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Numerical investigation of nanofluid flow and heat transfer in a pillow plate heat exchanger using a two‐phase model: Effects of the shape of the welding points used in the pillow plate ZAMM (IF 1.103) Pub Date : 20210114
Yusuf A. Al‐Turki; Ali Yarmohammadi; As'ad Alizadeh; Davood ToghraieIn this study, a numerical investigation of fluid flow and heat transfer of Al2O3‐water nanofluids in a pillow plate heat exchanger with a two‐phase model is investigated. The flow regime studied in this study is in the laminar flow regime such that the Reynolds numbers are 250, 500, 750, and 1000 and the volume fraction of the nanoparticles remained so that the fluid stayed in Newtonian. The volume

Mixed boundary value problems for Rayleigh wave in a half‐plane with cubic anisotropy ZAMM (IF 1.103) Pub Date : 20210114
Onur ŞahinThe paper deals with mixed boundary value problems in an elastic half‐plane with cubic symmetry. The formulation of the problem depends on an asymptotic model derived for anisotropic materials. It is demonstrated that defining the displacements in terms of a pair of plane harmonic functions reduces the problem to a classical isotropic form, which can be formulated within the framework of the asymptotic

Investigation of non‐Newtonian blood flow with power‐law model: Effects of coronary congenital heart defect on a specific age type ZAMM (IF 1.103) Pub Date : 20210114
Shahab Naghdi Sedeh; Ali Yarmohammadi; Davood Toghraie; As'ad AlizadehNowadays, humans are suffering from chronic cardiovascular diseases, including Congenital Heart Defect (CHD). These diseases have far‐reaching consequences, such as disruption of the daily life of humans by reducing their ability to perform daily routines. This problem is due to impaired cardiac pumping capability. The present numerical simulation studied the effects of CHDs on pressure drop and AWSS

Vibration busters: An interdisciplinary approach to learning of dynamical systems ZAMM (IF 1.103) Pub Date : 20210108
Ryszard Walentyński; Damian Słota; Marcin SzczygiełA group of six pre‐graduated students of Civil Engineering, Mathematics and Mechatronics studied problems of dynamics of structures within a project called Vibration Busters implemented in a formula of Project Based Learning. They worked under supervision of professors from the above mentioned faculties. Students, according to their competencies, implemented a procedure of numerical analysis of the

The pneumatic wheel model with plastic elements and force loss ZAMM (IF 1.103) Pub Date : 20210108
Tomasz MiroslawWheel construction and adhesion to the road decide on transport economy and safety. People are still developing wheel rims and tries to increase vehicle stability, reduce energy consumption and noise emissions. For many years designers have developed many models to describe the tire‐road phenomena. The models are created in a couple of ways, some tried to find the mathematical equation which follows

Inverse analysis of metamaterials and parameter determination by means of an automatized optimization problem ZAMM (IF 1.103) Pub Date : 20210108
Navid Shekarchizadeh; Bilen Emek Abali; Emilio Barchiesi; Alberto Maria BersaniIn this paper, a novel parameter determination technique is developed for material models in continuum mechanics aimed at describing metamaterials. Owing to their peculiar mechanical properties and behaviors, such as extreme elasticity or high strength‐to‐weight ratio, metamaterials are of interest to be simulated by reduced‐order modeling by means of the generalized mechanics. Such models incorporate

Double‐diffusive convection in a rotating viscoelastic fluid layer ZAMM (IF 1.103) Pub Date : 20210108
Kondethimmanahalli Rangadhamappa Raghunatha; Inapura Siddagangaiah ShivakumaraThe linear instability and a weakly nonlinear stability of a rotating double‐diffusive convection in a viscoelastic fluid layer are investigated. An Oldroyd‐B constitutive equation is used to describe the rheological behavior of the viscoelastic fluid. Several remarkable departures from those of single‐diffusive and double‐diffusive viscoelastic fluid systems are explored by performing the linear instability

