propagation direction is formulated. Then, the solution of the equation is assumed and the amplitude ratios to that of the electric potential are derived. At last, the surface conditions lead to a coefficient determination about the wave velocity and the dispersive curves can be obtained. The influences of the semiconduction effect and the material gradient index in FGPS on the dispersive curves are discussed. The result can provide theoretical support for the application of FGPS materials.
PubDate: 2022-06-01

• Mathematical modeling of nanomachining with bimodal dynamic scanning
thermal microscope probe

Abstract: The aim of current study is to present and study the bimodal dynamic Scanning Thermal Microscope (SThM) for nanomachining. Bimodal SThM is the same as conventional SThM where the base is excited simultaneously at a frequency close to the 1st and 2nd resonance frequency of probe. Bimodal excitation makes two separated channels for monitoring sample data for different purposes. Thus, a mathematical model for bimodal SThM is provided. The nonlinear coupled equations of motion are solved analytically. The presented model is compared with the literature and the behavior of bimodal SThM is compared with conventional type. It is shown that the shifted resonance frequencies are independent of the type of excitation and bimodal excitation increases amplitudes at all shifted resonance frequencies. By decreasing ratio of base excitation amplitudes, the amplitude in the 2nd base excitation frequency and all shifted resonance frequencies increase. Bimodal technique amplifies the amplitudes at the 2nd shifted resonance frequency, this data can improve resolution in thermal images. Then, the effects of tip radius on the final surface are simulated. It is shown that the nanomachining depth increases significantly for bimodal SThM and nanomachined surface roughness is increased. It is declared increase in temperature gradient does not necessarily improve the roughness and the final surface always depends on the interactions of three parameters: the tip radius, the total shape of the vibrational response and the location of the peaks with large amplitudes.
PubDate: 2022-06-01

• Simulation framework for crystallization in melt flows of semi-crystalline
polymers based on phenomenological models

Abstract: Polymer components are shaped mostly out of the molten state. As in the case of semi-crystalline polymers, crystallization can be suppressed by shock cooling, thermal process design allows to influence the solid bodies properties. A simulation approach that enables to predict these properties based on a forecast of crystallinity is presented in this paper. The main effects to consider and possibilities of modeling and simulation are discussed. A detailed description of how to create an experimental foundation using dynamic scanning calorimetry (DSC) and a rheometer is provided. Suppression of crystallization is modeled by a novel phenomenological approach, based on data over a large band of cooling rates. Special focus is put on parameter identification and extension of insufficient DSC data. The mechanical behavior is modeled using a weighted approach based on a nonlinear-thermoviscoelastic model for the molten state and a highly viscous Newtonian model for the solid state. Parameterization of both models is highlighted. An implementation in OpenFOAM is documented, emphasizing specific methods that were applied. Results of simulations for a simplified profile extrusion and injection molding case are presented. Basic relationships are forecasted correctly by the method, and important findings are presented for both processes.
PubDate: 2022-06-01

• A semi-analytical formula for estimating notch stress field and N-SIF of
double edge V-notched orthotropic thin plate

Abstract: The notch stress intensity factor (N-SIF) is widely used to characterize the notch stress concentration under different crack opening angles. At present, the evaluation formula of notch stress intensity factor is too complicated and inconvenient for engineering applications. Therefore, based on the isotropic V-notch plate, this paper introduces the concept of singular strength factor $$as_{i}$$ , and further presents the notch stress field and the simple evaluation formula of N-SIF for double edge V-notched orthotropic thin plate. The formula is simple in form and clear in physical meaning. After numerical verification and verification with the evaluation results of traditional literature, the results show that the semi-analytical formula proposed in this paper has a wider application range and can be applied to different materials and loads simultaneously.
PubDate: 2022-06-01

• On a virtual element formulation for trusses and beams

Abstract: The virtual element method (VEM) was developed not too long ago, starting with the paper [2] related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements; however, it has so far not applied to one-dimensional structures like trusses and beams. Here we study several VEM elements suitable for trusses and beams and show that the virtual element methodology produces elements that are equivalent to well-known finite elements but also elements that are different, especially for higher-order ansatz functions. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same number of unknowns as finite beam elements. Furthermore, the formulation allows to compute nonlinear structural problems undergoing large deflections and rotations.
PubDate: 2022-06-01

