Generalization of the continuous and discrete structural approaches to the solution of problems of the dynamics of laminated composite plates and structures with stratification. Part 2. Analytic decomposition of unknown functions. Results and comparisons

A three-dimensional solution of the problem of determination of the frequencies and modes of natural vibrations of multilayer plates is obtained on the basis of the method of analytic separation of variables. We compare the models with analytic separation of variables and polynomial approximation of unknown functions over the thickness of the structure. Within the framework of the continuous structural approach, the applied model enables one to determine the frequencies and modes of natural vibrations for a broad range of problems with sufficiently high accuracy. If it is necessary to improve the accuracy of results, then one can pass to the discrete structural version of the model. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 93–99, November–December, 1999.     

Numerical simulation of heat transfer in multilayer structures with generalized nonideal contact

A procedure is proposed for calculation of a class of problems on heat transfer in multilayer structures with generalized nonideal contact. The procedure is illustrated by calculating the heat transfer in a stack of plates with liquids moving in gaps between the plates. Institute of Technical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 5, pp. 773–778, September–October, 1996.     

Mixed-hybrid scheme of the finite element method for solving the problems on bending,free vibration,and stability of plates

To solve a problem on bending, vibration, and stability of plates, a hybrid finite element has been constructed on the basis of Zienkiewicz’s triangle. A mixed approximation is used for the plate deflection and turning angles. It is shown that with a decrease in the triangle dimensions the mixed approach ensures convergence both for the plate deflection and the bending moments, which is practically independent of the way the plate is split into triangular elements. In the problems on free vibrations and stability of plates, the mixed approach yields more exact values of the eigenfrequencies and critical loads as compared to a classical Zienkiewicz’s triangle. The results of the numerical analysis of the convergence and accuracy of the solutions to a number of test problems on bending, free vibration, and stability of a square plate are presented. __________ Translated from Problemy Prochnosti, No. 4, pp. 108–122, July–August, 2008.     

Investigation of Free Vibrations of Multilayer Shallow Shells and Plates of Complex Shape in Plan

We propose an algorithm for the solution of the problem of free vibrations of multilayer shallow shells and plates based on the variational methods and the theory of R-functions. By using this algorithm, we solve the problems posed for shallow shells (spherical and cylindrical) and plates of complex shape in plan. We present the results of investigation of the dependences of the natural frequencies of vibrations of shallow shells and plates with different number of layers on the angle of rotation of the principal directions of each layer.     

Forced stationary vibrations of flexible plates induced by random narrow-band excitations

We consider some problems related to the analysis of the modes of forced vibrations of elastic plates induced by random narrow-band excitations. The investigation of nonlinear vibrations of a plate is performed within the framework of a reduced discrete model constructed by using the Hamilton variational principle, finite-element methods, and generalized coordinates. To study the dynamical state of the analyzed structure, we perform numerical simulation of the vibrations induced by a particular realization of narrow-band excitations. Each realization of random narrow-band excitations is obtained with the help of a shaping filter of the second order and describes harmonic oscillations with slowly varying amplitude and phase. We also consider the scenarios of transitions between different modes of vibrations of the plate and estimate the time of its residence in different dynamical states. Kiev National University of Civil Building and Architecture, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 105–117, March–April, 2000.     

Measurement of viscoplastic properties of a liquid in experiments with a torsion viscosimeter

The results of a numerical solution of the problem of vibrations of a torsion viscosimeter filled with an incompressible viscoplastic liquid are presented. It has been shown that in the vicinity of the rotation axis there appears a dead zone, whose boundary changes in the process of vibrations. The influence of plastic properties of the liquid on the characteristics of viscosimeter vibrations has been determined. A method for identifying viscoplastic properties by the observed parameters of vibrations is proposed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 1, pp. 124–127, January–February, 2007.     

Determination of the thermodynamic properties of liquid <Emphasis Type="Italic">n</Emphasis>-hexadecane from the measurements of the velocity of sound

The density, the isobaric expansion coefficient, the specific heats at constant pressure and constant volume, and the isothermal compressibility coefficient of liquid n-hexadecane have been calculated in the range of temperatures 298–433 K and pressures 0.1–140 MPa from the data on the velocity of sound. The coefficients of the Tate equation in the above parametric range have been determined. The table of the thermodynamic properties of n-hexadecane has been presented. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 150–156, January–February, 2009.     

