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In this paper, a new method for the balancing of rotor-bearing systems supported on fluid film bearings is proposed. The influence coefficients necessary for balancing are calculated using a novel simulation method called the Numerical Assembly Technique. The advantages of this approach are quasi-analytical solutions for the equations of motion of complex rotor-bearing systems and very low computation times. The Numerical Assembly Technique is extended by speed-dependent stiffness and damping coefficients approximated by the short-bearing theory to model the behavior of rotor systems supported on fluid film bearings. The rotating circular shaft is modeled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, influence coefficients, eigenvalues, and the Campbell diagram of the rotor. These values are compared to simulations with the Finite Element Method to show the accuracy of the procedure. Two numerical examples of rotor-bearing systems are successfully balanced by the proposed balancing method.

The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models.

Vibration in rotating machinery leads to a series of undesired effects, e.g. noise, reduced service life or even machine failure. Even though there are many sources of vibrations in a rotating machine, the most common one is mass unbalance. Therefore, a detailed knowledge of the system behavior due to mass unbalance is crucial in the design phase of a rotor-bearing system. The modelling of the rotor and mass unbalance as a lumped system is a widely used approach to calculate the whirling motion of a rotor-bearing system. A more accurate representation of the real system can be found by a continuous model, especially if the mass unbalance is not constant and arbitrarily oriented in space. Therefore, a quasi-analytical method called Numerical Assembly Technique is extended in this paper, which allows for an efficient and accurate simulation of the unbalance response of a rotor-bearing system. The rotor shaft is modelled by the Rayleigh beam theory including rotatory inertia and gyroscopic effects. Rigid discs can be mounted onto the rotor and the bearings are modeled by linear translational/rotational springs/dampers, including cross-coupling effects. The effect of a constant axial force or torque on the system response is also examined in the simulation.

Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model.

The increasing use of high-speed machinery leads to a growing demand for efficient balancing methods for flexible rotors. Conventional balancing methods are costly and time-consuming since they require multiple trial runs. For this reason, recent research focuses on model-based balancing methods, which substitute measurements with simulations. This work presents and examines a model-based modal balancing method, which utilizes the Numerical Assembly Technique (NAT) for the in situ balancing of warped rotors with flexible behaviour. NAT is a successive modification of discrete–continuous modelling that leads to analytical harmonic solutions and is very computationally efficient. In this version of NAT, internal damping is also included with a viscoelastic material model using fractional time derivatives. The modal balancing procedure is adapted to handle measurements outside of the critical speeds and the effect of the pre-bend on the rotor. The accuracy of the simulations is shown by comparing measured mode shapes and eigenvalues with values calculated with NAT. Furthermore, the first two modes of a rotor test bed are successfully balanced without trial runs.

Within the Space@Sea project floating offshore islands, designed as an assembly of platforms, are used to create space in offshore environments. Offshore structures are exposed to harsh environment conditions. High wind speeds, heavy rainfall, ice and wave forces lead to highly stressed structures. The platforms at the Space@Sea project are connected by ropes and fenders. There exists the risk of a rope failing which is therefore investigated subsequently. To ensure the safety of the structure, the rope parameters are monitored by the Extended Kalman Filter (EKF). For platform arrangements, a large number of sensors is required for accurate fault diagnosis of these ropes, leading to high investment costs. This paper presents a strategy to optimize the number and placement of acceleration sensors attached to the floating platforms. There are also high demands on the sensors due to the harsh offshore conditions. Material deterioration and overloading may lead to decayed sensor performance or sensor defects. Maintenance of offshore sensors is difficult, expensive and often not feasible within a short time. Therefore, sensor measurement deviations must not affect reliable structure fault detection. The influence of defect sensors on the rope fault detection is examined in this study: Types, intensities, number, place of occurrence of defect sensors and the distance between defect sensors and rope faults are varied.

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

In 2000, Kennedy and O’Hagan proposed a model for uncertainty quantification that combines data of several levels of sophistication, fidelity, quality, or accuracy, e.g., a coarse and a fine mesh in finite-element simulations. They assumed each level to be describable by a Gaussian process, and used low-fidelity simulations to improve inference on costly high-fidelity simulations. Departing from there, we move away from the common non-Bayesian practice of optimization and marginalize the parameters instead. Thus, we avoid the awkward logical dilemma of having to choose parameters and of neglecting that choice’s uncertainty. We propagate the parameter uncertainties by averaging the predictions and the prediction uncertainties over all the possible parameters. This is done analytically for all but the nonlinear or inseparable kernel function parameters. What is left is a low-dimensional and feasible numerical integral depending on the choice of kernels, thus allowing for a fully Bayesian treatment. By quantifying the uncertainties of the parameters themselves too, we show that “learning” or optimising those parameters has little meaning when data is little and, thus, justify all our mathematical efforts. The recent hype about machine learning has long spilled over to computational engineering but fails to acknowledge that machine learning is a big data problem and that, in computational engineering, we usually face a little data problem. We devise the fully Bayesian uncertainty quantification method in a notation following the tradition of E.T. Jaynes and find that generalization to an arbitrary number of levels of fidelity and parallelisation becomes rather easy. We scrutinize the method with mock data and demonstrate its advantages in its natural application where high-fidelity data is little but low-fidelity data is not. We then apply the method to quantify the uncertainties in finite element simulations of impedance cardiography of aortic dissection. Aortic dissection is a cardiovascular disease that frequently requires immediate surgical treatment and, thus, a fast diagnosis before. While traditional medical imaging techniques such as computed tomography, magnetic resonance tomography, or echocardiography certainly do the job, Impedance cardiography too is a clinical standard tool and promises to allow earlier diagnoses as well as to detect patients that otherwise go under the radar for too long.

In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.

Type B aortic dissection (TBAD) carries a high risk of complications, particularly with a partially thrombosed or patent false lumen (FL). Therefore, uncovering the risk factors leading to FL thrombosis is crucial to identify high-risk patients. Although studies have shown that morphological parameters of the dissected aorta are related to FL thrombosis, often conflicting results have been reported. We show that recent models of thrombus evolution in combination with sensitivity analysis methods can provide valuable insights into how combinations of morphological parameters affect the prospect of FL thrombosis. Based on clinical data, an idealized geometry of a TBAD is generated and parameterized. After implementing the thrombus model in computational fluid dynamics simulations, a global sensitivity analysis for selected morphological parameters is performed. We then introduce dimensionless morphological parameters to scale the results to individual patients. The sensitivity analysis demonstrates that the most sensitive parameters influencing FL thrombosis are the FL diameter and the size and location of intimal tears. A higher risk of partial thrombosis is observed when the FL diameter is larger than the true lumen diameter. Reducing the ratio of the distal to proximal tear size increases the risk of FL patency. In summary, these parameters play a dominant role in classifying morphologies into patent, partially thrombosed, and fully thrombosed FL. In this study, we point out the predictive role of morphological parameters for FL thrombosis in TBAD and show that the results are in good agreement with available clinical studies.