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One of the problems encountered by developers of inertial systems, such as gyroscopes and accelerometers, is the critical dependence of the eigenfrequencies of elastic suspensions (ES) on temperature when using substrates for sensors made of dielectric materials, such as borosilicate glass. The internal stresses arising in the ES caused by the difference in the temperature coefficients of linear expansion (TCLE) lead to deformation of the sensor and complication of the electronic part of the sensor. The purpose of this paper is to approach for in-plane and out-of-plane ES are considered that allow for minimization of the influence of internal stresses on eigenfrequencies.

Analytical, finite element and experimental results are considered. The temperature coefficient of thermal expansion, the Young’s modulus and the Poisson ratio are given as a function of temperature. The shape of the spring elements (SEs) and the construction of the elastic suspension are the main topics of focus in this study. The authors’ out-of-plane ES based on a meander-like spring element implemented via finite element modeling show good agreement with the experimental results.

Meander-like SEs have been developed that have lower temperature errors in comparison with traditional types of SEs. The main contribution to the change in the eigenfrequency from temperature is made by internal stresses that arose from the deformation of the bonded materials with different TCLE. The change of eigenfrequency from the temperatures that were calculated by finite element method did not exceed 0.15%, however, in practice, the scatter of the obtained characteristics for different samples showed a change of up to 0.3%.

This study shows a way to design and optimize the structure and theoretical background for the development of the microelectromechanical systems (MEMS) inertial module combining the functions of gyroscope and accelerometer. The obtained results will improve and expand the manufacturing technology of MEMS gyroscopes and accelerometers.

The purpose of this paper is to analyse the eigenforms and eigenfrequencies of stator core stack by experimental and numerical investigation. The influence of material parameters on the structural vibrations is carried out in order to describe the laminated structure of stator core stack with a homogeneous material model.

The finite element method is applied for a numerical modal analysis. Therefore, a homogeneous transversally isotropic material model is introduced and the influence of each material parameter on the dynamical behavior is investigated. These material parameters are stepwise adjusted to the results from the experimental modal analysis. The investigation includes results from different stator core stacks.

The influence of material on the modal parameters is shown. Furthermore, material parameters are carried out for stator core stacks, which describe the measured dynamical behaviour.

The presented investigations show a useable material model and corresponding parameters to the description of the laminated structure of stator core stacks.

The purpose of this paper is to describe how the method recently developed for mass‐spring systems and frame structures is modified to include the free vibration of trusses.

Here, two methods are presented for calculating the eigenfrequencies of structures. The first approach is graph theoretical and uses graph symmetry. The graph models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels contain the eigenvalues of the entire model. The second method has an algebraic nature and uses special canonical forms. The present method is illustrated through three simple examples with odd and even number of bays.

The inter‐relation for the mechanical properties of elements is established using new weighted graphs, enabling easy calculation of the eigenvalues involved. Two methods are presented for calculating the eigenfrequencies of the truss structures.

Symmetry is used for easy calculation of the eigenfrequencies of structures.

The purpose of this paper is to develop a topology optimization algorithm considering natural frequencies.

To incorporate natural frequency as design criteria of shell-infill structures, two types of design models are formulated: (1) type I model: frequency objective with mass constraint; (2) type II model: mass objective with frequency constraint. The interpolation functions are constructed by the two-step density filtering approach to describe the fundamental topology of shell-infill structure. Sensitivities of natural frequencies and mass with respect to the original element densities are derived, which will be used for both type I model and type II model. The method of moving asymptotes is used to solve both models in combination with derived sensitivities.

Mode switching is one of the challenges faced in eigenfrequency optimization problems, which can be overcome by the modal-assurance-criterion-based mode-tracking strategy. Furthermore, a shifting-frequency-constraint strategy is recommended for type II model to deal with the unsatisfactory topology obtained under direct frequency constraint. Numerical examples are systematically investigated to demonstrate the effectiveness of the proposed method.

In this paper, a topology optimization method considering natural frequencies is proposed by the author, which is useful for the design of shell-infill structures to avoid the occurrence of resonance in dynamic conditions.

The purpose of this paper is to study the resonance failure sensitivity analysis of straight-tapered assembled pipe conveying nonuniform axial fluid by an active learning Kriging (ALK) method.

In this study, first, the motion equation of straight-tapered assembled pipe conveying nonuniform fluid is built. Second, the Galerkin method is used for calculating the natural frequency of assembled pipe conveying nonuniform fluid. Third, the ALK method based on expected risk function (ERF) is used to calculate the resonance failure probability and moment independent global sensitivity analysis.

The findings of this paper highlight that the eigenfrequency and critical velocity of uniform fluid-conveying pipe are less than the reality and the error is biggest in first-order natural frequency. The importance ranking of input variables affecting the resonance failure can be obtained. The importance ranking is different for a different velocity and mode number. By reducing the uncertainty of variables with a high index, the resonance failure probability can be reduced maximally.

There are no experiments on the eigenfrequency and critical velocity. There is no experiments about natural frequency and critical velocity of straight tapered assembled pipe to verify the theory in this paper.

The originality of this paper lies as follows: the motion equation of straight-tapered pipe conveying nonuniform fluid is first obtained. The eigenfrequency of nonuniform fluid and uniform fluid inside the assembled pipe are compared. The resonance reliability analysis of straight-tapered assembled pipe is first proposed. From the results, it is observed that the resonance failure probability can be reduced efficiently.

Technological capabilities of manufacturing microelectromechanical system (MEMS) gyroscopes are still insufficient if compared to manufacturing high-efficient gyroscopes and accelerometers. This creates weaknesses in their mechanical structure and restrictions in the measurement accuracy, stability and reliability of MEMS gyroscopes and accelerometers. This paper aims to develop a new architectural solutions for optimization of MEMS gyroscopes and accelerometers and propose a multi-axis MEMS inertial module combining the functions of gyroscope and accelerometer.

