Prediction Of Natural Frequencies Research Articles

Recent advances in the integration of protein mechanics and machine learning

Mechanics underlies protein properties and behavior. From a theoretical standpoint, it is possible to derive these based on physical rules. This is appealing because they provide insights into physiology and disease, as well as aid in protein engineering; however, the convoluted nature of the biological system and current computational speeds limit its feasibility. Machine learning (ML) architectures are known for their ability to make inferences on complex data, such as the relationship between protein mechanics, properties, and behavior. Substantial efforts have been made to learn such correlations in tasks such as the prediction of structure, stability, natural frequency, mechanical strength, folding rate, solubility, and function. Each of these properties is interconnected through protein mechanics, and it is not surprising that the methods used in these tasks overlap highly in model input and architecture. In this review, we evaluate ML methods for the seven aforementioned prediction tasks to identify current trends in ML research in the field of protein sciences, focusing on the input and model architecture of each method. A short overview of de novo protein design is also provided. Finally, we highlight trends in the application of ML methods in the field of protein science, as well as directions for future improvements.

Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process.

The results of research on the influence of the chemical composition of cast iron and its potential changes in the production cycle on the elastic properties and the correctness of numerical simulations of the natural frequency of ventilated brake discs are presented. The tests were carried out for three grades of gray cast iron with flake graphite with a eutectic saturation coefficient ranging from 0.88 to 1.01. A quantitative metallographic assessment of the pearlitic cast iron matrix and graphite precipitates was carried out, and the hardness and compressive/tensile strength of individual cast iron grades were determined, taking into account the limit contents of the alloying elements. Next, ultrasonic tests were performed, and the elastic properties of cast iron were determined. Based on the obtained data, a numerical modal analysis of brake discs was performed, the results of which were compared with the actual values of an FRF frequency analysis. The error of the computer simulations was estimated at approx. 1%, and it was found that the accuracy of the calculations of the first natural frequency did not depend on the dimensions (size) of the discs and the chemical composition of the cast iron from which they were cast. The functional relationships between the chemical composition of cast iron, its strength and elasticity and the first natural frequency of the disc vibrations were determined, and a database of the material parameters of the produced cast iron grades was developed. An implementation example showed the validation of the brake disc design with natural frequency prediction and demonstrated a high convergence of the experimental results with the simulated values. Using I-MR control cards, both the effectiveness of designing and predicting the natural vibrations of brake discs based on the implemented material database as well as the stability of the gray cast iron production and disc casting processes were confirmed.

Continuous fiber path optimization in additive manufacturing: A gradient-based B-spline finite element approach

Additive manufacturing of continuous fiber enables the control of local material distribution and mechanical characteristics. This localized control is realized through fiber path generation and optimization, which is one of the core problems in the additive manufacturing of continuous fiber. Current fiber path generation and optimization methods mostly try to infill topology-optimized parts or align the fiber with the maximum stress directions, which may lead to sub-optimality or time-consuming computations. This paper provides a different approach to optimize the fiber path directly by parameterizing it with B-splines and manipulating its control points. A finite element model with B-spline fiber parameterization is established, with an analytical fiber-in-element probability. This framework streamlines the computation of local and global stiffness and mass matrices, enabling effective and efficient prediction of loading responses, stiffness, and natural frequencies. The probability framework also allows efficient calculation of the gradients of the stiffness and mass matrices, leading to a gradient-based fiber path optimization. The effectiveness and accuracy of both the finite element and optimization methods are verified with simulation and experiment case studies. Results demonstrate enhancements in stiffness and strength with less fiber usage compared to a commonly adopted principal stress direction method.

Analytical Kinetic Model for Accurate Square-slot Stator Natural Frequency Prediction

Analytical Kinetic Model for Accurate Square-slot Stator Natural Frequency Prediction

A machine learning approach for investigation of the natural frequency of a nitinol-reinforced composite beam

