Effect of break of the elastic axis of a rotor with transverse crack on its vibrational characteristics

We perform a numerical analysis of the effect of break of the elastic axis on the characteristics of bending vibrations of a multispanned unbalanced rotor with transverse crack mounted on elastic damping supports. The break of the elastic axis in the cross section with crack is caused by local plastic strains. The solution of the problem is sought in the form of a sum of the contributions of the forces of gravity, residual disbalance, and the crack responsible for the break of the axis. The problem is reduced to the numerical analysis of the trajectory of the shaft with its subsequent improvement by the method of iterations. Amplitudes and phases of several first harmonics of vibrational displacements are found as functions of sizes, initial orientation of the crack, and the ratio of vibrational and static displacements. In the presence of the break of the elastic axis, the magnitudes of vibrational characteristics undergo significant changes. The amplitudes of vibrations induced by the crack are comparable with the amplitudes of vibrations caused by disbalance. It is shown that the behavior of the trajectory of motion regarded as a function of principal parameters is nonlinear. Institute for Problems in Mechanical Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 82–89, July–August, 1997.     

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.     

Dissipation of energy of kinematically excited transverse oscillations in materials of elastic systems

We suggest a procedure for the calculation of kinematically excited transverse oscillations of rods with variable cross sections with regard for energy losses in cyclically strained materials. The procedure is based on the application of the asymptotic methods of nonlinear mechanics. We deduce analytic expressions both for the construction of amplitude-frequency characteristics of forced oscillations of the investigated dissipative elastic system and for the determination of the phase shift. These expressions make it possible to analyze the dynamic stressed states of rod-like engineering structures as functions of the parameters of applied loads in the stage of design. Translated from Problemy Prochnosti, No. 5, pp. 58–68, September–October, 1997.     

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.     

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.     

The effect of damping and force application point on the non-linear dynamic behavior of a cracked beam at sub-and superresonance vibrations

The finite element model of an elastic body with a closing crack is presented. Using this model, we show that the non-linear distortions of vibrations at superharmonic and subharmonic resonances are the high sensitive indicators of crack presence. The intensity of these indicators manifestation substantially depends on the level of damping in the system and on the load application point. __________ Translated from Problemy Prochnosti, No. 5, pp. 61–67, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).     

Investigation into nonlinear vibrations of composite plates using the <Emphasis Type="Italic">R</Emphasis>-function theory

We have developed an effective approach to the solution of problems on geometrically nonlinear vibrations of orthotropic multilayer plates of irregular shapes in a classical statement based on the use of the R-function theory, Ritz variational method and Bubnov-Galerkin method. Using the proposed method, problems of vibrations of both multilayer rectangular plates and plates of complex geometries have been solved. The effect of the domain geometry and boundary conditions on the amplitude-frequency characteristics has been investigated. __________ Translated from Problemy Prochnosti, No. 5, pp. 101–113, September–October, 2007.     

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.     

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.     

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.     

Longitudinal vibrations of a cantilever beam with a transverse crack. Part 2. Piecewise-linear model

A model of vibrations of a cracked body that is based on the difference in the stiffness characteristics in tension and compression is represented as a linear system with piecewise-constant parameters. We determine the parameters of vibrations of this system. We plot the relative crack size as a function of the difference in amplitudes in tension and compression, which is related to the vibration amplitude of a crack-free body with account for the resistance. The approaches described are applicable to evaluation of the “survival” of a structure (i.e., evaluation of the residual durability of a cracked structure). Zaporozh'e State University, Zaporozh'e, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 78–85, September–October, 1999.     

Distortion of the sinusoidalness of the forms of vibrations of systems with a disturbed rotary symmetry and the mode localization phenomenon. Report 1

An analysis is made of data available in the literature on investigation of the distortion of the sinusoidalness of the forms of vibration and the mode localization phenomenon of systems with disturbed rotary symmetry. The results are given of a calculational experiment on determination of the influence of the amount of elastic coherence of subsystems and detuning of their frequencies to distortion of the sinusoidalness of the forms of vibrations of the systems considered.Translated from Problemy Prochnosti, No. 10, pp. 45–52, October, 1992.     

Elastic characteristics of iron-glass materials at low temperatures

We present the results of an investigation of the influence of low temperatures on the elastic characteristics of iron-glass materials with 3, 5, 12, or 20 wt.% of glass at 77–300 K and show that Young’s modulus exponentially decreases as the glass content of the material increases. We suggest a relation for the evaluation of the Young’s modulus of a composite at various temperatures according to its value at room temperature. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 42 – 46, January – February, 1998.     

