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Nutation and precession resonances in an antiferromagnet subjected to a dc magnetic field are investigated by employing coupled linearized inertial Landau–Lifshitz–Gilbert equations describing the dynamics of magnetizations of antiferromagnet sublattices with uniaxial magnetocrystalline anisotropy. Analytical expressions for the eigenfrequencies of such an antiferromagnet are obtained for the longitudinal and transverse directions of the external dc field and for different ranges of its strength. The effect of inertia on the values of the resonant frequencies is shown for all possible states of the antiferromagnet in both the longitudinal and transverse directions of the external field. The estimated resonant frequencies are compared with those obtained from the numerical solution of the system of undamped inertial Landau–Lifshitz–Gilbert equations for closed trajectories of sublattice magnetizations. The good agreement of both independent estimations is demonstrated. [ABSTRACT FROM AUTHOR]

An inductor–capacitor passive wireless sensor is essential to physical, chemical, and biological sensing for scenarios where physical access is difficult. Exceptional points of parity-time symmetric inductor–capacitor systems featuring the linear loss and gain have been utilized for enhancing sensing. However, the exceptional point sensing scheme might bring about fundamental resolution limits and noise enhancement. Here we show, employing a nonlinear saturable gain, the responsivity has a cube-root singularity distinct from a square-root singularity of the linear exceptional point scheme. The saturable gain eliminates the imaginary part of the eigenfrequencies and significantly suppresses the noise. Through an example of inductor–capacitor wireless wearable temperature sensors, we demonstrate the high figure of merit for the nonlinear PT-symmetric configuration. Our results resolve a debate on the effectiveness of the exceptional point sensing scheme for inductor–capacitor sensors and provide a way of enhancing precision for these types of sensors. The authors demonstrate an exceptional point enhanced sensing scheme for inductively-coupled wireless sensor at a cube-root singularity. Due to high figure of merit, the sensor promises applications for scenarios where physical access is difficult. [ABSTRACT FROM AUTHOR]

As part of the development of advanced, data-driven methods for predictive maintenance of railway infrastructure, this paper analyzes and evaluates more realistic predictions of eigenfrequencies of railway bridges, also referred to as natural frequencies, based on a population of already assessed, measured existing bridges using regression techniques. For this purpose, Machine Learning (ML) techniques such as Polynomial Regression (PR), ANN and XGBoost are consistently evaluated and the application of the XGBoost algorithm is identified as the most suitable prediction model for these eigenfrequencies, usable for dynamic train-bridge interactions. The results of the post-processing are incorporated into the safety architecture for bridge verification (risk management). The presented data-based techniques are a steppingstone towards digitalization of structural health monitoring and offer safety and longevity of the railway bridges. Furthermore, the use of these methods can save costs that would be incurred by physical in-situ measurements. The types of bridges analyzed with ML are Filler Beam Bridges (FBE), which outnumber other construction types of bridges in Germany (DB InfraGO AG). This methodology is applicable to any bridge type as long as sufficient data are gathered for training, validation and testing. [ABSTRACT FROM AUTHOR]

This study presents an efficient and accurate method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures. The eigenequations for the surface waves in an ideal semi-infinite periodic structure and those eigenequations for the finite periodic structure within the bandgap are derived using the symplectic matrix. Based on these two eigenequations and the properties of the symplectic matrix, we show that the eigenfrequencies of the surface waves in an ideal semi-infinite periodic structure can be obtained using the eigenfrequencies within the bandgap of a finite periodic structure with different boundary conditions. The eigenfrequencies of the finite periodic structure can be calculated efficiently and accurately by the method combining the 2 N algorithm and Wittrick–Williams algorithm. The proposed method is also extended to solve the surface waves in defective semi-infinite periodic structures. The accuracy and efficiency of the proposed method are demonstrated using several numerical examples. [ABSTRACT FROM AUTHOR]

The effectiveness of a hybrid technique for identifying seismic damage in planar, multistory, steel X- or V-braced frames is demonstrated here through an example of a six-story frame. This proposed technique, referred to as "M and P", combines the instrumental monitoring (M) with pushover analysis (P). According to the methodology, the diagram of stepping eigenfrequencies of the frame in the inelastic region is initially plotted against seismic roof displacement. The fundamental natural frequency, detected through monitoring, is then utilized in this key diagram to reveal the inelastic roof displacement that corresponds to the damage state of the steel-braced frame. This displacement is subsequently used as the target in the pushover analysis, facilitating the identification of seismic damage within the existing steel-braced frame. Finally, the damage image is correlated with the damage stiffness matrix of the frame at the same inelastic roof displacement. The investigation results indicate that combining instrumental monitoring with pushover analysis using the eigenfrequencies curves established by the "M and P" technique allows for accurate identification of the seismic damage potential in existing damaged steel-braced frames. The "M and P" technique is a straightforward method for immediate damage assessment in steel structures after damage occurs, regardless of the cause. [ABSTRACT FROM AUTHOR]

Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other. Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet. Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions. Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.