Axisymmetric polyharmonic spline approximation in the dual reciprocity method ZAMM (IF 1.103) Pub Date : 20210106
Artem Karaiev; Elena StrelnikovaThe paper is devoted to developing the dual reciprocity boundary element method for axisymmetric problems based on usage of axisymmetric polyharmonic splines. The axisymmetric polyharmonic spline is introduced as a linear combination of polyharmonic radial basic functions and polynomial terms. The analytical expressions for proposed axisymmetric polyharmonic radial basic functions are obtained for

From image data towards microstructure information – Accuracy analysis at the digital core of materials ZAMM (IF 1.103) Pub Date : 20201230
Bernhard Eidel; Andreas Fischer; Ajinkya GoteA cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform discretizations of pixelized images in 2D are the raw‐data point of departure for simulation analyses. This paper proposes the concept of a unified error analysis for image‐based microstructure representations in uniform resolution

Analytical bending solutions of thin plates by two‐dimensional generalized integral transform method ZAMM (IF 1.103) Pub Date : 20201230
Xu Qian; Zhang Jinghui; Salamat Ullah; Zhong Yang; Geng LitaoIn this paper, analytical bending solution of a rectangular thin plate with different boundary conditions was obtained by using the two‐dimensional generalized finite integral transform method. During the solution procedure, the vibrating beam functions satisfying different boundary conditions of the plate are taken as integral kernels to form the integral transform pairs. This two‐dimensional integral

Unsteady hybrid nanofluid flow on a stagnation point of a permeable rigid surface ZAMM (IF 1.103) Pub Date : 20201230
Iskandar Waini; Anuar Ishak; Ioan PopThis study investigates the unsteady flow of Al2O3‐Cu/water hybrid nanofluid on a stagnation point of a permeable rigid surface. The similarity equations are obtained using similarity variables and then solved using the bvp4c solver. The outcomes show that dual solutions exist for the negative unsteadiness and some mass flux parameters. Besides, the heat transfer rate is intensified with the hybrid

Effect of temperature‐dependent and internal heat source on a micropolar thermoelastic medium with voids under 3PHL model ZAMM (IF 1.103) Pub Date : 20201219
Amnah M. Alharbi; Elsayed M. Abd‐Elaziz; Mohamed I. A. OthmanThe goal of the paper is to present the study of the effect of an internal heat source and the dependence of temperature on a micropolar voided medium that is thermoelastic in the theory of the three‐phase‐lag model of thermoelasticity. The governing equations are formulated and then the exact displacement component expressions, temperature field, microrotation components, the components of stress

Variational formulation and differential quadrature finite element for freely vibrating strain gradient Kirchhoff plates ZAMM (IF 1.103) Pub Date : 20201219
Bo Zhang; Heng Li; Liulin Kong; Xu Zhang; Zhipeng FengIn this paper, we apply the energy variational principle to arrive at the differential equation of motion and all appropriate boundary conditions for strain gradient Kirchhoff micro‐plates. The resulting sixth‐order boundary value problem of free vibration is solved by a thirty‐six‐DOF four‐node differential quadrature plate finite element. The C2‐continuity condition of the deflection is guaranteed

Memory response in a two‐dimensional transversely isotropic thick plate with varying heat source ZAMM (IF 1.103) Pub Date : 20201216
Mohsin Islam; Sudip MondalThis present survey deals with a novel mathematical model of generalized thermoelasticity which investigates the transient phenomena in a two‐dimensional problem for a transversely isotropic thick plate having a heat source. The upper surface of the plate is stress‐free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The

Editorial ZAMM (IF 1.103) Pub Date : 20201215
Jörg SchröderIn 1921 Richard von Mises founded the „Zeitschrift für Mathematik und Mechanik“ – Journal of Applied Mathematics and Mechanics (ZAMM) and the „Gesellschaft für Angewandte Mathematik und Mechanik“ – International Association of Applied Mathematics and Mechanics (GAMM). Richard von Mises' mission statement of breaking down the boundaries between pure mathematics and the application of mathematical theories

On the differential transform method of solving boundary eigenvalue problems: An illustration ZAMM (IF 1.103) Pub Date : 20201212
M. Narayana; M. Shekar; P.G. Siddheshwar; N.V. AnurajThe differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with