Many applications are using composites to improve performance and reduce weight, but it is essential to know the different properties of the composite before manufacturing. Properties like natural frequency and elastic modulus are also crucial in many applications. The use of shape memory alloys (SMA) composite has increased in the last few years due to various advantages of the shape memory alloys, like a shift in natural frequency and elastic modulus during phase transformation. Hence it is essential to know the composite’s natural frequency and elastic modulus before constructing it. Although experimental and numerical methods for calculating natural frequency exist, they are time-consuming and infrastructure-dependent. This paper explores relationships between SMA composite construction parameters and natural frequency to predict it better. Nitinol-reinforced silicon rubber composite beams are investigated with various parametric combinations using an orthogonal array. Different machine-learning techniques are applied for natural frequency prediction after training models on numerical results from varied construction combinations. The study identifies the best-performing algorithm and provides tuning recommendations. Linear regression model, Ridge regression model, and Decision Tree regression are the best-performing algorithms for the dataset in this paper. A weighted sum method finds optimal construction parameters for maximum natural frequency. These models can predict natural frequency before construction and the shift during SMA phase transformation. The research aids in designing SMA-reinforced beams by identifying optimal parameters like volume fraction, location, and activation pattern, targeting maximum natural frequency. The composite studied in this research shows a maximum natural frequency of 19.58 Hz for a 3.53% volume fraction of SMA, 3 mm distance of reinforcement, all wires activated, and austenite temperature.

A homogenization method for natural frequencies and damping of sandwich panels based on representative volume elements

The existing representative volume element (RVE) homogenization method, grounded in finite element analysis, assumes a planar configuration for the sections of sandwich panels, implying rigidity. To accommodate non-planar displacements, this study introduces a novel homogenization method reliant on the displacements obtained from four-point bending and four-point torsion. The present method is employed to investigate the mode shapes, natural frequencies, and loss factors of sandwich panels utilizing an equivalent single-layer shell model. Validation of the present method is conducted through the analysis of lattice sandwich panels and corrugated sandwich panels incorporating viscoelastic layers. Comparative analyses encompassing the results of the experiment, the conventional solid model method, the present method, and the conventional plane method are undertaken. The universality of the present method is substantiated. The present method enhances the precision of natural frequency prediction.

Pose-dependent natural frequency prediction for milling robot—A variable joint stiffness model

Low prediction accuracy of natural frequencies of a milling robot is one major obstacle to the avoidance of chatter vibration in low-speed robotic milling. For enhanced accuracy in predicting the natural frequency of mixed robot, a variable stiffness model is proposed featuring the dependency of joint stiffness on the joint variables, rather than the constant joint stiffness in the traditional assumption. By integrating the variable joint stiffness model into a mode-reduced 4DOF model modified for the present study, the new method for predicting the robot natural frequency is then built, analyzed, and verified through simulation and modal tests by both a 3-axis accelerometer and a laser vibrometer on the milling robot under different robot configurations. Comparison of the experimental values from the modal tests against the natural frequencies predicted by the proposed model reveals a predicting error of less than 10%, hence enhanced accuracy of the proposed variable joint stiffness model in a large operational space. Based on the model, milling parameters without structural vibration has been selected, and the quality of the robot milling for titanium alloy has been improved.

Effect of Additional Mass on Natural Frequencies of Weight-Sensing Structures.

The phenomena of variability and interference in the natural frequencies of weight-sensing structures applied in complex working conditions must solve the problem of reducing or eliminating resonance under low-frequency vibrations to maximize stability, accuracy and reliability. The influence laws of the additional mass with relevant characteristics on the natural frequencies, which include the components of mass, stiffness and center-of-mass distribution, etc. Firstly, the theoretical formulas of the mathematical model are given based on different characteristics of the weight-sensing structure, and various combinations of additional masses on the weight-sensing structures are adjusted in the X-, Y-, and Z-directions. The key factors to be specifically considered in the theoretical formulas are discussed through simulation analysis and experimental validation. Secondly, the locking strength of the fastening screws of some components was changed, and another component was placed on the experimental platform in the experiment. The results show that the mass, center-of-mass, stiffness distribution and other factors of the additional mass have different effects on the natural frequencies, which are important for the demand for high-precision, high-stability weighing measurement. The results of this research can provide an effective scientific evaluation basis for the reliable prediction of natural frequencies.