• Experimental investigation of a reduced-order model for a vortex-induced
vibration wind converter

Abstract: In this paper, the vortex-induced vibrations (VIV) of two bladeless wind energy converters (BWECs) are investigated through wind tunnel experiments, CFD-FEM simulations reduced-order model. BWECs consist of a blunt body attached to the tip of two flexible coaxial beams. In BWEC1, the blunt body is a truncated conic cylinder, whereas in BWEC2 it is a right cylinder. Due to periodic shedding vortices, the BWECs undergo vibrations that can be converted to electrical energy. An analytical reduced-order model is derived for the BWECs by incorporating a semiempirical model for the fluctuating aerodynamic lift coefficient into the Euler–Bernoulli theorem for the flexible support. The reduced-order model involves two principal assumptions: linear mode shapes for the aerodynamic lift force and a semiempirical model for the lift coefficient. The objective of the present research is to study and validate the accuracy of these two assumptions. To this end, wind tunnel experiments were accomplished to measure the tip displacement and CFD-FEM simulations were performed to obtain lift force distribution. Parameters of the reduced-order model are obtained using a genetic algorithm that minimizes the least squared error between the results of the model and the measurements of the experiments. To examine the assumptions of the reduced-order model, further CFD-FEM simulations are performed. The results of the CFD-FEM simulations confirmed the validity of the presumed lift force mode shapes. Moreover, it is justifiably inferred that the semiempirical lift model is the source of inconsistencies between the model and the wind tunnel experiments in high wind speeds of the post-lock-in region. In conclusion, the proposed reduced-order model is shown to be adequately accurate near the lock-in wind speed, which is the most significant working condition of the VIV energy harvesters.
PubDate: 2022-06-01

• Probabilistic assessment of footbridge response to single walkers

Abstract: Among the load scenarios considered for the serviceability assessment of human-induced footbridge vibration, is that of the transient action of a single pedestrian or a small group of pedestrians. Although such action is stochastic due to the variability of gait parameters, available Codes and Guidelines all assume it is deterministic and equal to that coming from the “worst pedestrian ever” for the given footbridge. This approach is sound from an engineering point of view but does not allow control of the probability of failure. The present work deals with a reliability-based procedure for the serviceability assessment of the footbridge peak characteristic accelerations due to pedestrian induced actions. Based on the results obtained incorporating the effects of the inter-subject variability of gait parameters and of the uncertainties in footbridge dynamic properties, a design response spectrum is proposed for both vertical and lateral vibrations. The proposed procedure lends itself for immediate Code implementation.
PubDate: 2022-06-01

• Analytical modeling and experimental validation of a butterfly-shaped
piezoelectric composite transducer

Abstract: This paper presents an analytical model of a butterfly-shaped piezoelectric composite transducer. The vibration model of the transducer is firstly established based on the lateral and longitudinal deformations of the uniform and variable cross-sectional beams. Next, the electromechanical coupling model of the transducer is derived according to the vibration model. Then, the results of the derived model are presented, both the influence of the length of the rear-end block and the height of the cross beam are discussed based on the analytical model. Finally, an experimental prototype of the transducer is fabricated. The vibration modes and impedance characteristics of the transducer are, respectively, tested by using a laser Doppler vibro-meter, and an impedance analyzer and the testing results validate the proposed analytical model. The experimental results show that the relative errors of the analytical model are 2.253% and 2.230%, and the relative errors of the effective electromechanical coupling coefficients were 8.826% and 8.203%. In addition, the mode shapes of the analytical model are in good agreement with the experiment results.
PubDate: 2022-06-01

• Large deflections of functionally graded sandwich beams with influence of
homogenization schemes