This study presents a meshless modeling approach to design variable-stiffness laminates considering manufacturing constraints. The governing equations are derived using lamination parameters and first-order shear deformation theory. The solution approach uses Chebyshev polynomials and Galerkin's method to obtain the discretized equations of motion. The developed framework was used to maximize the fundamental frequency of composite plates. The variable-stiffness designs provided up to 28.4% higher frequencies compared to optimum constant-stiffness laminates, although the actual level of improvement depends on the number of layers. Finally, manufacturable fiber paths were obtained considering the allowed fiber curvature, which can also reduce the frequency values. [ABSTRACT FROM AUTHOR]

We present an isogeometric analysis (IGA) framework for structural vibrations involving complex geometries. The framework is based on the Complex-Geometry IGA Mesh Generation (CGIMG) method. The CGIMG process is flexible and can accommodate, without a major effort, challenging complex-geometry applications in computational mechanics. To demonstrate how the new IGA framework significantly increases the computational effectiveness, in a set of structural-vibration test computations, we compare the accuracies attained by the IGA and finite element (FE) method as the number of degrees-of-freedom is increased. The results show that the NURBS meshes lead to faster convergence and higher accuracy compared to both linear and quadratic FE meshes. The clearly defined IGA mesh generation process and significant per-degree-of-freedom accuracy advantages of IGA over FE discretization make IGA more accessible, reliable, and attractive in applications of both academic and industrial interest. We note that the accuracy of a structural mechanics discretization, which may be assessed through eigenfrequency analysis, plays an important role in the overall accuracy of fluid–structure interaction computations. [ABSTRACT FROM AUTHOR]

Track tests of ballistic aircraft in flight conditions are used to confirm their viability. A problem with track tests is vibration of the shoes in nonsteady slip along the rails. The monorail track at the Safronov State Government Testing Center for Aviation Systems has gaps between the track beams to allow for their expansion and contraction at different times of the year. In the acceleration of a test vehicle using the thrust of solid fuel rocket engines, parametric vibration appears. Its source is the dynamic interaction between the contact surface of the shoes and the upper surface of the monorail at the junction between sections. The dynamic vibrational stability of the moving test vehicle is studied in high-speed monorail tests. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate the influence of boundary conditions of rigid fastening on the boundaries of regions of dynamical instability of closed shells of revolution, close by their forms to cylindrical ones, with an elastic filler. It is assumed that a shell is under the action of external pressure which varies in time and temperature. We consider the shells of average length whose shape of generatrix of the middle surface is a parabolic function. We consider the shells of positive and negative Gaussian curvature. The formulas are obtained for finding eigenfrequencies and boundaries of regions of dynamical instability depending on the boundary conditions, Gaussian curvature, initial stressed state, temperature and amplitude of a shell deviation from cylindrical form. The focus is on finding the moot dangerous area of dynamical instability and on the lowest eigenfrequencies of shells under consideration. [ABSTRACT FROM AUTHOR]

This study examined the vibration behavior of a beam with linear spring attachments using finite element analysis. It aims to determine the natural frequency with both consistent/coupled mass and lumped mass matrices. The natural frequencies and corresponding mode shapes were correctly determined which formed the basis of any further noise vibration and severity calculations and impact or crash analysis. In order to obtain eigenfrequencies subject to the attached spring, the characteristic equation was obtained by eigenfunctions expansion whose roots were extracted using the root-finding technique. The finite element method by coupled and lumped mass matrices was then used to determine complete mode shapes against various eigenfrequencies. The mode shapes were then analyzed subject to supports with varying stiffness thereby comparing the analytical and numerical results in case of consistent and lumped masses matrices so as to demonstrate how the present analysis could prove more valuable in mathematical and engineering contexts. Utilizing a consistent mass matrix significantly enhanced accuracy compared to a lumped mass matrix, thereby validating the preference for the former, even with a limited number of beam elements. The results indicated that substantial deflection occurred at the beam's endpoints, supporting the dynamic behavior of the spring-beam system. [ABSTRACT FROM AUTHOR]

Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ω e could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ω o is field independent. To realize the tunability of Ω e , the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ , equal frequencies of both modes were obtained. At this resonant point Ω o (Φ) = Ω e (Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes. [ABSTRACT FROM AUTHOR]

The concept of a 2D cylindrical High Pass Ladder (2D c-HPL) is used in the development of this ultra-high radio frequency (UHRF) volumetric head coil for 7 T tuned at the Larmor frequency of 298 MHz. The architecture of the 2D c-HPL helps to overcome the challenges associated with non-uniform magnetic field distribution. The prototype consists of an individual resonating array of inductance-capacitance (LC) elements and each component is tuned to the precise fo frequency. The tuning of the (i) inductance, (ii) capacitance, (iii) mesh size, and (iv) coupling coefficient play critical roles to attain the desired Larmor frequency. For this proof-of-concept, the prototype of a volumetric head coil consists of a cylindrical array size of 4 × 6, with individual LC components of inductance magnitude, 98 nH and four fixed value capacitors and one tunable capacitor that allowed to achieve the desired precession frequency, fr = 298 MHz. The model was tested for three different fo values of 269, 275, and 286 MHz. The mutual coupling and the eigenfrequencies were compared through bench testing and dispersion equation. The experimental data were in good agreement (<5%) with the theoretical eigenfrequencies from the dispersion relation. The theoretical eigenfrequencies and the experimental eigenfrequencies are in good agreement for eigenmodes (1,2), (1,3), (2,2), (2,3), and (4,3). [ABSTRACT FROM AUTHOR]

Shell structures are primarily used in the aerospace and maritime sectors. Such structures often oscillate, and undesirable oscillations can cause structural damage. So, to eliminate resonance and prevent damage to vibrating structures, it is necessary to build optimal shells. Maximizing the frequency gap between the first two eigenfrequencies is essential so that they do not coincide with the resonance frequency. Depending on the requirements of the design, the external frequencies might be placed between zero and the first natural frequency or between the first and second natural frequencies in order to prevent failure. This study proposes an efficient finite element model based on first-order shear deformation theory in combination with a genetic algorithm to maximize the frequency separation of laminated cylindrical shell panels. The maximum first natural frequency determined by the current FE-GA formulation is verified by previously published data, and it is found that the present results are better than the literature for 56% of the test cases. Moreover, for real-world situations like a clamped shell or a simply supported shell, the present solutions are approximately 0.6 to 2% better than the literature. Effect on the optimal design due to changes in mass ratio, curvature ratios of the shell panels, carrying dispersed mass over the entire shell panel, and dispersed patch mass at the middle is analyzed. The ideal stacking sequence for greatest frequency separation values is presented for a variety of curvature ratios and mass ratios. [ABSTRACT FROM AUTHOR]

We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the direct solution method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0 S 2, and higher frequency modes, namely 2 S 2, 0 S 7 and 0 S 10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3-D perturbations in density and seismic wave speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalization of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra. [ABSTRACT FROM AUTHOR]

This study analyzes the thermo-mechanical behavior of a brick vault and the effect of a fire on its dynamic characteristics. Based on the results of an experimental test of a real barrel vault with a net span of 161 cm and a net rise of 46.5 cm, an accurate numerical model to simulate the behavior of the brick-and-mortar structure under thermo-mechanical stresses has been implemented. The comparison of the evolution of the displacement in the keystone and the temperatures at various points of the vault allows us to affirm that the adopted micro-modeling approach presents a good accuracy and a feasible computational effort. Finally, this study shows, from a numerical point of view, how the variation in the structure's eigenfrequencies can be predicted for extreme situations, such as fire damage. This aspect can be critical to develop effective intervention and prevention strategies, which can be useful for the preservation of our valuable cultural and historic resources. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) printing has emerged as a promising technique for high-resolution additive manufacturing, but the frequency limits and optimal operating ranges for drop-on-demand EHD printing remain elusive. This lack of clarity has significant implications for printing efficiency and accuracy. Here, we present a theoretical model based on the Lagrange equation to calculate the eigenfrequency in EHD printing. Our study elucidates the dynamic relationships between the eigenfrequency and key process parameters (e.g., voltage, meniscus diameter, and center angle), and reveals the intrinsic relationship between the jetting frequency and the oscillation eigenfrequency, demonstrating that the jetting frequency is limited by the eigenfrequency. This conclusion has significant implications for the design of high frequency EHD printing systems; it highlights opportunities to increase the eigenfrequency by optimizing parameters such as meniscus radius/center angle. In addition, it is interesting to note that the high-order-mode jetting phenomenon can be utilized to break through the traditional frequency limit of the low-order mode. This work can serve as an instructive benchmark of the EHD printing frequency, which provides a basis for designing a high-frequency EHD printing system. [ABSTRACT FROM AUTHOR]