An Accurate Calculation Method of Natural Frequencies of the Radial-Flux Slotted Motors Considering End Covers

Accurately calculating and reasonably adjusting the natural frequencies of the motor are the key technologies to predict and weaken the electromagnetic vibration of the motor. This paper first gives the general equivalent models of the stator including the stator core, windings, and casing. After that, the characteristic equation of natural frequencies of the stator is established based on the energy method, and the complex structures of the stator teeth, windings, and casing are accurately considered. Taking into account the orthotropic characteristics of laminated core and windings, the calculation methods of the equivalent material parameters of stator core and windings are introduced, and the accuracy is verified by the finite element method (FEM) and the modal test method. In order to accurately replicate the actual constraints of the end covers to the casing, an accurate calculation method combining the energy method and the artificial springs equivalent method (ASEM) is proposed. By modifying the stiffness coefficients of the artificial springs, any boundary condition including classical boundary conditions can be simulated. Based on this, the natural frequencies of the radial-flux slotted motor including the stator core, windings, casing, and end covers are calculated accurately by the accurate calculation method. Finally, a general formula for determining the stiffness coefficients of artificial springs corresponding to casings with different thicknesses, lengths, and average diameters is summarized, which facilitates the prediction of natural frequencies of the radial-flux slotted motors considering the influence of the end covers.

Natural frequency prediction of the 3-RPS parallel manipulator using the substructure synthesis technology

AbstractThis paper proposed an elastodynamic modeling method combined with independent displacement coordinates and substructure synthesis technology. Firstly, the connecting rod was discretized, and the elastodynamic control equation for each element was established. The multipoint constraint element theory, linear algebra, and singularity analysis were used to identify the globally independent displacement coordinates of the manipulator. On this basis, the elastodynamic model using the substructure synthesis for the 3-PRS parallel manipulator (PM) was developed, with its natural frequencies distribution in the regular workspace discussed. The comparison with the finite-element results showed that the maximum error of the first three-order natural frequencies was within 1.03%, which verified the correctness of the analytical model. The proposed elastodynamic model included all the kinematic constraints of the manipulator without increasing the Lagrangian multiplier. The method is computationally efficient and assesses the dynamic behaviors of the mechanism at the predesign phase.

Free Vibration Analysis of Functionally Graded Graphene-Reinforced Composite-Laminated Plates

Graphene is recognized as one of the most alluring reinforcements for composite materials due to its exceptional mechanical capabilities. However, the existing models disregarding the compatible requirements of interlaminar stresses in the literature may meet severe challenges for the dynamic analysis of functionally graded graphene-reinforced composite (FG-GRC) laminated thick plates. If transverse shear deformations cannot be described accurately, the prediction of natural frequencies for FG-GRC laminated plates will be seriously and directly affected. Accordingly, an attractive plate theory in conjunction with the analytical approach and finite-element formulation is proposed for free vibration analysis of FG-GRC plates. An improved transverse shear stress field is acquired in terms of the three-dimensional (3D) elasticity equations and the Reissner mixed variational theorem (RMVT). The performance of the suggested model was evaluated using 3D elasticity solutions and the results obtained from other models. Numerical results showed that the suggested model can produce promising results for the thick laminated and sandwich plates. Additionally, a thorough investigation was conducted to study the effects of several graphene parameters, including volume fractions, distribution patterns, span-to-thickness ratios, aspect ratios, boundary conditions, and stacking sequences, on the dynamic responses of FG-GRC laminated plates.

Prediction of natural frequencies of Rayleigh pipe by hybrid meta-heuristic artificial neural network

Prediction of natural frequencies of Rayleigh pipe by hybrid meta-heuristic artificial neural network

Dynamic analysis of graphene-reinforced sandwich plates with piezoelectric macro fiber composite face sheets

Graphene is considered as an ideal candidate for composite materials owing to the outstanding physical characteristics. However, existing higher-order shear deformation theories in the literature may meet severe challenges for the accurate prediction of natural frequencies of graphene-reinforced sandwich plates with piezoelectric macro fiber composite (MFC) face sheets. If transverse shear deformations cannot be described accurately, the dynamic behaviors of piezoelectric sandwich plates with graphene reinforcements will be significantly impacted by the large differences of material properties at interfaces of adjacent layers and electro-mechanical coupling characteristic. Thereby, a novel electro-mechanical coupling theory is to be proposed for the free vibration of graphene-reinforced sandwich plates with MFC face sheets. Based on the Reissner mixed variational theorem (RMVT), the precision of the interlaminar shear stresses including the electro-mechanical coupling effect can be improved. The modified interlaminar shear stress field is absorbed in the strain energy, which can enhance the accuracy of the free vibration response of piezoelectric sandwich plates. Additionally, the second-order derivatives of in-plane displacements have been eliminated from the interlaminar shear stress components, which can substantially simplify the finite element implementation. Thus, a simple C0-type finite element formulation is developed for the free vibration of piezoelectric sandwich plates with graphene reinforcements. The 3D elasticity solutions and the results obtained from other theories are used to evaluate the performance of the proposed theory. In comparison with the existing higher-order theories, the proposed theory can produce more accurate results. In addition, a comprehensive parametric study is conducted to explore the impacts of significant parameters on the free vibration behaviors of piezoelectric graphene-reinforced sandwich plates.

