Dynamic characteristic analysis of fuzzy-stochastic truss structures based on fuzzy factor method and random factor method

A new method for random vibration analysis of stochastic truss structures

Random seismic response analysis of truss structures with uncertain parameters

Interval natural frequency and mode shape analysis for truss structures with interval parameters

The reliability-based optimization of active bars' placement and feedback gains of a closed-loop control system for stochastic intelligent truss structural active nonstationary random vibration control is presented. The optimal mathematical model with the reliability constraints on the mean square value of structural dynamic displacement and stress response are built based on the maximization of dissipation energy due to control action, where not only the structural physics parameters, geometric dimensions, and damping are considered as random variables, but also the applied forces are considered as nonstationary random excitation. The numerical characteristics of the nonstationary random responses of stochastic intelligent structure are developed by the random factor method. The rationality and validity of the presented model are demonstrated via an engineering example, and the effect of randomness of the structural parameters on the control performance is also examined.

Stochastic homogenized effective properties of three-dimensional composite material with full randomness and correlation in the microstructure

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs.

Supply chain coordination for fuzzy random newsboy problem with imperfect quality

The random factor method (RFM), an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of uncertain structure system. The natural frequencies of the system can be expressed as the function of the random factors. By using the random variable’s algebra synthesis method, the expressions for the mean value and standard deviation of natural frequencies are derived from Rayleigh quotient. The reliability mode and the safety probability of random systems are defined, and then the frequency reliability sensitivity analysis method is presented. The formulas of failure probability sensitivity are derived when random variables are normally distributed. The reliability index is evaluated, and its sensitivity to mean values and variances are mathematically expressed, then the efficiency and accuracy of the proposed method are demonstrated by a numerical example.

The paper reports on interferometric measurements of flow over a NACA0015 airfoil model during flutter limit cycle oscillations. The airfoil model is fixed on an elastic support allowing motion with two degrees of freedom — pitch and plunge. The structural mass and stiffness matrices can be tuned to certain extent, so that the eigenfrequencies of the two modes approach as needed. The model is equipped with dynamic pressure probes and sensors measuring the airfoil vertical position. The flow field around the airfoil was measured by Mach-Zehnder interferometer and registered using a high-speed camera synchronously with the mechanical vibration and pressure measurements. The Mach number of the incident airflow was gradually increased and the response of the aeroelastic system to initial impulse measured, until the flutter instability onset occurred. Flutter boundaries were evaluated for various additional masses attached (i.e., for various plunging mode eigenfrequencies), and post-critical behavior of the system investigated. The interferograms recorded by the high-speed camera were postprocessed, yielding pressure distribution around the airfoil during its vibration and an estimate of the total aerodynamic force and energy transfer from the airflow to the structure.

In the present paper, a framework of dimension-reduction modeling method is developed for a dual stochastic dynamic structural system of spectrum-compatible non-stationary stochastic ground motion processes and stochastic structures. With the aid of the proposed method, the random variables used to describe the stochastic characteristics of the non-stationary ground motion processes and the structural parameters are respectively represented by the one-elementary-random-variable functions, contributing to an entire stochastic dynamic structural system readily described by merely two elementary random variables. Owing to the fact that the number of the elementary random variables needed is extremely small, the set of the representative points associated with the elementary random variables can thus be selected by the widely-used number theoretical method, and then the probability density evolution method can be conveniently combined to conduct the dynamic response analysis and dynamic reliability evaluation of nonlinear stochastic structures. In the numerical examples, the probability density evolution analysis of an eight-storey reinforced concrete frame structure with random parameters subjected to spectrum-compatible non-stationary stochastic ground motion processes is investigated as a case study. Numerical results fully demonstrated the effectiveness and robustness of the proposed method.

The performance of an updated time-domain least-squares identification method for identifying a reduced-order linear system model in case of limited response measurements and its use in structural health monitoring is evaluated. It is shown that the incorporation of a mass-invariability constraint enhances the robustness of the parametric identification procedure. The full structural stiffness and mass matrices are identified from the identified reduced-order model by using the condensed model identification and recovery method. The damage state is considered to be represented by an incremental stiffness degradation model. The degradation in stiffness is estimated through the minimization of an error function defined in terms of Rayleigh quotients. The performance of the proposed scheme is examined with reference to the simulated damage due to earthquake excitation in a 10-story building with rigid floor diaphragm.

