Frequency Contour-Strip Method for Characterization of Damage in Structures under Noisy Conditions

Eigen-frequency, compared with mode shape and damping, is a more practical and reliable dynamic feature to portray structural damage. The frequency contour-line method relying on this feature is a representative method to identify damage in beam-type structures. Although this method has been increasingly applied in the area of damage identification, it has two significant deficiencies: inefficiency in establishing the eigen-frequency panorama; and incompetence to identify cracks in noisy conditions, considerably impairing the effectiveness in identifying structural damage. To overcome these deficiencies, a novel method, termed the frequency contour-strip method, is developed for the first time. This method is derived by extending the frequency contour line of 1D to frequency contour strip of 2D. The advantages of the frequency contour-strip method are twofold: (i) it uses the isosurface function to instantly produce the eigen-frequency panorama with a computational efficiency several orders of magnitude higher than that of the frequency contour-line method; and (ii) it can accommodate the effect of random noise on damage identification, thereby thoroughly overcoming the deficiencies of the frequency contour-line method. With these merits, the frequency contour-strip method can characterize damage in beam-type structures with more efficiency, greater accuracy, and stronger robustness against noise. The proof of concept of the proposed method is performed on an analytical model of a Timoshenko beam bearing a crack and the effectiveness of the method is experimentally validated via crack identification in a steel beam.

Stiffness-Oriented Structure Topology Optimization for Hinge-Free Compliant Mechanisms Design

This paper presents a stiffness-oriented structure topology optimization (TO) method for the design of a continuous, hinge-free compliant mechanism (CM). A synthesis formulation is developed to maximize the mechanism’s mutual potential energy (MPE) to achieve required structure flexibility while maximizing the desired stiffness to withstand the loads. Different from the general approach of maximizing the overall stiffness of the structure, the proposed approach can contribute to guiding the optimization process focus on the desired stiffness in a specified direction by weighting the related eigen-frequency of the corresponding eigenmode. The benefit from this is that we can make full use of the material in micro-level compliant mechanism designs. The single-node connected hinge issue which often happened in optimized design can be precluded by introducing the eigen-frequency constraint into this synthesis formulation. Several obtained hinge-free designs illustrate the validity and robustness of the presented method and offer an alternative method for hinge-free compliant mechanism designs.

Analysis of influence of elastic properties of deadwood bearings on shaft line operability

The paper considers the ship shafting and its design. Depending on the constructive features, operating conditions, effects of continuous, dynamic, variable and random loads the operation of the shaft line is accompanied by wear of the shafting structure and auxiliary parts. The formulas for calculating the maximum permissible clearances during operation in stern bearings of propeller shafts are given, according to the norms and technical and operational requirements. A graph of the maximum permissible clearances in metal stern bearings is presented. There has been carried out a dynamic design of the shaft line in order to define the influence of rigid characteristics of the stern bearings on eigen frequency of transverse vibrations. It is noted that the service life of the shaft line depends on the material of bushings or liners of the bearings (bakout, babbit, textolite, caprolon, bronze, polyurethanes, rubber) and their wear degree. The design scheme of the ship shaft line on elastic supports with a coefficient of rigidity is presented. To assess the influence of the elastic properties of deadwood bearings, the method of initial parameters was used. According to the researchers’ opinion, the greater the wear, the lower their stiffness coefficient. At a certain wear degree of deadwood bearings, there occurs resonance at the lowest operating frequencies. It has been proved that the greater the deflection at the attachment point of the propeller, the lower the eigen frequency of transverse vibrations of the shaft line. It has been pointed out that the calculations should include the separation of the shaft line from the deadwood bearing, since it contributes to a decrease in eigen frequency and causes a resonance during transverse vibrations.

Crack modeling of metal rod eigen-frequencies

The paper presents the development of approaches to the crack detection in metal rod structures based on the analysis of the lowest eigen-frequency modes. Full-scale experiments and numerical calculations are carried out, and the obtained results are compared. A vibration analyzer is used for full-scale experiments, and numerical calculations are performed by using Autodesk Inventor. With regard to the internal friction, the antinodes of various vibration forms were identified using a specially developed program. The model includes sensors for the the field experiment as masses affecting the frequency-response characteristics. The dependences are obtained for eigen-frequencies in the presence of cracks and for the crack locations. The polynomial dependences of the crack location on the lowest eigen-frequency modes of the rod can be used to analyze the crack position of in cantilever beams.

Effect of the inner-surface baffles on the tangential acoustic mode in the cylindrical combustor

The combustion instability in a propulsion system is a ubiquitous problem. The radial baffles usually installed on the injector faceplate eliminate the combustion instability (acoustic pressure oscillation) in the propulsion system. In this article, the longitudinal baffles are installed on the inner surface of the combustor wall to control the combustion instabilities. The first-order and second-order tangential modes are induced in the experiments. The effects of the parameters of the baffle on the acoustic pressure oscillation in the cylindrical combustor are investigated. The effect of the combustor nozzle on the tangential modes has been systematically investigated. It is concluded that the eigen-frequency and amplitude of the first-order tangential mode decline with the increase in the longitudinal baffle number and height. For the second-order tangential mode, the eigen-frequency and amplitude monotonically increase until a maximum value (four baffles), subsequently decrease with the increase in the baffle number and height. The combustor without the nozzle obtains a lower frequency than that with the nozzle, especially for the low baffle height in the combustor.

Estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements

The previous research described estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements in continuous change in variable rod parameters. It is however known that in construction, rods are generally designed with piecewise constant change in the section parameters. Besides, in another work, the criterion was formulated for assessment of optimum solutions of piecewise constant sections of I-rods with stability or the first eigen-frequency limits, without considering the strength requirements. This paper focuses on a more general problem of estimated closeness of optimum piecewise constant section width in I-rods with stability or first eigen-frequency limits to the predicted minimum material consumption with regard to strength requirements.

Assessment criterion for optimum design solutions of piecewise constant sections in I-rods with stability or first eigen-frequency limits

The criterion for the minimum material consumption of strips strengthening the I-rod with stability or first eigen-frequency limits is formulated in previous studies for the case of continuous change of the variable parameter. It is known that this solution allows evaluating a real design project not only by the criterion of its proximity to the minimum material consumption, but also by the reference point in the real design. In many cases, it is used to replace the continuous change in the variable size of the rod-strengthening piecewise constant sections. The boundaries of these sections are based on the minimum material consumption. The width of the strengthening strips is determined by the optimization methods. The paper proposes the criterion allowing to correctly assess the termination of the optimization processes.