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Abstract Bolt connection is one of the main fixing methods of cylindrical shell structures. A typical bolted connection model is considered as a tuned system. However, in the actual working conditions, due to the manufacturing error, installation error and uneven materials of bolts, there are always random errors between different bolts. To investigate the influence of non-uniform parameters of bolt joint, including the stiffness and the distribution position, on frequency complexity characteristics of cylindrical shell through a statistical method is the main aim of this paper. The bolted joints considered here were simplified as a series of springs with random features. The vibration equation of the bolted joined cylindrical shell was derived based on Sanders’ thin shell theory. The Monte Carlo simulation and statistical theory were applied to the statistical analysis of mode characteristics of the system. First, the frequency and mode shape of the tuned system were investigated and compared with FEM. Then, the effect of the random distribution and the random constraint stiffness of the bolts on the frequency and mode shape were studied. And the statistical analysis on the natural frequencies was evaluated for different mistuned levels. And some special cases were presented to help understand the effect of random mistuning. This research introduces random theory into the modeling of bolted joints and proposes a reference result to interpret the complexity of the modal characteristics of cylindrical shells with non-uniform parameters of bolt joints.

The coupling vibration of a blade-disk-shaft unit is generally studied on the assumption that all the blades are identical. However, the mistuning feature always occurs due to manufacturing tolerances and other reasons in engineering practice. Therefore, a shaft-disk-blades coupling model with the random mistuning feature is derived based on our previous work. Then the statistical analysis on vibration characteristics of a blade-disk-shaft unit is performed. The uncertainty effects of blade parameters on coupling characteristics between the subcomponents are exhibited. The Monte Carlo simulation and statistical theory are used to capture the probability distributions of coupling characteristics. The natural frequency distributions of coupling modes are obtained under different mistuning levels and evaluated through confidence intervals. Then the mode shapes, obtained by eigenvector, are plotted to derive the evolution law of coupling mode type in a random mistuning system. At last, the localization factor is defined, then its statistical results are obtained to evaluate the mode localization magnitude under different mistuning levels. [ABSTRACT FROM AUTHOR]

Bolt connection is one of the main fixing methods of cylindrical shell structures. A typical bolted connection model is considered as a tuned system. However, in the actual working conditions, due to the manufacturing error, installation error and uneven materials of bolts, there are always random errors between different bolts. To investigate the influence of non-uniform parameters of bolt joint, including the stiffness and the distribution position, on frequency complexity characteristics of cylindrical shell through a statistical method is the main aim of this paper. The bolted joints considered here were simplified as a series of springs with random features. The vibration equation of the bolted joined cylindrical shell was derived based on Sanders' thin shell theory. The Monte Carlo simulation and statistical theory were applied to the statistical analysis of mode characteristics of the system. First, the frequency and mode shape of the tuned system were investigated and compared with FEM. Then, the effect of the random distribution and the random constraint stiffness of the bolts on the frequency and mode shape were studied. And the statistical analysis on the natural frequencies was evaluated for different mistuned levels. And some special cases were presented to help understand the effect of random mistuning. This research introduces random theory into the modeling of bolted joints and proposes a reference result to interpret the complexity of the modal characteristics of cylindrical shells with non-uniform parameters of bolt joints. [ABSTRACT FROM AUTHOR]

• The highlights of this manuscript can be summarized as. • Two finite element models are presented to simulate coated blisks under elastic support. • Reduced order models are developed for coated blisks with random mistuning and variable support stiffness. • New phenomena are observed for tuned, deterministic and randomly mistuned blisks and the mechanism is explained. Boundary conditions significantly affect the vibration characteristics of mechanical structures. Hard coatings are applied to reduce the vibration levels of blisks, and the modelling methods and vibration characteristics of mistuned coated blisks have been investigated under hard-support boundary conditions. However, the behavior of coated blisks under elastic support has not been previously studied. This paper presents a finite element model to simulate elastic support using two methods and develops reduced-order models to analyze coated blisks under elastic support. Furthermore, the effects of elastic support on the vibration characteristics of tuned, deterministic, and randomly mistuned blisks are investigated with a detailed discussion of the underlying mechanisms. The results indicate that elastic support has a notable impact on the natural frequencies and resonant responses at nodal diameters 1 and 2 in tuned-coated blisks. For deterministic mistuned blisks, the amplitude amplification factor varies in frequency-veering regions and frequency-intersecting regions with increasing support stiffness. Elastic support can reduce the forced responses of randomly mistuned blisks, and the well-known peak-value phenomenon is not observed in some cases based on statistical analyses. [ABSTRACT FROM AUTHOR]

The mistuning modeling methods and mistuning effects on the vibration characteristics of uncoated blisks have been extensively investigated over the past years. Most of these studies mainly focus on single-factor mistuning. In this work, we study the effect of coating thickness random mistuning on the forced response, which contains mass, stiffness and damping mistuning simultaneously and has not yet been investigated in previous studies. Furthermore, to satisfy the requirement of variable coating thicknesses, a new finite element model (FEM) is presented to resolve the new stiffness and mass matrices when the coating thickness changes. This FEM only needs the element node coordinates of one sector for the uncoated blisk and is verified by ANSYS software. For the mistuned blisk, the Craig-Bampton (C-B) method and the subset of nominal system modes (SNM) are employed to statistical analysis. The results indicate that the maximum amplification factor of forced response grows monotonously with the increased mistuning value of coating thickness. [ABSTRACT FROM AUTHOR]