Eigenmodes in equilateral and isosceles triangular trimers of infinite cylinders have been studied using the theory of multiwave scattering. Equations have been derived for the eigenfrequencies of the exceptional points where eigenfrequencies and eigenvectors are degenerate. The symmetry of the isosceles triangular trimer determines the separation of modes antisymmetric in the base direction. In the case of the equilateral triangular trimer, modes are separated into symmetric and double degenerate rotational modes. It has been found that damping symmetric modes in the trimer have a higher Q-factor compared to a dimer, which is of significant importance for applications of effects based on exceptional points. The behavior of complex eigenfrequencies in the isosceles triangular trimer has also been studied depending on the ratio of the lengths of its base and leg. At the point corresponding to the equilateral triangular trimer, the Q-factors of symmetric and antisymmetric modes have the local maximum and minimum, respectively. [ABSTRACT FROM AUTHOR]

The classical time-harmonic plane strain problem for a fluid-loaded cylindrical elastic shell is revisited. The results of the low-frequency asymptotic analysis, including explicit formulae for eigenfrequencies, are presented. A refined version of the semi-membrane shell theory is formulated. It is shown that the shell inertia does not affect significantly the lowest eigenfrequencies. It is also demonstrated that the ring stress component has a parabolic linear variation. [ABSTRACT FROM AUTHOR]

The recent development of wearable devices is revolutionizing the way of human–machine interaction (HMI). Nowadays, an interactive interface that carries more embedded information is desired to fulfill the increasing demand in era of Internet of Things. However, present approach normally relies on sensor arrays for memory expansion, which inevitably brings the concern of wiring complexity, signal differentiation, power consumption, and miniaturization. Herein, a one‐channel based self‐powered HMI interface, which uses the eigenfrequency of magnetized micropillar (MMP) as identification mechanism, is reported. When manually vibrated, the inherent recovery of the MMP causes a damped oscillation that generates current signals because of Faraday's Law of induction. The time‐to‐frequency conversion explores the MMP‐related eigenfrequency, which provides a specific solution to allocate diverse commands in an interference‐free behavior even with one electric channel. A cylindrical cantilever model is built to regulate the MMP eigenfrequencies via precisely designing the dimensional parameters and material properties. It is shown that using one device and two electrodes, high‐capacity HMI interface can be realized when the magnetic micropillars (MMPs) with different eigenfrequencies have been integrated. This study provides the reference value to design the future HMI system especially for situations that require a more intuitive and intelligent communication experience with high‐memory demand. [ABSTRACT FROM AUTHOR]

We consider the quasinormal modes, quasibound states and superradiant instability of a rotating hairy black hole, which possesses a Horndeski hair as deviation from Kerr black hole, under the perturbation of massive scalar field. With the use of the matrix method, we mainly calculate the eigenfrequencies related to those modes of the perturbation. Under the perturbation of the massless scalar field, the Horndeski hair and spin parameter have significant influences on the quasinormal frequency, but its imaginary part is always finite negative and no unstable mode is found. Under the perturbation of the massive scalar field, we focus on the eigenfrequencies of quasibound states and find the modes of which the imaginary part of eigenfrequencies is positive, indicating that the black hole undergoes superradiant instability. Then we scan the parameters and figure out a diagram in the space of Horndeski hair and spin parameters to distinguish the rotating hairy black hole with superradiant instability from the stable one. [ABSTRACT FROM AUTHOR]