Stochastic stability of performance properties for materials with non‐deterministic microstructure ZAMM (IF 1.103) Pub Date : 20201208
Inna M. Gitman; Mikhail B. Gitman; Sergei E. Batin; Dmitriy A. BoyarshinovIn this contribution an original concept of stochastic stability (P‐stability), formulated here to represent realistic stochastic nature of materials, is employed for stability analysis of material performance characteristics. Stochasticity in materials can be related, for example, to manufacturing processes, potential treatment of material, or properties of raw materials. On the other hand, performance

Stabilization for an inhomogeneous porous‐elastic system with temperature and microtemperature ZAMM (IF 1.103) Pub Date : 20201208
Baowei Feng; Ling Yan; Dilberto da Silva Almeida JúniorIn this paper we are concerned with a one‐dimensional linear theory of inhomogeneous porous‐thermo‐elastic materials with microtemperatures. The main results contain the global well‐posedness and stability of the system. By using Lumer–Philips theorem, we prove that the system is well posed. By using energy method, we establish exponential decay rate of the system.

Onset of synchronous and asynchronous convection in modulated nanofluid filled porous media ZAMM (IF 1.103) Pub Date : 20201205
S. Saravanan; M. KousalyaA theoretical study of the effect of gravity modulation on a nanofluid filled porous medium subjected to a constant temperature gradient across is made. In particular the onset of convection in water based nanofluids containing conventional metallic and metal oxide particles ( C u ‐water, A l 2 O 3 ‐water, T i O 2 ‐water, and A g ‐water) is investigated. The nanofluid behaves more like a single‐phase

Integral equation technique for water wave interaction by an array of vertical flexible porous wave barriers ZAMM (IF 1.103) Pub Date : 20201203
Santanu Koley; Trilochan SahooScattering of obliquely incident surface gravity waves by an array of partial flexible vertical porous wave barriers of varied configurations is studied in finite water depth and deep water cases. For the mathematical modeling purpose, linearized water wave theory is considered. Firstly, the problem associated with double vertical barriers is handled for a solution. To solve the problem, the associated

Thermodynamic entropy of a magnetized Ree‐Eyring particle‐fluid motion with irreversibility process: A mathematical paradigm ZAMM (IF 1.103) Pub Date : 20201202
Muhammad Mubashir Bhatti; Sara I. AbdelsalamThis article deals with the entropy generation and irreversibility process under the effects of partial slip on magnetic dusty liquid induced by peristaltic wave through a porous channel. The Ree‐Eyring fluid model has been used for a governing flow. Mathematical modelling is based on Ohm's law, continuity equation, Darcy law and momentum equation. Analytical solutions are presented for fluid and particle

Free convection of non‐Newtonian nanofluid flow inside an eccentric annulus from the point of view of first‐law and second‐law of thermodynamics ZAMM (IF 1.103) Pub Date : 20201128
Amin Shahsavar; Shahla Noori; Davood Toghraie; Pouya BarnoonThe current work aims to perform the hydrothermal and entropy generation (EG) characteristics in a naturally cooled eccentric horizontal annulus filled with non‐Newtonian water‐magnetite/CNT nanofluid (NF). The wall temperature of both cylinders is constant and the temperature of the outer cylinder is lower than that of the inner cylinder. The impacts of vertical eccentricity, nanoadditive concentration

Free vibration characteristics of nonlocal viscoelastic nano‐scaled plates with rectangular cutout and surface effects ZAMM (IF 1.103) Pub Date : 20201126
Maysam Naghinejad; Hamid Reza OvesyIn the present study, the viscoelastic free vibration behavior of nano‐scaled plates is studied by employing a finite element method based on the two‐phase nonlocal integral theory. Various boundary conditions, surface effects and cutouts have been assumed. The principle of total potential energy is used for developing the nonlocal finite element method, and the classical plate theory is assumed to

A note on the exact closed form solution for coupled Hill equations ZAMM (IF 1.103) Pub Date : 20201120
Kazumi WatanabeAn exact closed form solution for coupled (simultaneous) Hill equations is found. The Hill equations are derived from the displacement equations for the 2D orthotropic elastic solid by introducing polar coordinate variables to the Cartesian components of the displacement, and a solution method for a little bit generalized form of the Hill equations is presented.