When interblade coupling is weak, the dynamic response of a bladed disk is very sensitive to the presence of uncertainties. Excessive response variation can be very harmful. Previous studies have indicated that introducing blade-to-blade difference in nominal design, known as intentional mistuning, could reduce the level of response variation. In this research, an efficient computational framework that yields the optimal design of intentional mistuning is developed to maximize the bladed disk reliability. Both the random uncertainty of blades and the interval uncertainty of disk connections are considered. The Metropolis–Hastings algorithm is applied to find the worst case response under interval uncertainty, and Monte Carlo simulation is employed to account for the random mistuning effect. A gradient-based approach is then established to find the minimum design modification needed to achieve a designated reliability level. Case studies are carried out to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In a multi-packet blade system, random mistuning always exists among blades due to several reasons such as manufacturing tolerance, material irregularity and operation wear. It is well known that mistuning in a periodic structure often results in vibration phenomena such as mode and transient response localization. In this paper, a structural dynamic model of a randomly mistuned rotating multi-packet blade system subjected to cyclic nozzle forces is proposed. The accuracy of the proposed model is first validated by comparing its numerical results to those obtained with a finite element model. Then, using the proposed model, the relation between mode and transient response localization is investigated and a design guideline for multi-packet blade systems subjected to cyclic nozzle forces is suggested. [ABSTRACT FROM AUTHOR]

A multi-packet blade system consists of several blades which are attached to a disk and connected through shrouds. The blades of a multi-packet blade system are usually assumed to be identical. However, there always exists small, random mistuning among the blades due to manufacturing tolerance, in-operation wear and environmental changes. Such mistuning may cause significant increase in the forced vibration responses of some blades in the multi-packet blade system. Critical fatigue problems often occur in mistuned systems since the forced vibration response of a mistuned system is often significantly larger than that of a tuned system. Therefore, it is very important to predict the maximum blade response. In this study, blades are idealized as cantilever beams and the flexibilities of the disk and shrouds are idealized as discrete springs. Equations of motion are derived using the hybrid deformation variable method. To realize vibration localization with random mistuning, transient analysis is carried out for a multi-packet blade system excited by multiple nozzle jet forces. [ABSTRACT FROM AUTHOR]

Blade-to-blade mistuning is always inevitable in bladed disk assemblies due to imperfections in the manufacturing progress as well as wear during operation. As a result, the forced response of a mistuned bladed disk may be drastically larger than that of the nominal or tuned design. The attendant increase in stress can lead to premature high cycle fatigue (HCF) of the blades. Therefore, it is of great importance to predict and, ultimately, to reduce the blade forced response levels caused by mistuning. In this paper, intentional and random mistuning is introduced into a simplified 12-bladed disk model by varying the stiffness of the blades. The combined effects of intentional mistuning, damping and coupling are examined. The numerical results indicate that there is some threshold value of intentional mistuning and coupling that leads to maximum mistuning effects and certain relations among intentional mistuning strength, integer harmonics, damping and coupling can suppress the response levels of bladed disks with random mistuning, which provides useful guidelines for safe and reliable designs of bladed disk systems. [ABSTRACT FROM PUBLISHER]

imed at the difficulty in revealing the vibration localization mechanism of mistuned bladed disks by using simple non-linear model, a mechanical model of the bladed disk with random mistuning of hysteretic dry friction damping was established. Then, the incremental harmonic balance method was used to analyze the effects of the parameters of bladed disks, such as the mistuning strength of dry friction force, coupled strength, viscous damping ratio and friction strength, on the forced response of the bladed disks. The results show that the vibrational energy localization phenomenon turns up in the tuned bladed disks if the nonlinear friction damping exists, and the random mistuning of the dry friction force intensifies this kind of vibration localization. [ABSTRACT FROM AUTHOR]

The problem of determining the worst-case mistuning pattern and robust maximum mistuning forced response of a mistuned bladed rotor is formulated and solved as an optimization problem. This approach is exemplified on a two-degrees-of-freedom per blade disk model, two three-degrees-of-freedom per blade disk models, and a mistuned two- stage bladed rotor. The results of the optimum search of the worst-case mistuning pat- terns for the lumped parameter models are analyzed, which reveals that the maximum blade forced response in a mistuned bladed disk is associated with mistuning jump, which causes strong localization of the vibration response in a particular blade. The mistuning jump-localization phenomenon has been observed for all of the numerical examples, and it is also demonstrated that the highest response was always experienced by a blade of mistuning value jump. The two- and three-degrees-of-freedom per blade disk models are also for determination of its sensitivity coefficients with respect to mistuning variation. Studies show that there is not a threshold of mistuning beyond which the maximum forced response levels off or even drops, as the degree of mistuning is increased further: The maximum magnification factor is found to increase as the mistuning level is increased and reaches a maximum value at the upper limit of the mistuning level. The influence of the multistage coupling is revealed by comparing the results of single-stage analysis with that of the multistage case. The computed results have been compared with the Monte Carlo simulation produced, and it is demonstrated that the accuracy and efficiency of the maximum amplitude magnification factor computed by the presented method can be better than that of Monte Carlo simulations. [ABSTRACT FROM AUTHOR]