Abstract: Functionally graded materials (FGMs) are increasingly used in sandwich construction to improve mechanical performance of structures. The effective material properties used in modelling FGM structures, however, are dependent on a chosen homogenization scheme. For the first time, the influence of different homogenization schemes on large deflections of dual-phase FGM sandwich beams is studied in this paper by using a nonlinear finite element procedure. The material properties of the sandwich beams are considered to vary in the thickness direction by a power function. Four homogenization schemes, namely the schemes due to Voigt, Mori–Tanaka, Hashin–Shtrikman and Tamura–Tomota–Ozawa, are employed to estimate the effective elastic moduli of the beams. Based on the total Lagrange formulation, a first-order shear deformable nonlinear beam element is formulated and employed in the study. Newton–Raphson iterative method is used in combination with the arc-length technique to obtain the large deflection curves and stress distribution of the beams. Numerical results reveal that the material distribution indicated by the material grading index and the homogenization scheme have play an important role on the behaviour of the beams, and the influence of the material grading index on the large deflection response is dependent on the homogenization scheme. Among the four homogenization schemes studied, it is shown that the large deflection response obtained by the Voigt model is more conservative than that using the other schemes.
PubDate: 2022-06-01

• Vibration control and energy accumulation of one-dimensional acoustic
black hole structure with damping layer

Abstract: In the view of the potential for vibration control and energy harvesting of the acoustic black hole (ABH), the transfer matrix scheme combined with the finite element method is utilized to establish the governing equation of a one-dimensional ABH beams attached with a damping layer. According to the continuous condition of generalized forces and displacements between the two adjacent uniform sections, the transfer relationship is derived. The energy ratio is defined as the ratio of the edge part to the entire wedge, which illustrates the energy concentration effect. A damping layer is introduced for controlling the fluctuation. Numerical simulation is presented to illustrate the effectiveness of presented control method. The influences of physical parameters such as excitation frequency, power exponent and thickness of the damping layer on energy concentration are discussed.
PubDate: 2022-06-01

• Dynamic equations of motion for inextensible beams and plates

Abstract: The large deflections of cantilevered beams and rectangular plates are modeled and discussed. Traditional nonlinear elastic models (e.g., von Karman’s) employ elastic restoring forces based on the effect of stretching on bending, and these are less applicable to cantilevers. Recent experimental work indicates that elastic cantilevers are subject to nonlinear inertial and stiffness effects. We review a recently established (quasilinear and nonlocal) cantilevered beam model, and consider some extensions to two spatial dimensions, namely inextensible plates. Our principal configuration is that of a thin, isotropic, homogeneous rectangular plate, clamped on the one edge and free on the remaining three. We proceed through the geometric and elastic modeling to obtain equations of motion via Hamilton’s principle for the appropriately specified energies. We then enforce effective inextensibility constraints through Lagrange multipliers. Multiple plate analogs of the established 1D model are obtained, based on assumptions. In total, we present three distinct nonlinear partial differential equation models and, additionally, describe a class of “higher-order” models. Each model has particular advantages and drawbacks for both mathematical and engineering analyses. We conclude with a discussion of the various models, as well as some analytical problems.
PubDate: 2022-06-01

• Stress analysis of anti-plane finite elastic solids with hole by the
method of fundamental solutions using conformal mapping technique

Abstract: Stress fields of anti-plane finite elastic solids containing hole subjected to the traction or displacement boundaries are studied by using the method of fundamental solutions (MFS) in this paper. The conformal mapping technique is applied to achieve the robustness in computation for the anti-plane elastic problem. The performances of the MFS utilizing the direct MFS method and the MFS based on the conformal mapping technique are studied in solving multi-connected anti-plane elastic problem. Based on the complex analysis, the approximate solution of the complex analytic function is derived for the MFS. To avoid the derivatives on the traction boundaries, a modified boundary condition utilizing the value of the analytic function is given to construct the interpolation equations. Furthermore, the interpolation equations are given in the mapped plane by the conformal mapping technique. The accuracy of the solutions of stress with the MFS is compared between the direct MFS method and the MFS based on the conformal mapping technique in three numerical examples of the traction boundary and the mixed boundary conditions. It is illustrated that stress fields obtained by the MFS based on the conformal mapping technique can achieve good accuracy for the multi-connected anti-plane problems, whereas the direct MFS can not. The proposed method is an expansion of the traditional MFS in solving the elastic problems and can be applied for the heat transfer and the electrostatics problems with the simple concept and the easy numerical implementation.
PubDate: 2022-06-01