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates ZAMM (IF 1.103) Pub Date : 20201112
Xianhui Wang; Fanglin Li; Jiangong Yu; Xiaoming Zhang; Zhi LiAn improved Legendre polynomial series approach (AILPSA) is presented to investigate the circumferential thermoelastic Lamb wave in a fractional order orthotropic cylindrical plate. In the AILPSA, the analytical integration is developed based on the orthogonality and recursive properties of the Legendre polynomial to simplify the integral computation involved in the solving progress. As a consequence

Dynamics of a coupled system for nonlinear damped wave equations with variable exponents ZAMM (IF 1.103) Pub Date : 20201109
Khaled Zennir; Tosiya MiyasitaWe consider a coupled system of viscoelastic wave equation with weak, strong damping and power nonlinearity. For a single viscoelastic wave equation, we have already obtained a global solution, its decay rate and finite‐time blow‐up [1]. In this paper, we extend these results to a coupled system. First, we obtain a global solution and derive its decay rate by a decreasing energy. Finally, we apply

Geometrically nonlinear models of static deformation of micropolar elastic thin plates and shallow shells ZAMM (IF 1.103) Pub Date : 20201109
Armenuhi Sargsyan; Samvel SargsyanThe present paper considers micropolar plates and shallow shells, the elastic deflections of which are comparable with their thickness and are small in comparison with characteristic cross‐section size. At the same time, both rotation angles of the normal to the median surface before deformation and their free rotations are small. Also, in the tensors of deformation and flexures‐torsions, the nonlinear

Editorial ZAMM (IF 1.103) Pub Date : 20201109
Holm AltenbachCelebrating the 100th anniversary of the founding of the ZAMM (Journal of Applied Mathematics and Mechanics) reasonably means that the focus of this year's issues is on some important persons and papers from the last century. This ZAMM jubilee is however an exceptional case: we celebrate this year during the COVID‐19 pandemic that has partly paralyzed our ordinary and scientific life. With respect

On build‐up of epidemiologic models—Development of a SEI3RSD model for the spread of SARS‐CoV‐2 ZAMM (IF 1.103) Pub Date : 20201013
Michael WolffThe present study investigates essential steps in build‐up of models for description of the spread of infectious diseases. Combining these modules, a SEI3RSD model will be developed, which can take into account a possible passive immunisation by vaccination as well as different durations of latent and incubation periods. Besides, infectious persons with and without symptoms can be distinguished. Due

The regularity of semi‐hyperbolic patches near sonic curves for the two‐dimensional compressible magnetohydrodynamic equations ZAMM (IF 1.103) Pub Date : 20200904
Jianjun Chen; Geng Lai 
Stability analysis of multiple solutions in case of a stretched nanofluid flow obeying Corcione's correlation: An extended Darcy model ZAMM (IF 1.103) Pub Date : 20201104
Rakesh Kumar; Tanya Sharma; Ravinder Kumar; Mohsen Sheikholeslami; Kuppalapalle VajraveluThe bi‐dimensional flow of a F e 3 O 4 ‐water nanofluid perfusing a porous medium has been considered for investigation. The porous space is in contact with a constantly heated sheet stretching at a linear rate. To simulate the nanofluid flow through the pores, an extended Darcy model due to Brinkman and Forchheimer is utilized considering porosity and permeability effects in a convective environment

Model hierarchy for the shape optimization of a microchannel cooling system ZAMM (IF 1.103) Pub Date : 20201104
Sebastian Blauth; Christian Leithäuser; René PinnauWe model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three‐dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived via a homogenization of the geometry in 3D and a transformation of the three‐dimensional models to two dimensions. A shape optimization problem based on the tracking

Comparison analysis of analytical and lattice Boltzmann methods for simulation of turbulence decay in flows in converging and diverging channels ZAMM (IF 1.103) Pub Date : 20201102
Andriy A. Avramenko; Andrii I. Tyrinov; Igor V. Shevchuk; Nataliia P. DmitrenkoThe paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical

Transient response analysis of anisotropic solids with nano‐cavities by BEM ZAMM (IF 1.103) Pub Date : 20201102
Sonia Parvanova; Petia DinevaТwo‐dimensional in‐plane transient elasto‐dynamic problem for isotropic/anisotropic, finite/infinite solids with nano‐cavities is formulated. The mechanical model combines: (a) classical elastodynamic theory for the bulk anisotropic solid; (b) non‐classical boundary conditions and localized constitutive equation for the interface between nano‐cavities and anisotropic matrix within the frame of the

Modeling of electrodynamic processes by means of mechanical analogies ZAMM (IF 1.103) Pub Date : 20201027
Elena A. IvanovaThis study continues the line of earlier research in mechanical models of electrodynamic processes suggested in previous works. The basic steps we take to construct these models are: to formulate equations of a special type Cosserat continuum, and then to suggest analogies between quantities characterizing the stress–strain state of the continuum and quantities characterizing electrodynamic processes

Modeling stress‐affected chemical reactions in composite materials ZAMM (IF 1.103) Pub Date : 20201024
Elena VilchevskayaThe paper focuses on the modeling of the stress‐affected localized chemical reaction in particles embedded in a matrix material. The self‐consistent field method is used to account for the interaction between particles and to calculate the effective stress field acting on a separate particle. The kinetics of chemical reaction front is governed by the chemical affinity tensor that depends on the stress‐strain

On delamination of bi‐layers composed by orthotropic materials: Exact analytical solutions for some particular cases ZAMM (IF 1.103) Pub Date : 20201024
K. B. Ustinov; D. M. IdrisovEarlier [1, 2, 3], exact analytical solutions were obtained for three configurations of composed bi‐layers with semi‐infinite interface cracks: (i) the bilayer composed of two isotropic layers of equal thicknesses; (ii) an orthotropic layer with the central semi‐infinite crack; (iii) an isotropic layer on isotropic half‐plane of a different material (may be considered as a bilayer, the thickness of

Non‐stationary axially symmetric displacement of elastic half‐space in mixed boundary conditions ZAMM (IF 1.103) Pub Date : 20201024
Veniamin D. Kubenko; Ihor V. YanchevskyiThe exact solution of the axially symmetric problem concerning the non‐stationary load action on the elastic half‐space surface in the condition of mixed boundary value problem with the given normal stress and tangent displacement on the boundary is obtained. The Laplace and Hankel integral transforms are used. Integral transforms inversion is carried out by means of tabular ratios and convolutions

Editorial ZAMM (IF 1.103) Pub Date : 20201019
Lothar Collatz passed his first mathematics university exam in Berlin in 1933 supervised by Richard von Mises, who founded Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) in 1921. Since his graduation L. Collatz published short contributions [13] in ZAMM that summarized his presentations from the annual GAMM conferences. His first regular article appeared in ZAMM in 1935, right after the

Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz ZAMM (IF 1.103) Pub Date : 20201019
Götz Alefeld; Michael Plum; Christian Wieners 
Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method ZAMM (IF 1.103) Pub Date : 20201016
Jinghui Zhang; Jiale Lu; Salamat Ullah; Yuanyuan Gao; Dahai ZhaoThis paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving

The Caputo‐Fabrizio heat transport law in vibration analysis of a microscale beam induced by laser ZAMM (IF 1.103) Pub Date : 20201006
Abhik Sur; Sudip MondalIn the application of pulsed laser heating, such as laser hardening of metallic surfaces, conduction limited process is the dominant mechanism during the laser–workpiece interaction. As a consequence, time unsteady analysis of this problem becomes necessary. The present study examines the effect of ultra‐short‐pulsed laser heating in coupled thermoelastic vibration of a microscale beam resonator. The

A novel finite volume scheme for hyperbolic conservation laws ZAMM (IF 1.103) Pub Date : 20201006
Mingtian XuIt is well known that the conventional shock capturing schemes for hyperbolic systems of conservation laws yield oscillatory solutions near discontinuities when the mesh is not fine enough. In this article, an improved finite volume scheme (IFVS) is proposed to simulate hyperbolic conservation laws. In this scheme, some weighting coefficients are introduced to discretize the convection term. By eliminating