Most of the rotating machines used in process industries or in manufacturing plant need maintenance and repair. However, failure of just one of these machines can disturb an entire process with losses in terms of production, manpower, and equipment repair or replacement. Also failure of a single machine component in process industries like petrochemicals or power stations can result in the loss of millions of rupees per down time hour. These facts together with higher costs for new equipment have placed increased demand on plant maintenance to keep existing equipment operating efficiently with higher availability. A number of non-destructive crack detection techniques have been developed, such as ultrasonic testing, X-ray technique, magnetic particle method etc. Every method has some advantages and disadvantages. In recent years, ultrasonic testing has gained greater attention for monitoring the cracks in structures and machine components. Most of these methods are very laborious and time consuming, in the case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by the use of vibration monitoring technique such as model analysis. Therefore the development of vibration monitoring techniques has received increasing attention in recent years. Damage in structure alters its dynamic characteristics. The change is characterized by a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus a vibration technique can be suitably used as a nondestructive test for crack detection of components to be tested. In this paper, theoretical and experimental analysis of a vibrating cantilever beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies are sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size.

Research and /or Engineering Questions/Objective: Friction-induced vibration is a common phenomenon on the frictional contact interface between two solids in relative motion, which can be observed in many mechanical applications, especially for the brake system. The friction-induced vibration originated from the friction interface can transmit through the rigid connection structure of mechanical system and forms a vibration transmission path. The vibration transmission path, mainly reflected by the natural frequency and the damping ratio, influences the friction-induced vibration of system, even under the same friction interface. However, there is limited report on the friction-induced vibration of mechanical system under different vibration transmission paths. Therefore, the effect of structural stiffness in vibration transmission path on friction-induced vibration is investigated and discussed. Methodology: The friction tests are carried out on a small-scale tribometer, which achieves a frictional contact between the balls and disc samples. The structural stiffness of vibration transmission paths is reflected by different fixtures of samples, whose dynamic characteristics are tested by the hammer method. In addition, a detailed three-dimensional finite element model based on different structural stiffness in vibration transmission paths is established to simulate the experimental process. At last, a four-degree-of-freedom friction-induced vibration model, including the interaction between the structure characteristics and the friction interface, is established to investigate the influence of the vibration transmission paths on the system stability. Results: The instability of the friction system decreases with the increasing structural stiffness in vibration transmission path. However, when the structural stiffness exceeds the critical value, the instability of friction system is excited again, accompanied by severe friction-induced vibration and high frequency squeal noise. Similarly, the wear morphology is also influenced by vibration transmission paths. The higher structural stiffness is, the better tribological behavior of the contact interface is displayed. Once the critical stiffness is exceeded, more complicated tribological behavior of the contact interface is shown. Limitations of this study: Applying the findings to practice system is still under studied since a real friction system is much more complex comparing to the customized small-scale tribometer.</p><p>What does the paper offer that is new in the field in comparison to other works of the author: The effect of structural stiffness in vibration transmission path on friction-induced vibration is investigated. The conclusions obtained by experimentally and numerically are beneficial for understanding the effect of structural stiffness in vibration transmission path on stability, vibration response and tribological behavior of the friction system. Conclusion: The results show that the stability and vibration response of the friction system is significantly affected by vibration transmission paths. Evaluating and eliminating the influence of vibration transmission path on the friction-induced vibration is extremely crucial and meaningful for investigating the generation mechanism of the friction-induced vibration more precisely.

Engineering computation under uncertainty – Capabilities of non-traditional models

Air foil bearing supports the rotating journal using hydrodynamic force generated at thin air film. The bearing performances, stiffness, damping coefficient and load capacity, depend on the rotating speed and the performance of the elastic foundation, bump foil. The main focus of this study is to decide the dynamic performance of corrugated bump foil, structural stiffness and Coulomb damping caused by friction between bump foil and top foil/bump foil and housing. Structural stiffness is determined by the bump shape (bump height, pitch and bump thickness), dry-friction, and interacting force filed up to fixed end. So, the change of the characteristics was considered as the parameters change. The air foil bearing specification for analysis follows the general size; diameter 38.1 mm and length 38.1 mm (L/D=1.0). The results show that the stiffness at the fixed end is more than the stiffness at the free end, Coulomb damping is more at the fixed end due to the small displacement, and two dynamic characteristics are dependent on each other.