Resonant conversion of plasmons in a rippled metal-insulator structure

The propagation of long-range plasmons on a rippled metal film embedded in an insulator is studied. It is shown that the ripple of the film leads to the appearance of additional dissipative losses of these plasmons. It is established that these additional losses are caused by resonant coupling between long-range and short-range plasmons produced by the ripple of the film. Pis’ma Zh. Tekh. Fiz. 24, 22–29 (September 26, 1998)     

Numerical investigation of intercoupling vibration of a mistuned turbomachinery compressor rotor wheel

Results of numerical experiments involving the determination of possible causes of disk rim failure of a rotor wheel with blades, having the root of a dovetail joint type, are presented. The theory of coupling vibration of mechanical systems is used to elucidate the cause of rather high vibration stresses in the disk rim. Numerical investigation into the influence of specific features of the natural vibration spectrum of the rotor wheel as a system with cyclic symmetry and of the blade frequencies mistuning upon resonant vibrations have been performed. The investigation has been performed in the framework of the project “Development of Methods for Lowering the Level of Vibration Stresses in GTE Parts” of the State Scientific and Technical Program “Enhancing the Dependability and Life of Machines and Structures”. Translated from Problemy Prochnosti, No. 2, pp. 67–78, March–April, 1997.     

Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 1. Prescribed motion

The behavior of an open mechanical dissipative system formed by a viscoelastic hardening body and an elastic working element used for the energy transfer between the testing machine and the deformed body is described by a third-order dynamic differential equation with controlling parameters that depend on the reduced mass and stiffness of the system, its viscous resistance, the degree of strain hardening, the type of the stressed state of the body, and the dissipation of energy in a viscous ambient medium. We analyze the dynamics of uniaxial tension of the deformed body below and above its elasticity limit for the case where the forces induced in the process of motion are determined by the kinematics of the testing machine with prescribed motion. We establish the dynamic nature of the nonlinear section of the tensile stress-strain diagram beyond the elasticity limit of the viscoelastic body corresponding to the so-called “nonlinear elasticity”. It is shown that the appearance of this section is connected with a transient relaxation process. Upon the termination of this process, the forces acting in the system are determined by the viscous flow of the body corresponding to its yield limit. Above the elasticity limit of the body, we observe the formation of a bistable state of the system caused by changes in the controlling parameters and lag effects and leading to its macroscopic acoustic activity. I. N. Frantsevich Institute for Problems in Material Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 16–27, July–August, 1998.     

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 2. Bending vibrations, analytical solution

We discuss the possibility of efficient application of the harmonic analysis of strain cycles formed in an elastic rod in the process of natural or resonance vibrations to the evaluation of the degree of fatigue damage. Fatigue damage is simulated by discontinuities of the material resulting in different values of the modulus of elasticity in the processes of tension and compression. In determining the potential strain energy of a rod in the presence of a crack on the basis of linear fracture mechanics, this model enables us to deduce expressions for relative changes in the stiffness of the rod in the presence of edge and surface cracks. By using the asymptotic method of nonlinear mechanics, we find the second approximation to the solution of the differential equation of vibrations of the rod whose nonlinearity is explained by the effect of “breathing” of the discontinuity formed in the material. It is shown that the discontinuity of the material caused by fatigue damage is responsible both for changes in the natural frequency of vibrations of the rod and for significant contributions of the constant component and even harmonics to the spectrum of strain cycles in the rod. The values of the constant component and the amplitudes of even harmonics (mainly of the second one) may serve as an efficient parameter for the detection of fatigue damage to materials. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 9–22, November–December, 1998.     

Improving the accuracy of the determination of elastic characteristics and their temperature dependence

The paper describes a method and setup that provide a better accuracy of the determination of the modulus of elongation and Poisson's ratio at various temperatures in comparison with the widely used methods. As an example, we give experimental data on the temperature dependence of elastic characteristics of D-20 aluminum alloy rods over a temperature range from 77 to 293 K, as obtained by this method. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 36–44, May–June, 1999.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 2. Experimental and calculation results

The results of experimental investigation of the relationship between the natural frequency of the first mode bending and longitudinal vibrations of titanium alloy and alloyed steel cantilever beams and the crack parameters (crack depth and location) are presented together with the data on calculation of the relative change of the vibration frequency of cracked beams, which are obtained by the proposed analytical approaches. Based on a comparative analysis, we choose fairly simple and sufficiently accurate formulas for calculating the frequencies of bending and longitudinal vibrations of a cantilever beam with an open or closing crack. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 45–53, May–June, 1999.