In this study, the vibrational behavior of Rayleigh and shear beams placed over the Hetényi and Pasternak foundations is investigated, with special attention paid to the effects of axial stresses (both tensile and compressive). The uniqueness of the work comes from the thorough consideration of how axial forces, shear deformation, rotational inertia, and foundation factors affect the eigenfrequencies and eigenmodes that control beam vibrations. Eigenfrequencies and eigenmodes are determined through computational analyses with the Galerkin finite element method (GFEM) employing quadratic and cubic polynomials. Comparisons between finite element results and analytical outcomes, both in generalized and specialized contexts, serve to demonstrate the correctness and effectiveness of the approximate solution. The study shows that the Hetényi foundation's influence on eigenfrequency depends on foundation stiffness and relative beam magnitudes, and that shear deformation affects eigenfrequencies more than rotary inertia does. Higher frequencies are largely unaffected by compressive and tensile stresses, but the fundamental frequency is rigorously influenced. Further demonstrating its accuracy, the finite element approach shows great agreement in forecasting eigenmodes and eigenfrequencies. A variety of real‐world situations involving elastically confined beams resting on elastic foundations and being subjected to axial forces are the focus of the study. Axial forces commonly result from external loads, thermal expansion, or structural interactions in real‐world settings. Therefore, it is crucial to understand how they affect beam vibration when designing structures that can endure expected stresses and vibrations while maintaining safety and performance criteria. [ABSTRACT FROM AUTHOR]

The problem of finding the natural frequencies and eigenfunctions of the fuel element of a nuclear reactor is considered. A rod with a piecewise constant material density in the longitudinal direction is used as a model. The frequency equation is explicitly derived, and the natural frequencies of the first twelve harmonics are determined numerically and analytically. Analytical expressions for eigenfunctions are obtained, which are in good agreement with calculations made using the Galerkin method and numerical calculations in the ANSYS program. The results will be used to simulate the dynamics of the NEPTUN pulsed reactor for examining the stability of its operation. [ABSTRACT FROM AUTHOR]

The Helmholtz method is developed to predict the self-excited thermoacoustic instabilities in a gas turbine combustor, combining flame describing functions, the measured damping rates under the firing condition, and the non-uniform spatial distributions of the physical parameters. The impact of the hydrodynamic and geometrical parameters on the thermoacoustic instabilities is investigated. The measured damping rates show lower values under a hot condition compared with those in a cold state. The experimental results indicate that the relative errors of the predicted eigenfrequencies and the velocity fluctuation levels are below 10%. The pressure amplitude decreases and the phase increases in the axial direction, indicating a typical 1/4-wavelengh mode. At a higher equivalence ratio, the mode shape in the axial direction becomes steeper due to the elevated fluctuation amplitude at the pressure antinode after enhancing the thermal power. When the air flow rate increases, the discrepancies between the pressure shape on the flame tube side and that on the plenum side are reduced. The velocity fluctuation level increases as the combustor length increases at a constant damping rate. In fact, the velocity fluctuation level first increases and then declines, caused by more significant damping rates when employing longer flame tubes. Self-excited thermoacoustic instabilities can be well predicted using the proposed method. [ABSTRACT FROM AUTHOR]

Acceleration sensors are vital for assessing engineering structures by measuring properties like natural frequencies. In practice, engineering structures often have low natural frequencies and face harsh environmental conditions. Understanding sensor behavior on such structures is crucial for reliable measurements. The research focus is on understanding the behavior of acceleration sensors in harsh environmental conditions within the low-frequency acceleration range. The main question is how to distinguish sensor behavior from structural influences to minimize errors in assessing engineering structure conditions. To investigate this, the sensors are tested using a long-stroke calibration unit under varying temperature and humidity conditions. Additionally, a mini-monitoring system configured with four IEPE sensors is applied to a small-scale support structure within a climate chamber. For the evaluation, a signal-energy approach is employed to distinguish sensor behavior from structural behavior. The findings show that IEPE sensors display temperature-dependent nonlinear transmission behavior within the low-frequency acceleration range, with humidity having negligible impact. To ensure accurate engineering structure assessment, it is crucial to separate sensor behavior from structural influences using signal energy in the time domain. This study underscores the need to compensate for systematic effects, preventing the underestimation of vibration energy at low temperatures and overestimation at higher temperatures when using IEPE sensors for engineering structure monitoring. [ABSTRACT FROM AUTHOR]

