Measurement of dynamic characteristics of latex foams by the antiresonance method

Measuring and calculation methods for the dynamic characteristics of tubular specimens of low-modulus latex foams and composites based on them, under longitudinal vibrations in a low-frequency region (up to 200 Hz), are developed. The method is based on the effect of antiresonance. Data on the influence of the basic formulation-processing factors on the dynamic characteristics (gelatination time and content of the plasticizer and chopped fibers) are presented. The results obtained can be used to choose the composition of latex foams for lining acoustic channels, injectors, ejectors, and phase inverters, as well as to control products quality. This method can be applied directly to full-size articles. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 249–258, March–April 2000.     

Resonance methods for determining the complex shear moduli of orthotropic composites

A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented. The errors in the computed values of dynamic shear moduli caused by inaccuracies in the experimental determination of resonance frequencies are examined. A new variant of the resonance method is developed, which permits one to find three complex shear moduli of a composite from the resonant frequencies and the damping of torsional vibrations of three rods oriented along three symmetry axes of the material. For computing the moduli in the case of an overdetermined system, an algorithm of nonlinear optimization based on the least-squares method is recommended. From the results obtained it follows that, for determining the interlaminar shear moduli with a necessary accuracy, the rods must be sufficiently thick. It is shown that a good agreement alone between calculated and experimental frequencies of flexural and torsional vibrations of rods does not ensure a reliable determination of the moduli of interlaminar shear if experiments are carried out on wide test specimens cut out from a thin plate. Recommendations are given for the choice of geometrical sizes of test specimens for resonance experiments. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 721–744, November–December, 2007.     

Determination of the vibration displacements and stresses in the vibrations of structurally inhomogeneous shells using the method of holographic interferometry

We develop a method of determining the vibration displacements and stress-strain state of the surface of a shell of revolution with structural singularities during resonance vibrations. We give the results of experimental studies. Four figures. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, 112–118.     

Torsional vibrations and dispersion of torsional waves in orthotropic composite rods

The Barr’s refined theory of torsional vibrations of isotropic rods of noncircular cross section is generalized for an orthotropic material. An analysis of natural frequencies of torsional vibration of free-free orthotropic prismatic rods of rectangular cross section is carried out with the help of an exact solution of the frequency equation. For orthotropic CFRP and GFRP rods, the improved theory, which takes into account the normal stresses and inertia forces in the axial direction, in some cases, predicts a noticeable raise in the natural frequencies compared with those following from the Saint-Venant classical theory. A good agreement is obtained between the experimental and calculated values of natural frequencies of torsional vibrations of rectangular quartz and fiber glass rods. The dispersion of torsional waves in an orthotropic quasi-homogeneous rod is considered. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 165–182, March–April, 2008.     

Active damping of forced resonance vibrations of an isotropic shallow viscoelastic cylindrical panel under the action of an unknown mechanical load

Using a new approach, we consider the problem of active damping of the forced resonance vibrations of a viscoelastic isotropic cylindrical panel with simply supported edge faces. The mechanical load is assumed to be unknown; it can be found from the experimental data of a sensor. The problem is solved by the Bubnov–Galerkin method. A relation was obtained for the potential difference that has to be supplied to an actuator for the damping of resonance vibrations of the panel. We also study the influence of sizes of sensors and actuators, the dissipative properties of materials, and temperature on the efficiency of active damping of the forced resonance vibrations of a cylindrical panel.     

Steady-state vibrations of a thin two-layer plate with delamination

We consider the problem of harmonic vibrations of a thin two-layer plate with horizontal crack. The problem is solved with the help of the null-field approach. The influence of the shape of the crack contour on the amplitude-frequency characteristics of plate vibrations is investigated. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 83–89, April–June, 1998.     

Quasi-one-dimensional method for the two-dimensional magnetotelluric sounding inverse problem

The two-dimensional magnetotelluric sounding inverse problem is solved by a quasi-one-dimensional method. A linearization method is proposed for one-dimensional inverse problems. The appearance of false conducting structures in the solution of the inverse problem is considered and some counter-measures are suggested. The quasi-one-dimensional method is applicable to many-dimensional magnetotelluric sounding inverse problems if the electrical conductivity is a priori known to vary slowly along the Earth’s surface. __________ Translated from Prikladnaya Matematika i Informatika, No. 22, pp. 5–11, 2005.     

Influence of physical nonlinearity on resonance vibrations and dissipative heating of inelastic rectangular plates

On the basis of a concept of complex characteristics, we present a statement of nonlinear conjugate problems of forced resonance vibrations and dissipative heating of inelastic plates of physically nonlinear materials, for which the real and imaginary parts of mechanical complex characteristics depend on the amplitude of deformations. Numerical-analytical methods for the solution of the indicated nonlinear problems are presented. An analysis of the influence of physical nonlinearity on the amplitude–frequency and temperature–frequency characteristics and on the coefficient of damping of vibrations of rectangular plates is performed.     