Influence of soil-structure interaction on the dynamic characteristics of railroad frame bridges

Explicit dynamic calculations are required in various standards for bridges on high-speed lines to ensure normative limits. This dynamic analysis is based on the resonance phenomena between the train crossing and the frame's natural frequencies in bending. It is obvious that, especially here, an exact determination of the natural frequencies in the numerical models is important for determining the resonance speed, as there is no conservative consideration in dynamics. Furthermore, considering radiation damping based on soil-dynamic approaches can noticeably reduce the maximum amplitudes at the resonance point when simulating train crossings. However, due to the massive dimensions of structural members and a large number of constraints, the dynamic system of railroad frame bridges is usually not clearly to be identified. Hence, a prediction of natural frequency and radiation damping are currently large uncertainties for the design of frame bridges, making dynamically good-natured behaviour, characterised by large damping, particularly desirable.This paper examines the dynamic behaviour of embedded frame bridges, including the effect of soil-structure interaction, under 2D and 3D numerical approaches. Different modelling methods with respect to the unbounded domain and the satisfaction of the Sommerfeld's radiation condition are compared: (1) direct modelling using tuned damper elements, (2) coupled BEM-FEM, and (3) simplified substructure method. It is shown that the coupled FEM-BEM approach reproduces the relationships of three-dimensional dynamic soil-structure interaction (SSI) more accurately than a planar FEM approach since the SSI does not result independently of the chosen modelling method, which is reflected in divergent radiation damping. Furthermore, the governing rigid body modes can be identified using a simplified substructure method.The following parameters influencing the SSI are investigated and discussed in detail: (a) influence of the soil stiffness; mainly described by the ratio between the natural frequencies of the frame and the soil-abutment system, (b) layering of the underlying soil, (c) degree of superstructure clamping, and (d) material properties of the backfill. It is shown that the natural frequencies react robustly to the SSI and are thus mainly influenced by the structural stiffness of the frame. In contrast, radiation damping exhibits various dependencies. In particular, the superstructure slab's clamping ratio and the vertical rigid-body mode frequency (direct relation to soil stiffness) should be mentioned here, significantly influencing the vibrating system. Finally, based on these results, a recommendation for the dynamic design is given.

A Beam Finite Element for Static and Dynamic Analysis of Composite and Stiffened Structures with Bending-Torsion Coupling

This research presents a new beam finite element capable of predicting static and dynamic behavior of beam structures with bending-torsion coupling. The model here derived establishes a relation between the bending and torsional nodal degree of freedom of a two node beam element. The equilibrium equations are derived neglecting the non-linear terms while the stiffness and mass matrices are derived with Galerkin’s method. The shape functions are obtained considering Timoshenko’s hypothesis and the torsional moment constant along the element. The model has been validated through numerical and experimental results for static and dynamic simulation. The comparison revealed a relative difference mostly lower than 5% for static deformations and natural frequency prediction, while the Modal Assurance Criterion (MAC) confirmed the consistency with numerical and experimental results in terms of mode shape similarity.

Prediction of natural frequencies of functionally graded circular and annular plate via differential quadrature method (DQM)

In this paper, numerical approach for free vibration response of functionally graded material (FGM) circular and annular plate is examined using differential quadrature method (DQM), and first-order shear deformation theory. The effective material properties through the thickness of the plate are obtained via power-law distribution. The governing partial differential equations (GDEs) are obtained using Hamilton’s principle. The five GDEs are discretized via DQM. Several comparison studies were carried out by those published in the literature. The free vibration analysis is investigated to reveal the effects of outer radius to thickness ratio, grading index, radii ratio and boundary conditions.