In recent years, the development of quick and streamlined methods for the detection and localization of structural damage has been achieved by analysing key dynamic parameters before and after significant events or as a result of aging. Many Structural Health Monitoring (SHM) systems rely on the relationship between occurred damage and variations in eigenfrequencies. While it is acknowledged that damage can affect eigenfrequencies, the reverse is not necessarily true, particularly for minor frequency variations. Thus, reducing false positives is essential for the effectiveness of SHM systems. The aim of this paper is to identify scenarios where observed changes in eigenfrequencies are not caused by structural damage, but rather by non-stationary combinations of input and system response (e.g., wind effects, traffic vibrations), or by stochastic variations in mass, damping, and stiffness (e.g., environmental variations). To achieve this, statistical variations of thresholds were established to separate linear non-stationary behaviour from nonlinear structural behaviour. The Duffing oscillator was employed in this study to perform various nonlinear analyses via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The calculation of magnetically induced vibrations in the stator of an electric machine involves, on the one hand, the determination of the magnetic forces originating from the air gap field and, on the other hand, the calculation of the mechanical eigenmodes and eigenfrequencies. This work presents a new method for the mechanical modelling of the stator using shell elements in 3D, as an extension of a recently published method using beam elements in 2D. It is applied to the case of a hydro generator with a complex mechanical construction, including the frame, and the results are validated by measurements performed on a $55\,\text {MVA}$ machine. It is shown that the developed method allows a time-efficient calculation of the eigenmodes and eigenfrequencies, providing an advantageous alternative to the classical analytical and finite element (FE) methods typically used for this purpose. This outcome is particularly relevant and applicable to the design and optimisation of large electric machines, as well as troubleshooting vibration problems in existing machines.

Introduction. This paper presents the results of the decomposition of the synthesized free damped vibrations of a linear cantilever dynamic model into elementary components using singular value decomposition of the displacement matrix.Materials and methods. The well-known representation of a rectangular matrix in the form of a product of three matrix multipliers, called singular value decomposition (SVD), was used in the study.Results. Representing the dynamic response of a structure in a certain matrix form allows for the results of the singular value decomposition to have a clear physical interpretation: the left singular vectors approximate the eigenvectors, the singular values themselves determine the contribution of individual eigenmodes to the overall dynamic response, and the products of singular values and right singular vectors approximate the modal coordinates of the dynamic system at the time under consideration. Singular value decomposition allows to “automatically” obtain an a priori vector basis based on the external manifestations of the dynamic reaction (displacement, velocity or acceleration of the points of the structure), whereas the eigenvectors traditionally used for these purposes are a posteriori basis based on the study of the internal inertia, stiffness and damping properties.Conclusions. This study confirmed the possibility of using displacement matrix SVD to determine the major dynamic parameters of linear dynamic systems: eigenmodes, eigenfrequencies and quantitative damping parameters. All stages of obtaining and subsequent analysis of the dynamic response elementary components are easily automated, which allows to consider SVD as a basis for software development of automatic dynamic monitoring systems of structures under construction and in operation.

We present the experimental demonstration of the occurrence of exceptional points of degeneracy (EPDs) in a single resonator by introducing a linear time-periodic variation of one of its components. This is in contrast with the requirement of two coupled resonators with parity time-symmetric systems with precise values of gain and loss. In the proposed scheme, only the tuning of the modulation frequency is required, which is easily achieved in electronic systems. The EPD is a point in a system parameters' space at which two or more eigenstates coalesce, and this leads to unique properties not occurring at other non-degenerate operating points. We show theoretically and experimentally the existence of a second-order EPD in a time-varying single resonator. Furthermore, we measure the sensitivity of the proposed system to a small structural perturbation and show that the two shifted system's eigenfrequencies are well detected even for relative perturbations of 0.3 % , with distinguished peaks well above the noise floor. We show that the regime of operation of the system at an EPD leads to a unique square-root-like sensitivity, which can devise new exceptionally sensitive sensors based on a single resonator by simply applying time modulation. [ABSTRACT FROM AUTHOR]

The regulation of mass is essential for the development and homeostasis of cells and multicellular organisms. However, cell mass is also tightly linked to cell mechanical properties, which depend on the time scales at which they are measured and change drastically at the cellular eigenfrequency. So far, it has not been possible to determine cell mass and eigenfrequency together. Here, we introduce microcantilevers oscillating in the Ångström range to monitor both fundamental physical properties of the cell. If the oscillation frequency is far below the cellular eigenfrequency, all cell compartments follow the cantilever motion, and the cell mass measurements are accurate. Yet, if the oscillating frequency approaches or lies above the cellular eigenfrequency, the mechanical response of the cell changes, and not all cellular components can follow the cantilever motions in phase. This energy loss caused by mechanical damping within the cell is described by the quality factor. We use these observations to examine living cells across externally applied mechanical frequency ranges and to measure their total mass, eigenfrequency, and quality factor. The three parameters open the door to better understand the mechanobiology of the cell and stimulate biotechnological and medical innovations. There is increasing interest in measuring the mechanical properties of living cells. Here, the authors develop a method to simultaneously measure the cell mass and two parameters related to its natural oscillation or resonance frequencies. [ABSTRACT FROM AUTHOR]

