Search

Time-varying reliability models of multi-cracked beam structures are established in this paper, which provide a theoretical method for the safety evaluation of multi-cracked beam structures. The reliability models proposed in this paper consider the interaction between the complex statistical correlations between system parameters during system operation and maintenance correlations, which is a difficult problem in the time-varying reliability modeling that takes into account work mechanisms and maintenance behavior. In the proposed models, multiple cracked elements are regarded as a dependent series system. The stresses, crack extensions, and multiple failure modes between each element constitute the complex failure dependence of the system. The time-varying reliability models of a multi-cracked beam structure are established via the neural network method and failure dependence analysis. Moreover, the failure dependence coefficient is proposed to quantify the time-varying failure dependence. Based on the working principle of the beam structures and the maintenance mechanism for the cracked state of the beams, a time-varying system reliability mode considering the maintenance dependence is proposed. Furthermore, the maintenance dependence coefficient index is proposed to quantitatively measure the interaction between the maintenance dependence and the failure dependence. Finally, the validity of the model is verified through the Monte Carlo simulation method. In the numerical examples, the relationship between maintenance dependence and failure dependence is illustrated and the influences of the statistical characteristics of the maintenance characteristic parameters on the maintainability and failure dependence are analyzed. [ABSTRACT FROM AUTHOR]

Time-varying reliability models of multi-cracked beam structures are established in this paper, which provide a theoretical method for the safety evaluation of multi-cracked beam structures. The reliability models proposed in this paper consider the interaction between the complex statistical correlations between system parameters during system operation and maintenance correlations, which is a difficult problem in the time-varying reliability modeling that takes into account work mechanisms and maintenance behavior. In the proposed models, multiple cracked elements are regarded as a dependent series system. The stresses, crack extensions, and multiple failure modes between each element constitute the complex failure dependence of the system. The time-varying reliability models of a multi-cracked beam structure are established via the neural network method and failure dependence analysis. Moreover, the failure dependence coefficient is proposed to quantify the time-varying failure dependence. Based on the working principle of the beam structures and the maintenance mechanism for the cracked state of the beams, a time-varying system reliability mode considering the maintenance dependence is proposed. Furthermore, the maintenance dependence coefficient index is proposed to quantitatively measure the interaction between the maintenance dependence and the failure dependence. Finally, the validity of the model is verified through the Monte Carlo simulation method. In the numerical examples, the relationship between maintenance dependence and failure dependence is illustrated and the influences of the statistical characteristics of the maintenance characteristic parameters on the maintainability and failure dependence are analyzed.

• The transverse vibration of a cracked non-uniform beam is studied. • Crack is modeled as an equivalent massless rotational stiffness. • An exact closed-form explicit solution is given. • Fundamental functions are proposed to satisfy boundary conditions more conveniently. • The frequency equation is derived based on a second-order determinant. Non-uniformity and damage are the two primary subjects in studying the vibrations of the beam-type elements. An exact closed-form explicit solution for the transverse displacement of a non-uniform multi-cracked beam with any type of boundary conditions is introduced. The generalized functions and the distributional derivative concepts are adopted. Four fundamental functions are introduced. These functions make the boundary conditions' process and compute the frequency equation more convenient. By introducing the non-dimensional parameters, the non-dimensional motion equation of the damaged beam with an arbitrary count of cracks is derived, and its exact closed-form explicit solution is obtained based on the four introduced fundamental functions. The standard method of computing these functions is presented, and the closed-form of these functions is determined for eight cases like uniform and conical beams. The closed-form of the frequency equation and mode shapes of the non-uniform multi-cracked beam are derived for several boundary conditions. The influence of the count of cracks, their location and intensity, and the boundary conditions on the natural frequency and mode shape are assessed by running a numerical study. The first and second frequencies of a conical beam are computed to verify the obtained results by applying this newly presented closed-form solution and the Differential Quadrature Element Method. A good agreement is evident when the obtained results are compared. [ABSTRACT FROM AUTHOR]

• Forced vibrations of the multi-cracked Timoshenko beams are studied analytically. • Closed-form solutions of the dynamic problems are derived. • Two types of springs are utilized to model the mechanical properties of cracked section. • The present solutions can be reduced to Rayleigh and Euler-Bernoulli cases. • Shearing effects to the solutions are significantly discussed. This paper concentrates on obtaining the closed-formed analytical solutions of the steady-state forced vibration of the multi-cracked Timoshenko beams with damping effects. Varying from the Euler-Bernoulli beam, the mechanical properties of a cracked section of the Timoshenko beam are described as a rotational spring and a transversal spring models. Initially, the Green's function of a one-cracked simple supported Timoshenko beam is derived. With the assistant of the solution of the one-cracked situation and the transfer matrix method, the Green's functions of the multi-cracked Timoshenko beams for various boundary conditions are also obtained. The present Green's functions can be degenerate to the Rayleigh and Euler-Bernoulli cases, and the multiple cracked-models can be reduced to the single-cracked cases when the depths of some cracks are specified to be zero. In the numerical section, the FEM results and the solutions in some references are used to validate the present solutions. Some numerical examples in this research are to reveal the influences of the shearing effect on the vibration performances of the one-cracked Timoshenko model as well as the multiple cracks cases. Additionally, the effects of some significant physical parameters, like the crack depth and crack locations, are also discussed in some numerical examples. [ABSTRACT FROM AUTHOR]

The nonlinear vibration analysis of cracked structures could be a suitable indicator for diagnosing defects. When breathing cracks appear on the beam, its behavior can be modeled as a bilinear oscillator. In this paper, the nonlinear vibration behavior of a cantilever beam with multiple breathing cracks is investigated. For this purpose, the multi-cracked beam's stiffness is calculated by introducing the effective length for the local stiffness reduction in the vicinity of cracks. Furthermore, owing to the importance of the damping variation in a cracked beam, its exact value is evaluated through theoretical expressions. A continuous polynomial function with the Weierstrass approximation is exploited to simulate the bilinear behavior of breathing cracks. By performing nonlinear analysis using the perturbation technique, the cracked beam's dynamic behavior is studied. Moreover, the sensitivity of the response to the crack parameters in the primary resonance of the structure is analyzed. Finally, the sensitivity of the beam's nonlinear response to the different number of breathing cracks and various crack depths is investigated. It is shown that the beam with a higher number of cracks or deeper ones has obvious softening behavior, and hence a more significant jumping can appear in the response. [ABSTRACT FROM AUTHOR]