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method ZAMM (IF 1.103) Pub Date : 20201005
Rajarama Mohan Jena; Snehashish Chakraverty; Subrat Kumar Jena; Hamid M. SedighiThe study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation

Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects ZAMM (IF 1.103) Pub Date : 20200927
Shahzad Enayat; Mohammad Hashemian; Davood Toghraie; Erfan JaberzadehIn the current paper, size‐dependent mechanical analysis of functionally graded porous (FGP) nanobeams resting on Pasternak foundation in thermal environment is presented based on nonlocal strain gradient theory and Gurtin‐Murdoch surface elasticity theory. The nanobeam is modeled based on Euler‐Bernoulli beam theory, Timoshenko beam theory and Reddy's third‐order shear deformation theory and the set

Optimization of the rectilinear motion of a capsule system along a rough plane ZAMM (IF 1.103) Pub Date : 20200926
Tatiana Figurina; Timur GlazkovA rectilinear motion of a capsule system along a horizontal rough plane is considered. The system consists of a housing and an internal mass moving periodically along an inclined straight guide rigidly connected to the housing. The friction between the housing and the underlying plane is assumed to be Coulomb's one. The motion of the housing with a periodically changing velocity is investigated. Such

Analysis of Rosen type energy harvesting devices from porous piezoceramics with great longitudinal piezomodulus ZAMM (IF 1.103) Pub Date : 20200926
Andrey V. Nasedkin; Pavel A. Oganesyan; Arkady N. SolovievThis paper describes analytical and numerical modeling of the energy harvesting device based on composite piezoelectric materials. The device is a nonuniformly polarized porous piezoceramic compound plate such as a Rosen‐type piezoelectric transformer with single bimorph section. The effective properties of porous piezoceramics with great longitudinal piezoelectric strain coefficient d33 were calculated

Two bonded half‐planes with a parabolic inclusion ZAMM (IF 1.103) Pub Date : 20200923
Xu Wang; Peter SchiavoneIn this paper, primarily with the aid of analytic continuation, we derive analytic solutions for Eshelby's problem of a parabolic inclusion undergoing uniform anti‐plane and in‐plane eigenstrains located in one of two well‐bonded dissimilar elastic half‐planes. We obtain elementary expressions of the analytic functions defined in all three phases characterizing the elastic fields representing displacements

Dynamics of a rectangular thin plate with lumped mass under harmonic foundation and in‐plane excitations ZAMM (IF 1.103) Pub Date : 20200922
Liangqiang Zhou; Peng Ji; Fangqi ChenNonlinear dynamic behaviors including global bifurcations and multi‐pulse chaotic dynamics of a rectangular thin plate with lumped mass subjected to a harmonic foundation excitation and in‐plane excitation are investigated in this paper. With the von K a ́ rm a ́ n equation and Galerkin method, the dynamic equation of the first two modes for this model is obtained. Utilized the method of multiple scales

Scaling‐equivalent rotating flows ZAMM (IF 1.103) Pub Date : 20200917
Eugen MagyariThree outstanding rotating disk flows described by an exact solution of the Navier–Stokes equations are revisited in this paper. The purpose is to find out to what extent the corresponding boundary value problems can be mapped on each other by scaling transformations. The three addressed, and seemingly basically different axisymmetric flows are (A) the flow induced by a rough rotating disk, (B) the

Application of the R‐functions in free vibration analysis of FGM plates and shallow shells with temperature dependent properties ZAMM (IF 1.103) Pub Date : 20200916
Jan Awrejcewicz; Lidiya Kurpa; Tetyana ShmatkoThe free vibration of plates and shallow shells with/without cutouts made of functionally graded materials (FGM) is investigated using variational FG shallow shells with temperature dependent mechanical characteristics of the constituent materials. First‐order shear deformation theory of shallow shells is employed. It is supposed that material properties vary through thickness according to a power‐law

Two‐grid method for miscible displacement problem with dispersion by finite element method of characteristics ZAMM (IF 1.103) Pub Date : 20200915
Yanping Chen; Hanzhang HuA combined method consisting of the mixed finite element method for the pressure equation and finite element method with characteristics for the concentration equation is proposed to solve the coupled system of incompressible two‐phase flow in porous media. Two‐grid algorithm based on the Newton iteration method is developed and analyzed for the nonlinear coupled system. It is shown, both theoretically