Dielectric properties of CaCu<Subscript>3</Subscript>Ti<Subscript>4</Subscript>O<Subscript>12</Subscript> prepared by sol–gel self combustion technique

The preparation of Calcium copper titanate (CCTO) nanopowder was carried out by a sol–gel self combustion method. The X-ray diffraction analysis indicated that the samples calcined at 800 °C were fully crystallized in the CCTO phase. The results of atomic force microscope showed the particles size of CCTO was in the range of 60–80 nm. The absorption bands corresponding to vibrations of Cu–O, Ti–O–Ti and νCa–O were observed at 512, 450 and 562 cm⁻¹ using FTIR. The samples sintered at 950 °C showed the densities as high as 97% of theoretical density. The grain sizes of sintered pellets were determined by HRSEM. The dielectric properties of prepared samples were studied by LCR meter.     

Vibroacoustic monitoring of the homogeneity and workability of concrete mixes by their hydromechanical state in the process of mixing

The method of monitoring of the homogeneity and determination of the workability index of a concrete mix from the level of vibroacoustic vibrations excited in the mixer in mixing of concrete has been described. The vibration-level values dependent on the hydromechanical state of a concrete mix and its rheological characteristics in the process of mixing and formation of its vibroacoustic image have been measured at the check point of the lining of the concrete mixer and have mathematically been processed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 342–347, March–April, 2009.     

Application of mixed variational formulations based on the finite element method to the solution of problems on natural vibrations of elastic bodies

We consider mixed variational formulations and the application of the mixed approximations of the finite element method to the solution of problems on natural vibrations of elastic bodies. To solve the generalized spectral problem, three forms of the mixed variational formulations are proposed. The correctness and stability of mixed variational formulations for displacements, strains and stresses are investigated. Matrix equations of the mixed method are given whose solution is performed using the modified algorithm of the steepest descent method. The results of calculations for natural frequencies of free vibrations of a straight and a circular beam are presented that are obtained in the solution of the problem in a two-dimensional formulation based on the classical and mixed finite-element method approaches. __________ Translated from Problemy Prochnosti, No. 2, pp. 121–140, March–April, 2008.     

Fracture of plates with variable thickness

We study the mechanics of fracture of plates with variable thickness weakened by rectilinear through cracks and propose a method for the solution of problems of the theory of elasticity for plates of this kind. We also generalize theoretical results of the investigation of crack propagation in deformable elastoplastic plates to plates with variable thickness and present solutions of new problems in the mechanics of structural arrest of propagating through cracks by local changes in the thickness of platelike structural members near the crack tip. Azerbaijan Technical University, Baku, Azerbaijan. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 46–54, May–June, 1996.     

Identification of the nonlinear viscous properties of fluids by the vibrational method

Effects occurring in an oscillatory viscosimeter upon its filling with nonlinear viscous fluids whose rheological properties are described by the Ostwald-Weyl model have been revealed. The possibilities of the vibrational method for identification of the rheological belonging of media to nonlinear viscous ones with a power rheological law and of their nonlinear properties in the regime of free damped and forced vibrations have been discussed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 5, pp. 70–77, September–October, 2005.     

High-temperature creep and long-term strength of structural elements under cyclic loading

We present a method for solving problems of high-temperature cyclic creep and damage accumulation in structural elements. The asymptotic expansion and averaging techniques both over the period of forced vibrations of a body and that of slowly varying loads are used for the set of equations describing the creep and damage processes in thin-walled structural elements. __________ Translated from Problemy Prochnosti, No. 5, pp. 45–53, September–October, 2008.     

On an approach to numerical solution of stress-strain state problems for nonthin plates and shells

Numerical solution of elastic equilibrium problems for nonthin plates and shells of constant and variable thickness is based on using a curvilinear-mesh method in combination with the Vekua method — reduction of three-dimensional elastic equations to a recurrent sequence of boundary problems in a two-dimensional region. Coefficients of the first and second quadratic forms for a conditional mediane surface are calculated by means of a metric of boundary faces without any derivatives with respect to their local bases. Specific examples of numerical solution of the test problems for a thick plate bending case, for which the exact and approximate solutions can be also found by other methods, have proven the proposed numerical approach to be efficient (in terms of a rapid convergence and accuracy). A numerical solution has been obtained for a problem of bending for a nonthin plate of constant and variable thickness made of an orthotropic material and for a shell with a circular recess under axial compression. __________ Translated from Problemy Prochnosti, No. 2, pp. 41–54, March–April, 2008.     