• Strain-based finite element formulation for the analysis of functionally

Abstract: This work introduces a novel four-node quadrilateral finite element based on the strain approach and the first-order shear deformation theory for static and free vibration responses of functionally graded (FG) material plates. Material properties of the plate are assumed to be graded across the thickness direction by using a simple power law distribution of the volume fractions constituents. The developed element possesses five essential degrees of freedom per node. This element is obtained by the superposition of two strain-based elements where the first is a membrane with two degrees of freedom per node and the second is a Reissner–Mindlin plate that has three degrees of freedom per node. The displacements field of the proposed element which contains higher-order terms is based on assumed strain functions satisfying compatibility equations. The performance of the suggested element is evaluated through several tests and the obtained results are compared with available solutions from the literature. The results of the present element have proved excellent accuracy and efficiency in predicting bending and free vibration of FG plates.
PubDate: 2022-05-17

• Elastic field of a rotating cubic quasicrystal disk

Abstract: Owing to anisotropy in the phonon and phason fields, the analysis of the elastic problems in quasicrystals is more difficult than conventional crystals. A rotating cubic quasicrystal disk is considered. Due to the nature of cubic quasicrystals, the associated problem is not axisymmetric. The semi-inverse solution method is applied to derive the closed-form solution. Explicit expressions for the phonon and phason displacements and stresses are obtained. With reference to polar coordinates, the shear stress components of the phonon and phason fields vanish everywhere in the disk, and the radial and hoop stress components of the phonon and phason fields are independent of the angular coordinate $$\theta$$ . However, the radial and hoop displacements of the phonon and phason fields are related to the angular coordinate. The influence of the material properties on the distribution of the elastic fields is discussed.
PubDate: 2022-05-16

• Effects of mobile charges on interface thermal stresses in a piezoelectric
semiconductor composite rod

Abstract: Abstract The interface thermal stresses in the extensional deformation of a composite rod of piezoelectric dielectric and nonpiezoelectric semiconductor layers have been detailed in the present study. A one-dimensional model for extension is used. Analytical expressions of distributed shear stresses along the interface and concentrated shear forces at the ends of the rod are obtained. The distributed shear stress relies on semiconduction and disappears when there are no mobile charges. The concentrated end force is independent of semiconduction. The resultant of the distributed shear stress is comparable to the concentrated end force and therefore is significant. The effects of various geometric and physical parameters are examined.
PubDate: 2022-04-28

• Numerical simulation for non-constant parameters effects on blood flow of
Carreau–Yasuda nanofluid flooded in gyrotactic microorganisms: DTM-Pade
application

Abstract: Abstract The peristaltic flow of Carreau–Yasuda fluid through a micro-vessel involving oxytactic microorganisms and nanoparticles in a vertical asymmetric channel is examined. In early times, scientific research shows that the cancer cells exposed to low oxygen conditions had the advantage of staying in the bloodstream more and can invade healthy cells as well, whereas the oxytactic microorganisms exhibit negative chemotaxis to gradients of oxygen (oxygen repellents). So, it had to be studied the behavior of oxytactic microorganisms and nanoparticle and their roles in the drug-carriers system. All non-dimensional physical parameters are supposed to be variable as the viscosity of blood variable with fluid temperature and nanoparticle concentration. This system of partial differential equations was formulated and transformed mathematically using new theories of differential transform method combined by Pade' approximation (DTM-Pade′). The solution of the mentioned system is displayed digitally in tables and graphically in sketches. The existing study assured that the microorganism density in the direction near to the hypoxic tumor tissues regions grows with a rising in oxygen concentrations and the blood viscosity diminutions. Results show that the number of pores increases the flow and the particles of fluid moving more freely with increment in distribution of temperature.
PubDate: 2022-04-22

• Scattering of anti-plane waves by scalene triangular boundary with
embedded cavity in anisotropic medium based on mapping space

