Dynamic instability of a pipe with internal mobile liquid blocks

We consider the problem of parametric vibrations of a rectilinear pipeline with internal mobile liquid blocks. As a result of its solution, we determine the influence of the size of the liquid blocks and their velocity on the character of the loss of stability of the pipe. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 114–121, May–June, 1999.     

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.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 1. analytical approach

We consider a perfectly elastic cantilever beam with a crack. The influence of the crack depth and location on the vibration mode of the beam is simulated by a local change in the cross section. This problem is solved by the Rayleigh method. Fairly simple formulas for the determination of the natural frequency of the first mode of bending and longitudinal vibrations of a cantilever beam with an open and closing crack are derived. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 35–44, March–April, 1999.     

Influence of flow with separation on the statistical characteristics of vibrations of the profile a compressor cascade

For a plane compressor cascade, we study the influence of the modes of flow with and without separation on the character of vibrations of a profile as a part of the cascade. It is established that the transition to the region of flow with separation is accompanied by the appearance and rapid growth of the instability of vibrations of the profile. The analysis of statistical characteristics of vibrations of the profile shows that the absolute values of the coefficients of variation and asymmetry substantially increase in the case of flow with separation. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. SOYUZ Moscow Scientific and Industrial Association, Moscow, Russia. Translated from Problemy Prochnosti, No. 3, pp. 122–125, May–June, 1999.     

Deformation of a rectangular plate under impulsive loading

We report the results of the experimental investigation of the behavior of a rectangular plate in the processes of cutting by linear shaped charges according to the axisymmetric and asymmetric modes of unilateral loading and fracture caused by the explosion of a linear charge. It is shown that the transverse velocities and displacements of the same points of the plate subjected to unilateral explosive cutting by shaped charges are much higher (almost by an order of magnitude) than the corresponding parameters for the other modes of fracture. We also observed that the values of longitudinal mass velocities and displacements in the case of bilateral cutting by shaped charges are 1.5–7.0 times higher than the same parameters for unilateral cutting and explosive fracture without using shaped charges. It is also shown that the longitudinal accelerations attain their maximum values in the case where the shaped charge is placed at a focal distance from the plate. Subbotin Institute for Geophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 85–90, November–December, 1998.     

Procedure for numerical investigation of forced vibrations of three-dimensional structures with nonlinear elastic elements based on the finite-element method

We describe a numerical procedure which allows one to investigate forced vibrations of complex three-dimensional structures with nonlinear elastic elements, develop a computational dynamic model on the basis of the finite-element method and the method of generalized coordinates, and investigate vibrations of an actual structure of a load-bearing mounting of an aircraft engine. We also analyze the effect of nonlinear elastic elements on the dynamic behavior of the structure and evaluate the efficiency of their application. Kiev State Technical University of Civil Engineering and Architecture, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 107–116, July–August, 1997.     

Effect of the contact of crack lips under variable loads

We formulate a contact problem of the theory of elasticity with unilateral constraints for cracked bodies under random variable loading and consider a special case of harmonic loads very important for practical applications. The problem is solved by the method of boundary integral equations of the elastodynamic theory of cracked bodies. We also analyze typical singularities of the kernels of potentials of these equations and develop an algorithm for the solution of unilateral contact problems of the dynamics of cracked bodies based on the determination of the saddle point of a subdifferential boundary functional. We solve dynamical problems of propagation of plane harmonic compression-dilatation waves in a plane with cracks of finite lengths under the assumption of unilateral contact of the crack lips. We present numerical results and investigate the effect of contact interaction of the crack lips both quantitatively and qualitatively. Timoshenko Insitutes of Mechanics, Ukrainian Academy of Sciences, Kiev. Kharkov State Technical University of Motor Transport and Roads, Kharkov. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 1, pp. 38–52, January–February, 1996.     

On determination of vibration characteristics of a beam with a closing crack in bending vibrations

We consider free vibrations of an elastic cantilever beam with an edge crack, which is simulated as a beam portion with a decreased moment of inertia. The weight of this portion is assumed to be constant, while the dimensions of the portion are determined by the energy criterion of equivalence. We propose an analytical approach to determination of natural frequencies and vibration modes, of a beam with an open or closing crack and to investigation of nonlinear distortions of the displacement wave and acceleration and deformation of various sections of a beam with a closing crack. The solution allows for the possibility that more than one vibration mode of a beam can be generated at the moment of the crack opening and includes the effect of the crack on the strain distribution in the beam volume. It is demonstrated that the approach we propose gives reliable relationships between various vibration characteristics of a beam and the crack parameters and makes it possible to solve an inverse problem of damage diagnostics. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 5–23, May–June, 2000.     

Numerical study of vibrations of a nonlinear mechanical system simulating a cracked body

The paper presents the results of a numerical study of forced and decaying vibrations of a system simulating a body with a closing crack under the action of various modes of a nonlinear restoring force and nonlinear viscous friction or the hysteresis-type energy dissipation. We obtained the general patterns of appearance of higher harmonics of the Fourier expansion of time dependence of vibration of a cracked body model. The sensitivity of the higher-harmonic method to the presence of a crack is compared with that of some other vibration damage indicators. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 65–80, November–December, 1999.     

Free vibrations of spherical belts with circular and longitudinal ribs

We propose a procedure for the numerical evaluation of the frequencies of free vibrations of spherical belts with circular and longitudinal ribs, determine those frequencies, and study the influence of the parameters of the ribs on the natural frequencies of free vibrations of shell structures reinforced by ribs. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 124–127, May–June, 1998.     

Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 2. Action of external forces

We analyze the motion of a mechanical dissipative system containing a viscoelastic strain-hardening body with one degree of freedom under the action of an external tensile force depending on its controlling parameters and initial loading conditions. We construct periodic and aperiodic solutions of a nonautonomous third-order dynamical system taking into account transient processes of motion from the initial state. It is shown that the transient process of motion of the system is realized either as forced damped oscillations responsible for its acoustic activity or as an aperiodic process of damping. We also consider transient dynamic processes in a viscoelastic Maxwell body subjected to static loading in the case where strain hardening is absent. Frantsevich Institute for Problems in Materials Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 12–26, September–October, 1998.     

On the procedure of evaluating the damping ability of the materials of specimens subjected to torsional and bending vibrations

We describe a method for the design and numerical analysis of compact mechanical vibrating systems with generators of vibrations on their inertial weights and establish the conditions of damping of unwanted vibrations in these systems aimed at guaranteeing the absence of favorable conditions for the introduction of systematic errors to experimental results. The designed and manufactured vibrating systems are dynamically balanced, and predicted values of the frequencies of their natural vibrations satisfactorily agree with the experimental data. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 145–152, July–August, 1997.     

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 1. Applied mathematical model of the dynamic deformation of laminated composite structures

We construct an applied mathematical model of dynamic deformation of laminated structures. The proposed model can be regarded as a generalization of continous and discrete structural approaches to the analysis of laminated structures. This model enables one either to consider a structure as a single layer with reduced stiffness characteristics or split it across its thickness into a set of components each of which may include several layers and/or parts of layers. It is also possible to simulate various conditions of contact of layers (rigid or sliding). The differential operators appearing in the proposed model are similar to the operators used in the classical theory of shells, which simplifies the numerical realization of the model. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 86–91, July–August, 1999.     

Statement of the problem of optimization and control of tissue temeprature distribution in local hyperthermia of malignant tumors

We consider a model of thermal processes in treatment by local hyperthermia. The model is based on the classical nonlinear biothermal equation. We formulated a problem of optimization consisting of maximization of the mortality function of tumor cells and finding a control for which the temperature distribution in the tumor maximizes the therapeutic effect, while the injury function of healthy tissue is small. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev; Institute of Experimental Pathology, Oncology, and Radiology, National Academy of Sciences of Ukraine Kiev; Academic Scientific Complex “A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus,” Minsk; National Technical University, Kiev. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 4, pp. 641–646, July–August, 1996.     

Nonlinear free vibrations of thin-walled beams in torsion

Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional–axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped–clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin’s method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the modulation of the amplitudes and phases of the vibration modes. The obtained results are compared with the available results in the literature that are obtained from boundary element and finite element methods, which reveals an excellent agreement between different solution methodologies. Finally, the internal resonance and the stability of coupled and uncoupled nonlinear modes are investigated. This study can be a preliminary step in the understanding of complex dynamics of such systems in internal resonance excited by external resonant excitations.     

Effect of interlayer defects on the strength of carbon-fiber laminates

We show the effect of interlayer discontinuities on the load-carrying capacity of carbon-reinforced laminates. The interlayer defects are simulated by introducing polypropylene films between the layers. We describe the types of fracture of flat specimens for different stacking modes and defects of various sizes under both tensile loading and in the case of three-point bending. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 77–81, September–October, 1998.     

Stochastic response of nonlinear system in probability domain

A stochastic averaging procedure for obtaining the probability density function (PDF) of the response for a strongly nonlinear single-degree-of-freedom system, subjected to both multiplicative and additive random excitations is presented. The procedure uses random Van Der Pol transformation, Ito’s equation of limiting diffusion process and stochastic averaging technique as outlined by Zhu and others. However, the equations are rederived in generalized form and arranged in such a way that the procedure lends itself to a numerical computational scheme using FFT. The main objective of the modification is to consider highly irregular nonlinear functions which cannot be integrated in closed form and also to solve problems where analytical expressions for probability density function cannot be obtained. The procedure is applied to obtain the PDF of the response of Duffing oscillator subjected to additive and multiplicative random excitations represented by rational power spectral density functions (PSDFs). The results are verified by digital simulation. It is shown that the procedure provides results which compare very well with those obtained from simulation analysis not only for wide-band excitations but also for very narrow-band excitations, which are weak (when normalized with respect to mass of the system.) This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

Analysis of free vibrations for Rayleigh — Lamb waves in a microstretch thermoelastic plate with two relaxation times

The propagation of free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress-free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Green and Lindsay (G—L) theories of thermoelasticity. The secular equations for the microstretch thermoelastic plate in closed form for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. At short wavelength limits, the secular equations for both modes in a stress-free thermally insulated and isothermal homogeneous isotropic microstretch thermoelastic plate reduce to the Rayleigh surface wave frequency equation. The results for symmetric and skew-symmetric wave modes are computed numerically and presented graphically. The theory and numerical computations are found to be in close agreement. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 36–46, January–February, 2009.     

Influence of the modes of thermomechanical preloading on the resistance of heat-resistant steels to brittle fracture

We describe the methods and results of the experimental investigation of the influence of various modes of thermomechanical preloading on the resistance of nuclear pressure-vessel steels to brittle fracture. We studied specimens of different thickness (25–150 mm) made of the base and weld metals of the vessels of water-moderated, water-cooled nuclear power reactors. The materials under consideration belong to different strength classes. It is shown that the positive effect of thermomechanical preloading is preserved or even strengthened after the subcritical ductile growth of a crack in the process of preloading. We compare the available experimental data with the results of numerical calculations performed by using the Chell model. It is shown that the Chell model fails to explain some experimental data. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 126–138, March–April, 1999.     

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.