A thorough comparison between measurements and predictions of the amplitude dependent natural frequencies and damping of a bolted structure

Bolted joints are a significant source of damping and nonlinearity in built up structures. In the micro-slip regime (i.e. when the bolts do not slip completely) the log of the damping tends to increase linearly with the log of the vibration amplitude, the so-called power-law behavior. The natural frequency also tends to decrease slightly with vibration amplitude. While many works have successfully tuned phenomenological models to capture these behaviors, far fewer have sought to predict the nonlinearity in a bolted joint and validated the predictions with measurements over a range of bolt preloads and vibration amplitudes. This work presents a step towards such a prediction, using a detailed finite element model of a structure, including the preload forces in the bolts and Coulomb friction in the contact, to seek to predict the nonlinear damping and stiffness of the structure and how they vary with preload. The structure studied consists of two beams bolted together at their free ends, the so-called S4 Beam. While the contact interfaces were machined to be nominally flat, the micron-scale curvature in the contact interface is included in the model, approximated in two different ways, to seek to understand what fidelity is needed at the contact interface to successfully capture its dynamic behavior. The recently presented Quasi-Static Modal Analysis (QSMA) method is employed, where the amplitude dependent damping and natural frequency can be predicted from a single quasi-static simulation, avoiding the expense of numerical integration. The predicted damping and natural frequency are compared with measurements at various preloads, showing reasonable agreement if a Coulomb friction coefficient of 0.2 is used for all simulations. The simulations also revealed that, while the micron-scale curvature of the interfaces was important, the results were not very sensitive to how it was approximated.

Natural frequency prediction of functionally graded graphene-reinforced nanocomposite plates using ensemble learning and support vector machine models

Functionally graded materials (FGMs) are modern engineering materials with increasing application in various industrial fields. In this study, the free vibration behavior of graphene-reinforced FGM plate is investigated using finite element method and machine learning (ML) approaches. For this purpose, three advanced ML models including ensemble learning algorithms (bootstrap aggregation and gradient boosting) and Gaussian support vector machine are employed to predict the natural frequency of functionally graded graphene/epoxy nanocomposite plates. In this regard, first, hyperparameter optimization is carried out using Bayesian optimization algorithm. Then, regression analysis is performed using the aforementioned ML approaches. According to the obtained results, all ML models have a high coefficient of determination (more than 96%) with low mean squared error (MSE) values. However, the best performance is related to the gradient boosting method, followed by support vector machine and bootstrap aggregation, respectively. Finally, the significance degree of involved parameters on natural frequency is estimated using the Shapley values concept. The obtained results reveal that the most significant parameters affecting the natural frequency of graphene-reinforced FGM plates are clamp type, the volume fraction of graphene, followed by thickness ratio and distribution pattern, respectively.

Physics-guided mixture density networks for uncertainty quantification

This paper proposes a Physics-guided Mixture Density Network (PgMDN) model for uncertainty quantification of regression-type analysis. It integrates a Mixture Density Network for probabilistic modeling and physics knowledge as regularizations. This model can handle arbitrary distribution of data (e.g., strongly non-Gaussian, multi-mode, and truncated distributions). The physics knowledge from parameters and their partial derivatives is used as equality/ inequality constraints. The training of physics-guided machine learning is formulated as a constrained optimization problem. The constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm. Thus, the commonly used backpropagation algorithm can be used to train the neural network. With the physics constraints, the required training data size can be reduced, and the overfitting problem can be mitigated. This paper demonstrates the application of the PgMDN using a numerical example, an engineering problem for fatigue stress-life curve estimation, an engineering problem for natural frequency prediction of bridges, and an engineering problem for fatigue life prediction of corroded steel reinforcing bars. Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge when data are sparse, the improvement of the dynamic penalty function method compared with the static method, and the benefits achieved from the distribution mixture compared with a single Gaussian distribution.

A Prediction Model for Natural Frequencies on Kevlar/Glass Hybrid Laminated Composite using Artificial Neural Networks (ANN)

This paper aims to developa prediction model for the natural frequencies on Kevlar/Glass hybrid laminated composite plates using Artificial Neural Networks (ANN). Finite element simulations were performed to generate data for the natural frequencies under various lamination schemes and fibre angles. Rectangular symmetric and anti-symmetric hybrid laminated composite plates were modeled using commercial software, ANSYS, and meshed using shell elements. The Matlab-ANN tool was used to generate the prediction model, where the generated data (natural frequencies) from the finite element simulations were used for training and testing of the prediction model. The network adapted a two-layer feed-forward algorithm. The adequacy of using ANN in predicting natural frequencies was verified, where the coefficient of determination, R2, was found to be over 0.995. The overall results proved that ANN could be a useful tool, where the prediction model produced an error of less than 5%, when compared to the simulated values of natural frequency of various hybrid laminated composites using finite element analysis. These findings concluded that the current study had contributed significant knowledge in understanding the prediction of natural frequency on hybrid laminated composite using the ANN model.