An experimeental study of the natural vibrations of supported shells

We give the results of an experimental study of the frequencies and shapes of the natural vibrations of shells of zero Gaussian curvature that are closed in the circumferential direction. The study was conducted using the method of holographic interferometry. We consider the influence of support by elastic ribs and attachment of rigid bodies on the dynamic properties of the shell system. We describe the methodology of the experiment. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 80–86.     

A biodegradable polymer nanocomposite: Mechanical and barrier properties

The preparation of an environmentally friendly nanocomposite based on plasticized potato starch and unmodified montmorillonite clay is described. Data on the influence of montmorillonite concentration on the mechanical properties of the materials obtained are reported. The effective elastic constants of the nanocomposites are calculated. The calculation results are compared with experimental data. The influence of montmorillonite content on the moisture permeability is also investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 61–76, January–February, 2008.     

Large Elastic Strains of Plastic Foams

The elastic deformation of plastic foams with a low (< 6%) volume fraction of solid phase is described based on a 4-rod equivalent element. A criterion is proposed which allows one to determine the parameter of structure of this element. Based on an analysis of the equivalent element, a procedure is developed for constructing the compression diagram of plastic foams in the region of large (> 70%) strains. The calculation results are compared with data found in the literature and experimental results for polyurethane foams obtained by the present authors. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 619–632, September–October, 2005.     

Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method

As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved this nonlinear equation and obtained its amplitude–frequency relation by the homotopy analysis method (HAM). The accuracy of the present results is shown by comparison between our results and the perturbation method. Numerical results show that the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric plates.     

Nonlinear vibrations of circular plates with notches. Method of <Emphasis Type="Italic">R</Emphasis>-functions

We investigate vibrations of geometrically nonlinear circular plates with two notches. For the determination of natural frequencies of vibrations, the method of R-functions is used. Nonlinear vibrations of a plate are expanded in eigenmodes of linear vibrations containing R-functions. As a result of using the Bubnov–Galerkin method, we obtain a dynamic system with three degrees of freedom, which is investigated by the method of multiple scales.     

Soft-mode related origin of the boson peak and acoustic-phonon broadening in glasses

We study the origin of the boson peak and an associated mechanism for acoustic-phonon broadening (below the peak) in glasses exhibiting a high-frequency sound above the peak. The origin is related to the Ioffe-Regel crossover for inelastic (resonant) scattering of acoustic phonons from harmonic soft-mode vibrations. The broadening mechanism is due to the resonant interaction of a harmonic soft-mode vibration with acoustic phonons, which results in the resonant scattering. We find that the associated width of the phonon is independent of temperature and is characterized by a power-law frequency dependence with the exponent varying from ϰ=2 just below the boson peak to ϰ=4 at lower frequencies. The dependences seem to partly agree with some recent experimental data for the glasses under consideration. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 77–90, January, 2008.     

Spectral approach to quasi-3D inverse problem of vertical electric sounding

A method for solving the inverse problem of vertical electric sounding is proposed and investigated. The method uses the anomalous apparent resistivity spectrum. Translated from Prikladnaya Matematika i Informatika, No. 1, pp. 68–77, 1999.     

The uncoupled problem of thermoelastic vibrations of a cylinder

Using the theory of functions of a complex variable, we construct an approximate solution of the problem of steady thermoelastic vibrations of a cylinder with curvilinear cavities, not taking account of the interaction of the strain and temperature fields. The results of numerical computations are given in the case of radially symmetric vibrations of a cylinder with a cavity. Two figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 107–112.     

An experimental study of the vibrations of cylindrical shells with holes

We give the results of an experimental study of the frequencies and shapes of the natural vibrations of thin-walled cylindrical shells of revolution weakened by cuts; these results were obtained by the method of holographic interferometry. We establish the effect of the profile and the number of holes, reinforcement by elastic ribs, and attached solid bodies on the fundamental dynamic characteristics of the shell system. We describe the method by which the experiment was conducted. Four figures, 2 tables. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 121–125.     

Three-dimensional models of marine magnetotelluric sounding of nonhomogeneous media

We consider the direct problem of three-dimensional modeling of marine magnetotelluric sounding of nonhomogeneous media in the presence of a vertical magnetic field component in the primary field. The problem is reduced to a system of volume integral equations. __________ Translated from Prikladnaya Matematika i Informatika, No. 27, pp. 46–53, 2007.     

The effect of the quasistatic component of microacceleration on thermocapillary flows

The article presents the results of numerical calculations of thermocapillary convection in a rectangular cavity allowing for residual microaccelerations on board a spacecraft. The mathematical model is the quasihydrodynamic equation in the incompressible fluid approximation. __________ Translated from Prikladnaya Matematika i Informatika, No. 19, pp. 69–81, 2004.