Dynamics of three-layer bars

We study vibrations of a three-layer bar under local, pulse, and resonance loads of rectangular and sinusoidal forms. Bernoulli hypotheses are used for describing the kinematics of bearing layers. For rigid compressible filler, the elastic-theory relationships with linear approximation of the function of displacement of its points vs. the transverse coordinate z hold good. Analytical solutions to the problems have been obtained, numerically and comparatively analyzed. The probability of a spurious resonance occurrence is discussed. __________ Translated from Problemy Prochnosti, No. 6, pp. 133–146, November–December, 2006.     

Stress intensity solutions for cracked plates by the dual boundary method

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved. __________ Translated from Problemy Prochnosti, No. 5, pp. 81–93, September–October, 2007.     

Longitudinal vibrations of a cross-cracked cantilever beam. Part 1. Small vibrations

Based on the analysis of solutions to differential equations of longitudinal vibrations of a macroelastic body whose nonlinearity is due to “breathing” of the damaged material under tension-compression cycling, we estimate the suitability of the deformation-cycle characteristic of a body under free and forced vibrations for the diagnostics of fatigue damage in structural elements. We consider the following problems: the construction of a simplified model of longitudinal vibrations of mechanical elements with cross cracks, the investigation of free vibrations of a cracked body including resistance forces, the forced vibrations of a cracked body taking into account a perturbation force including and excluding resistance forces, and the study of vibrations of a beam with resistance different from the linear one. We show that the presence of a macrocrack is responsible for the occurrence of representative higher harmonics in the deformation-cycle spectrum. They can serve as a sensitive and efficient vibration-diagnostic parameter to detect cracks in structural elements. Zaporozh'e State University, Zaporozh'e, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 23–34, March–April, 1999.     

A novel method for synthesizing nano-crystalline MgTiO<Subscript>3</Subscript> geikielite

We report here for the first time a novel method of preparing nano-crystalline metatitanate, MgTiO₃ geikielite, with crystalline size varying from 20–40 nm. The preparation has been carried out by coprecipitation method involving titanium hydroxide and magnesium nitrate solution. The samples were characterized by using transmission electron microscopic, powder XRD and FT-IR spectroscopic studies. The sample annealed at 900 K for 2 h show ten X-ray diffraction peaks corresponding to the pure geikielite phase. FT-IR spectra of the nano-crystalline geikielite exhibit strong broad vibrational bands near 1000, 650 and 470 cm⁻¹ arising from normal vibrations of the TiO₃ group.     

Plane stress creep of damaged plates

Creep of plates that undergo damage due to in-plane mechanical loads is discussed. A method for solving the initial boundary value problem of creep is based on combined application of R-functions, Ritz, and Runge-Kutta-Merson methods. Solution structures have been obtained for main types of boundary conditions. The influence of a material’s heteroresistance and damage parameter on the creep and creep-rupture strength of a plate with a circular opening is studied. __________ Translated from Problemy Prochnosti, No. 6, pp. 51–60, November–December, 2007.     

Surfactant-assisted hydrothermal preparation of submicrometer-sized two-dimensional BiFeO<Subscript>3</Subscript> plates and their photocatalytic activity

2-Dimensional bismuth ferrite (BiFeO₃) plates were hydrothermally synthesized starting from Bi(NO₃)₃ and Fe(NO₃)₃ in the presence of cetyltrimethylammonium bromide (CTAB) as a morphology directing template. The amount of CTAB was altered to study their effects on the final results. The average diameter and thickness of BiFeO₃ plates were about 1.3–2 μm and 200–300 nm. X-ray diffraction (XRD), scanning electron microscopy (SEM), UV–visible diffuse reflection spectrum (UV–vis DRS) were used to investigate the samples’ crystallinity, purity, morphology, spectral features. Furthermore, the effect of the morphology on photocatalysis was also evaluated by photodecolorization of orange II under a blended-light mercury fluorescent lamp (λ ≥ 410 nm). As a result, BiFeO₃ plates showed a much higher photocatalytic activity than bulk BiFeO₃ for photodecolorization of orange II, suggesting potential application in photocatalysis.