V. V. Matveev

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 1. Longitudinal 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.

Approximate Analytical Determination of Vibrodiagnostic Parameters of the Presence of a Closing Crack in Bar Elements Under Subharmonic Resonance

The paper presents the results of approximate calculations of vibrodiagnostic parameters indicating the presence of a closing fatigue edge crack in bars with different boundary conditions versus the crack parameters and exciting load under subharmonic resonance in principal bending mode.

Approximate determination of vibrodiagnostic parameter of nonlinearity for an elastic body due to the presence of a breathing crack at a subharmonic resonance

The reliability of one of the simplest methods for calculating vibration parameters in the region of subharmonic resonance for an elastic body with a breathing crack, which is modeled by a single-degree-of-freedom system with a bilinear asymmetric characteristic of the restoring force is assessed. The method is based on the proposition that in a nonlinear system the subharmonic vibrations exist alongside with the fundamental forced ones and are the free vibrations maintained by a driving force.

On the Problem of Improvement of the Damping Ability of Rotor Blades of Contemporary Gas-Turbine Engines

We present the results of experimental investigations of the influence of structural and technological factors on the damping ability of lock joints of compressor blades carried out at the Pisarenko Institute of Problems of Strength of the National Academy of Sciences of Ukraine, study the possibility of using dampers mounted in shroud joints of turbine blades, and formulate some recommendations concerning the possibility of im proving the damping ability of rotor blades of contemporary gas-turbine engines.

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 2. Determination of Diagnostic Parameters in Principal and 2-nd Order Superharmonic Resonances

Using the constitutive equations derived by the author, variously approximated analytical expressions have been obtained for the determination of principal- and superharmonic-resonance vibrodiagnostic parameters of fatigue damage in the form of a Mode I closing crack in an elastic body. The reliability of the analytical solution is assessed by comparing the calculated and the numerical solution results.

Vibrodiagnostic Parameters of the Presence of a Semielliptic Breathing Crack in Circular Bars Under Super- and Subharmonic Resonances

The paper addresses the methods and results of approximate analytical and numerical calculation of vibrodiagnostic parameters of the presence of a closing semielliptic surface crack in a circular cantilever bar under super- and subharmonic resonances of the lower natural mode of bending vibrations at force and kinematic excitation. The dependences of vibrodiagnostic parameters on crack location and relative depth and on the point of load application are presented. The amplitude-frequency response under the strong superharmonic resonance is shown to differ from those under the weak superharmonic resonance and subharmonic resonance. The reasons why the results of the analytical solution differ from the numerical one obtained by using a finite-element model of the bar have been clarified.

The Influence of Inelastic Resistance on Vibrations of an Elastic Body with a Closing Crack under the Main and Subharmonic Resonances

The paper presents some findings of analytical and numerical investigations aimed at determining the influence of inelastic resistance on vibrodiagnostic parameters indicating the presence of damage, such as a breathing crack, in an elastic body under the main and subharmonic resonances.

Damping capacity of rods in a centrifugal-force field

One of the factors determining the reliability and longevity of the working blades of turbomachinery is their damping properties, e.g., the capacity of the material to dissipate vibration energy irreversibly. The characteristic operating conditions of the blades -the presence of centrifugal forces and high temperatures-exert a significant influence on the damping capacity of the material. Methods used to investigate the damping capacity of the blade material under conditions that approach the operating conditions as closely as possible are therefore of greatest practical interest. These possibilities are exhibited by equipment that permits determination of the vibration decrement of rods on a rotating disc by exciting vibrations in them kinematically through the disc [i].

Influence of Inelastic Resistance on Vibrodiagnostic Parameters of the Presence of a Closing Crack in an Elastic Body Under Superharmonic Resonance

The authors discuss the methods for approximate determination of vibrodiagnostic parameters of the presence of a closing mode I fatigue crack in an elastic body taking into account various types of inelastic resistance under second-order superharmonic resonance.

Vibration Characteristics of Fatigue Damage of Beam-Type Structural Components

We consider free vibration of an elastic cantilever beam with a closing edge crack. The crack is simulated by an elastic pivot whose compliance is taken to be finite and is determined from the energy equivalence criterion. An algorithm has been constructed for sequential calculation of the beam vibration modes for each beam vibration cycle, whereas the number of cycles is limited. It is demonstrated that the beam vibration modes other than the initially preset one are induced during the crack opening and closing. The distinct features of such modes have been studied. We have analyzed the sensitivity of the vibration-damage characteristics which are determined from the assessment of nonlinear distortions of the displacement, acceleration, and strain waveform of the cross sections of the beam with a closing crack.