Chaotic dynamics of size‐dependent curvilinear Euler–Bernoulli beam resonators (MEMS) in a stationary thermal field ZAMM (IF 1.103) Pub Date : 20200912
Anton V. Krysko; Jan Awrejcewicz; Ilya E. Kutepov; Vadim A. KryskoIn this work the chaotic dynamics of flexible curvilinear Euler–Bernoulli micro‐beams embedded into a stationary temperature field is investigated. The temperature field is modelled based on a the Duhamel–Neumann theory and is free from the restrictions on the temperature field distribution along beam thickness. The von Kármán geometric strain–stress relations are employed. The governing nonlinear

Three‐dimensional Hiemenz stagnation‐point flows ZAMM (IF 1.103) Pub Date : 20200910
Patrick D. WeidmanA modification of Hiemenz's two‐dimensional outer potential stagnation‐point flow of strain rate a is obtained by adding periodic radial and azimuthal velocities of the form b r sin 2 θ and b r cos 2 θ , respectively, where b is a shear rate. This leads to the discovery of a new family of three‐dimensional viscous stagnation‐point flows depending on the shear‐to‐strain‐rate ratio γ = b / a that exist

Upper bound on the solution for a class of 2‐D Chemotaxis model with generalized logistic damping ZAMM (IF 1.103) Pub Date : 20200909
Wenbin Lyu; Qiong WangIn this paper, we consider the upper bound of the solution for a class of 2‐D Chemotaxis model with generalized logistic damping in a smooth bounded domain. We show how upper bound of the solution qualitatively depends on the parameters in the equation.

Vibration analysis of multi walled piezoelectric nanoresonator conveying fluid flow: Influences of surface/interface energy and walled number effects ZAMM (IF 1.103) Pub Date : 20200909
Sayyid H. Hashemi KachapiIn current work, the surface/interface parameters effects and walled number of fluid‐conveying multi walled piezoelectric nanoresonator (FC‐MWPENR) are investigated on dimensionless natural frequency (DNF) with considering viscous fluid velocity. The mentioned nanostructures (FC‐MWPENR) are subjected to nonlinear electrostatic excitation, nonlinear van der Waals interaction and also viscoelastic foundation

Piezoaeroelastic system on the basis of a double aerodynamic pendulum ZAMM (IF 1.103) Pub Date : 20200907
Yury D. Selyutskiy; Andrei P. Holub; Ching‐Huei LinDuring last decades, possibilities to use piezoelectric generators to harvest energy from the flow‐induced vibrations of different structures are intensively studied. In particular, various wind power harvesters based on fluttering oscillations of wing sections are proposed. In this work, an electromechanical system is considered that consists of a double aerodynamic pendulum connected with a piezoelectric

Editorial ZAMM (IF 1.103) Pub Date : 20200907
Holm Altenbach; Valentin L. PopovWith issue 9 of the 100th volume of the Zeitschrift für Angewandte Mathematik und Mechanik we continue the publication of special papers devoted to the anniversary. The paper Ludwig Föppl and Gerhard Schubert: Unknown Classics of Contact Mechanics written by E. Popova and V. L. Popov highlights an outstanding but mostly unknown contribution of Ludwig Föppl and Gerhard Schubert to contact mechanics

Ludwig Föppl and Gerhard Schubert: Unknown classics of contact mechanics ZAMM (IF 1.103) Pub Date : 20200907
Elena Popova, Valentin L. Popov 
Stability of Poiseuille flow in an anisotropic porous layer with oblique principal axes: More accurate solution ZAMM (IF 1.103) Pub Date : 20200904
B.M. Shankar; I.S. ShivakumaraThe stability of fluid flow in an anisotropic porous medium of Brinkman type is investigated. Anisotropy in the permeability is considered such that its longitudinal principal axis is oriented arbitrarily with the horizontal, while transversely it is isotropic. A fourth‐order eigenvalue problem obtained by performing a linear stability analysis is solved numerically using the Chebyshev collocation