The finite element modeling (FEM) and the modal analysis in FEM are used for sensing, drive and control electrode capacitances of the multi-axis MEMS inertial module with the proposed new architecture. The description is given to its step-by-step process of manufacturing. Algorithms are developed to detect its angular rates and linear acceleration along three Cartesian axes.

Experimental results are obtained for eigenfrequencies and capacitances of sensing, drive and control electrodes for 50 manufactured prototypes of the silicon electromechanical sensor (SES). For 42 SES prototypes, a good match is observed between the calculated and simulated capacitance values of comb electrodes. Thus, the mean-square deviation is not over 20 per cent. The maximum difference between the calculated and simulated eigenfrequencies in the drive channel of 11 SES prototypes is not over 3 per cent. The same difference is detected for eigenfrequencies in the first sensing channel of 17 SES prototypes.

This study shows a way to design and optimize the structure and theoretical background for the development of the MEMS inertial module combining the functions of gyroscope and accelerometer. The obtained results will improve and expand the manufacturing technology of MEMS gyroscopes and accelerometers.

The purpose of this paper is to analyse analytically a control scheme in which the resonance frequencies of a rectangular plate is modified by applying a discrete lateral force proportional to the displacement of the plate measured at a single point.

An isotropic, elastic, rectangular, thin plate which is simply supported along all sides is actuated at point (x₂, y₂) by applying a force, and the displacement is measured at (x₁, y₁).

The main outcome is the full analytical solution for the controlled eigenfrequencies and mode shapes which allows a detailed study of the efficiency of the control method proposed.

The present study was made in the form of an exact analytical solution and demonstrates that it is possible to affect the eigenfrequencies and mode shapes of a plate by measuring the displacement and applying a pressure at discrete points on the plate.

The mechanical performances of 3D-printed parts are influenced by the manufacturing variables. Many studies experimentally evaluate the impact of the process parameters on specimens’ static and dynamic behavior with the aim of tailoring the mechanical response of the prints. However, this experimental approach is hampered by the very large number of parameters, 3D printers and materials, the development of computer simulation models being thus required. In the context, this study aims to fill a gap by experimentally investigating the influence of infill related parameters over the vibrations of 3D-printed specimens, as well as to propose and validate a parametric finite element (FE) model for the prediction of eigenfrequencies.

A generally applicable FE model is not yet available for the 3D printing technology based on the material extrusion process due to the large number of parameters settings that determine a large variability of outcomes. Hence, the idea of developing numerical simulation models that address sets of parameters and assess their impact on a certain mechanical property. For the natural frequency, the influence of the infill density and infill line width is studied in this paper. An FE script that automates the generation of the model geometry by using the considered set of parameters is developed and run. The results of the modal analysis are compared to the experimental values for validating the script.

Based on the experimental results, a linear regression between the weight of the part and the first natural frequency is established. The response surfaces indicate that the infill density is the most significant parameter of influence. The weight-frequency function is then used for the prediction of the natural frequency of specimens manufactured with other infill parameters and values, including different infill patterns.

As the malfunctions or mechanical damages can be caused by the resonant vibration of parts during use, this research develops a FE-parameterized model that evaluates and predicts the eigenfrequencies of 2D printed parts to prevent these undesirable events. The targeted functional applications are those in which 3D-printed polymer parts are used, such as drone arms or drone propellers.

This research studies the influence of process parameters on the natural frequency of 3D-printed polylactic acid specimens, a topic scarcely addressed in literature. It also proposes a new approach for the development of parameterized FE models for sets of parameters, instead of a general model, to reduce the time and resources allocated to the experimental tests. Such a model is provided in this paper for evaluating the influence of infill parameters on 3D prints eigenfrequency. The numerical model is validated for other infill settings.

The problem of damage and crack detection in structural components has acquired an important role in recent years. Since the presence of cracks in a structure may alter its vibrational characteristics, the estimation of such variations can be used to detect cracks and damage, and to monitor the integrity of structures. The use of fast, easy and inexpensive non‐destructive testing is thus a major task. In this paper, sensitivity analysis by measurement of the reduction of eigenfrequencies was utilized to localize a crack in a non‐rotating shaft coupled to an elastic foundation. The shaft was modeled by the finite element method and coupled to an experimentally identified foundation model. The detection of a crack with different depths and orientations was verified experimentally and a good agreement between actual and detected crack positions was achieved. Finally easiness, effectiveness, applicability of the method and its extensions are also shown.

This paper aims to analyze the frequency characteristics of wireless power transfer (WPT) systems with relay resonators in terms of the power delivered to the load and system efficiency. Based on the analytical results, system parameters can be optimized to achieve maximum power transfer and higher system efficiency.

Based on Kirchhoff’s voltage law equations, WPT systems with relay resonators are described by the coupled linear second-order differential equations. Splitting frequencies are estimated by using the matrix theory. In addition, critical coupling conditions are demonstrated based on discriminant analysis.

It was found that multi-maximum values exist for the power delivered to the load and total system efficiency owing to multiple eigenfrequencies of the system. Also, frequency conditions of maximum power transfer and system efficiency, as well as their critical coupling conditions, were quantitatively estimated.

During our analytical process, we assume that quality factors of resonators in the system are high and the crossing coupling between resonators is negligible.

In previous works, the exact analysis of frequency characteristics is limited to WPT systems with two resonators. The appealing feature of this work lies in its ability to present a simplified analytical method with negligible approximation errors for WPT systems with relay resonators.