Abstract: Abstract Both surface boundary motion and cavity stress concentration have always been concerned in anisotropic medium. In this paper, the mapping function from anisotropic medium to homogeneous medium was established, and the relationship between the free boundary of anisotropic medium and the mapping of homogeneous medium boundary was proved. In the space of homogeneous medium mapping, the wave displacement function was obtained by solving the equation of motion that meets the zero-stress boundary conditions by the variable separation method and the symmetric method. Based on the complex function, the multi-polar coordinate method and the region-matching technique, the algebraic equations were established at auxiliary boundaries and free boundary conditions in the complex domain. Then, according to the sample statistics, instead of the Fourier expansion method, the least square method was used to solve the undetermined coefficient of the algebraic equations by discrete boundary. Finally, the process of the wave propagation was shown in the time domain by inverse Fourier transform.
PubDate: 2022-04-21

• Bending analysis of two-directional functionally graded beams using
trigonometric series functions

Abstract: Abstract In the present paper, Navier’s method based on the first-order shear deformation theory for bending analysis of two-directional functionally graded beams subjected to various sets of boundary conditions is presented. In Navier's method, different trigonometric series functions are proposed for each boundary condition. The accuracy of these proposed functions was investigated and compared with the literature. It is also presented in a parametric study. The governing equations are derived according to Lagrange’s principle. The variation of the components of the beam material in the volume is defined by a power-law rule. The normalized maximum transverse deflections, the normalized axial and transverse shear stresses are obtained for various boundary conditions, gradation exponents (px, pz) in the x- and z-directions, and the slenderness (L/h). The trigonometric series functions used in this study give results that are quite compatible with the literature. In addition, the parametric study contributes to the literature.
PubDate: 2022-04-21

• Evaluation of the contact problem of functionally graded layer resting on
rigid foundation pressed via rigid punch by analytical and numerical (FEM
and MLP) methods

Abstract: Abstract In this paper, frictionless contact problem for a functionally graded (FG) layer is considered. The FG layer is subjected to load with a rigid punch and the FG layer is bonded on a rigid foundation. Analysis of this contact problem was carried out by analytical method, finite element method (FEM) and multilayer perceptron (MLP), comparatively. The main target of this study is to investigate the applicability of MLP analysis for frictionless contact problem of FG layer bonded on a rigid foundation. Analytical solution of the problem is based on the theory of elasticity and integral transform techniques. The physical contact problem is transformed to mathematical system of integral equation. The integral equation in which the contact pressures are unknown functions is numerically solved with the Gauss–Jacobi integration formulation. Finite element analysis of the problem is carried out with ANSYS software by using the two-dimensional modeling technique. Finally, MLP analysis has been used to obtain the contact distances of the problem. Three-layer MLP was used for this calculation. Material properties and loading conditions were created by giving examples of different values in MLP training and testing stages. Program code was rewritten in C++. As a result, average deviation values such as 1.67 and 0.885 were obtained for FEM and MLP, respectively. It has been determined that the contact areas and contact stresses obtained from FEM and MLP are quite compatible with the results obtained from the analytical method.
PubDate: 2022-04-20

• A geometrically nonlinear spring element for structural analysis of
helical springs

Abstract: Abstract Helical springs belong to structures with spiral shapes and large curvatures, especially, traditional views that elemental shape functions are applied to interpolate shapes of structures, will result in plenty of elements and enormous computational cost. It is proved by this paper that selecting some characteristic parameters describing their shape regulations as variables can model the helical springs with almost no errors of model. Based on this thought, a geometrically nonlinear spring element for structural analysis of helical springs is proposed. First, strains irrelevant to rigid motions of cross sections and virtual deformation power of the curved beam with geometrical nonlinearity are derived. Next, parameters that generalized strains of spring elements depend on, namely helical radius, azimuth angles, height coordinates and torsion angles at one node of each coil are chosen as variables. A special shape function is built, in contrast of traditional shape functions, they can approximate the structure of helical springs accurately using less parameters. Then, nodal forces and generalized external forces as well as equilibrium equations are given, and in order to improve the computational efficiency, the Jacobian matrices are derived. Finally, two examples are considered to evaluate the accuracy of modeling and simulation against to ANSYS. Stiffness properties of cylindrical and conical springs are analyzed by the spring element. The proposed elements can give high-precision numerical results using less parameters from the comparison and be used an effective auxiliary tool for design of springs.
PubDate: 2022-04-20

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