Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 2. Strong resonance

Using the approach proposed in Part 1, an approximate calculation of vibration parameters is made for an elastic body with a closing crack, in the region of a strong 1/2-order subharmonic resonance with the lower-harmonic amplitude of free vibration spectrum larger than the main amplitude of forced vibrations. __________ Translated from Problemy Prochnosti, No. 3, pp. 5–16, May–June, 2008.     

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 1. Available and Proposed Methods of Solution

The paper discusses the available analytical methods and the results of investigation of vibrations of elastic bodies with a bilinear asymmetric characteristic of restoring force that simulates the behavior of a local discontinuity in a material in the form of a closing fatigue crack. An approximate analytical method is put forward for the determination of vibrodiagnostic parameters of the vibration process of the nonlinear system under study in the range of weak superharmonic resonances.     

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 fatigue damage in rectangular plates. Part 1. A procedure of determination of damage parameters

We describe a procedure of approximate analytical determination of fatigue damage parameters of rectangular plates. As an initial damage characteristic we apply the relative value of the plate potential-strain-energy variation due to availability of a Mode I crack, and, based on this value, we find relations for determination of the plate natural frequency variation, as well as parameters of distortion of monoharmonic oscillations in the modes of main resonance and superharmonic resonance of the 2nd order.Translated from Problemy Prochnosti, No. 6, pp. 5–16, November–December, 2004     

Approximate analytical determination of vibrodiagnostic parameters of the presence of a crack in an elastic body under superharmonic resonance

We discuss an approximate analytical method for calculating the main parameter of nonlinearity of vibration of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force, under a strong 2nd-order superharmonic resonance.     

Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 2. Straight cracks of constant depth

The paper discusses the results of analytical determination of vibrodiagnostic parameters of fatigue damage in the form of Mode I straight cracks of constant depth in a rectangular homogeneous uniform-thickness plate with various plate fastening conditions and vibration modes. It is demonstrated that, in the range of the relative crack depth up to 0.3, the parameter of distortion of vibration monoharmonicity in the 2nd-order superharmonic resonant mode is one-two orders of magnitude higher than the value of a relative change of the plates natural frequency.Translated from Problemy Prochnosti, No. 1, pp. 43–59, January–February, 2005.