The instability of a floating object is the main factor preventing near-field acoustic levitation (NAFL) from being widely used in the manufacture of micro-electro-mechanical systems. Therefore, investigating the restoring force due to the generation mechanisms of NAFL is necessary to ensure the stable levitation of the floating object. This study presents a theoretical analysis to evaluate the restoring force based on the gas-film-lubrication theory. The gas-film pressure between the reflector and the radiator is expressed in the form of the dimensionless Reynolds equation in a cylindrical coordinate system, which is solved by an eight-point discrete grid method due to the discontinuous gas-film distribution. An experimental rig is constructed to measure the restoring force at various eccentricities, which can be used to support the developed numerical model. The theoretical results show that the restoring force increases with an increment in eccentricity, which agrees with experimental results. Furthermore, theoretical prediction results indicate that the restoring force increases when the amplitude of the radiator and weight of the levitator increases, which indicates higher system stability. The results of the radiator vibration mode on the restoring force show that the restoring force is the largest in the first-order mode.

Stability is a well-known challenge for rotating systems supported by hydrodynamic bearings (HDBs), particularly for the condition where the misalignment effect and the parametric uncertainty are considered. This study investigates the impact of misalignment and inherent uncertainties in bearings on the stability of a rotor-bearing system. The misalignment effect is approximately described by introducing two misaligned angles. The characteristics of an HDB, such as pressure distribution and dynamic coefficients, are calculated by the finite difference method (FDM). The stability threshold is evaluated as the intersection of run-up curve and borderline. Viscosity and clearance are considered as uncertain parameters. The generalized polynomial chaos (gPC) expansion is adopted to quantify the uncertainty in parameters by evaluating unknown coefficients. The unknown gPC coefficients are obtained by using the collocation method. The results obtained by the gPC expansion are compared with those of the Monte Carlo (MC) simulation. The results show that the characteristics of the HDB and the stability threshold are affected by misalignment and parameter uncertainties. As the uncertainty analysis using the gPC expansion is performed on a relatively small number of predefined collocation points compared with the large number of MC samples, the method is very efficient in terms of computation time.

Damage detection, using vibrational properties, such as eigenfrequencies, is an efficient and straightforward method for detecting damage in structures, components, and machines. The method, however, is very inefficient when the values of the natural frequencies of damaged and undamaged specimens exhibit slight differences. This is particularly the case with lightweight structures, such as fiber-reinforced composites. The nonlinear support vector machine (SVM) provides enhanced results under such conditions by transforming the original features into a new space or applying a kernel trick. In this work, the natural frequencies of damaged and undamaged components are used for classification, employing the nonlinear SVM. The proposed methodology assumes that the frequencies are identified sequentially from an experimental modal analysis; for the study propose, however, the training data are generated from the FEM simulations for damaged and undamaged samples. It is shown that nonlinear SVM using kernel function yields in a clear classification boundary between damaged and undamaged specimens, even for minor variations in natural frequencies.

This study identifies non-homogeneous stiffnesses in a non-destructive manner from simulated noisy measurements of a structural response. The finite element method serves as a discretization for the respective cantilever beam example problems: static loading and modal analysis. Karhunen–Loève expansions represent the stiffness random fields. We solve the inverse problems using Bayesian inference on the Karhunen–Loève coefficients, hereby introducing a novel resonance frequency method. The flexible descriptions of both the structural stiffness uncertainty and the measurement noise characteristics allow for straightforward adoption to measurement setups and a range of non-homogeneous materials. Evaluating the inversion performance for varying stiffness covariance functions shows that the static analysis procedure outperforms the modal analysis procedure in a mean sense. However, the solution quality depends on the position within the beam for the static analysis approach, while the confidence interval height remains constant along the beam for the modal analysis. An investigation of the effect of the signal-to-noise ratio reveals that the static loading procedure yields lower errors than the dynamic procedure for the chosen configuration with ideal boundary conditions.

Design of new materials is quite a difficult task owing to various time and length scales and affiliated uncertainties. The major challenge is to include all these in a conventional model. Hyperparameter models in machine learning can be used to overcome these issues. In this paper, an artificial neural network (ANN) model is developed to estimate the effective elastic parameters of unidirectional fiber reinforced composites using representative volume elements (RVE) considering uncertainty in the fiber diameter. The diameter probability distribution is constructed from the acquired gray images by employing image processing operations. The generalized Polynomial Chaos (gPC) expansion is then used to represent the distribution as a random input parameter for finite element analysis, from where the effective parameters are realized. Similarly, the outputs of the FE model, i.e., elastic parameters, are approximated by gPC expansions having unknown deterministic coefficients and random orthogonal Hermite polynomials. A set of collocation points are generated from roots of the random polynomials; from there, the unknown coefficients are estimated. The realization samples are utilized to train an ANN algorithm based on supervised deep learning. The developed ANN model is later tested and validated for a new sample set of data. It is shown that the ANN model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters.

Damping parameters of composite structures possess significant uncertainty due to the structural complexity of such materials. Considering the parameters as random variables, this work uses the generalized polynomial chaos (gPC) expansion to capture the uncertainty in the damping and in the vibration responses of structures. A non-sampling based stochastic finite element formulation for damped vibration analysis is developed in which the gPC expansion is used to represent damping uncertainty and stochastic responses with unknown deterministic functions. The constructed gPC expansions for the parameters are used as random inputs to the FEM model to realize the responses on a few number of collocation points generated in random space. The realizations then are employed to estimate the unknown deterministic functions of the gPC expansion approximating the responses. The application of the proposed method is practiced on sample fiber-reinforced composite plates having random modal damping parameters. Utilizing a few random collocation points, the method indicates a very good agreement compared to the sampling-based Monte Carlo simulations with large number of realizations.