A coupled chain of superconductor/ferromagnet/superconductor (S/F/S) with anomalous ground phase shift represents a system realizing long-range interaction between magnetic moments of the weak links. The interaction is of magnetoelectric origin and is mediated by the condensate phase of superconductors. The system is a paradigmic platform for investigation of collective magnetic states governed by the superconducting phase. Here we study the magnetic eigenmodes of such a system and demonstrate that the eigenfrequencies are determined by the magnetic configuration of the whole system and are controlled by the superconducting phase. Depending on the orientation of the magnetic easy axis the eigenmodes can be very different ranging from individual oscillations of different magnets to highly-cooperative behavior. [ABSTRACT FROM AUTHOR]

Can-annular combustors feature clusters of thermoacoustic eigenvalues, which originate from the weak acoustic coupling between N identical cans at the downstream end. When instabilities occur, one needs to consider the nonlinear interaction between all N modes in the unstable cluster in order to predict the steady-state behaviour. A nonlinear reduced-order model for the analysis of this phenomenon is developed, based on the balance equations for acoustic mass, momentum and energy. Its linearisation yields explicit expressions for the N complex-valued eigenfrequencies that form a cluster. To treat the nonlinear equations semianalytically, a Galerkin projection is performed, resulting in a nonlinear system of N coupled oscillators. Each oscillator represents the dynamics of a global mode that oscillates in the whole can-annular combustor. The analytical expressions of the equations reveal how the geometrical and thermofluid parameters affect the thermoacoustic response of the system. To gain further insights, the method of averaging is applied to obtain equations for the slow-time dynamics of the amplitude and phase of each mode. The averaged system, whose solutions compare very well with those of the full oscillator equations, is shown to be able to predict complex transient dynamics. A variety of dynamical states are identified in the steady-state oscillatory regime, including push-push (in-phase) and spinning oscillations. Notably, the averaged equations are able to predict the existence of synchronised states. These states occur when the frequencies of two (or more) unstable modes with nominally different frequencies lock onto a common frequency as a result of nonlinear interactions. [ABSTRACT FROM AUTHOR]

Diatoms have delicate and complex shells showing different lightweight design principles that have already been applied to technical products improving the mechanical properties. In addition, diatom inspired structures are expected to significantly affect the vibration characteristics, i.e., the eigenfrequencies. Directed eigenfrequency shifts are of great interest for many technical applications to prevent undesired high vibration amplitudes. Therefore, numerous complex diatom inspired dome structures primarily based on combs, ribs, and bulging patterns were constructed and their eigenfrequencies were numerically studied. Different structural patterns were identified to significantly affect eigenfrequencies. The results were compared to dome structures equipped with rib patterns in combination with a common structural optimization tool. The study indicates that a combination of (1) selecting diatom inspired structural patterns that strongly affect eigenfrequencies, and (2) adapting them to the boundary conditions of the technical problem is an efficient method to design diatom inspired lightweight solutions with high eigenfrequencies. [ABSTRACT FROM AUTHOR]

The problem of controlling the vibrations of a string by a discrete applied force is considered. The vibrations of the string are modeled by the linear wave equation and the control is provided by an added force term. The wave equation is solved for controlled and uncontrolled cases with and without control force term. The applied force is chosen to be proportional to string displacement at some specified point. In the controlled case; the wave equation involves a control parameter (gain) and related terms involving the value of the displacement at a single point and a delta function. This makes the equation quite different from the usual wave equation. The problem is solved analytically using a modified (compared to usual wave equation) solution procedure and an equation relating the string eigenfrequencies to the proportionality constant (gain) is derived. This allows the observation of the change in eigenfrequencies with the gain. Finally, examples of uncontrolled and controlled responses are presented, graphically. The results show that the resonances can be avoided by the applied control procedure. [ABSTRACT FROM AUTHOR]

Engineers have consistently prioritized the maintenance of structural serviceability and safety. Recent strides in design codes, computational tools, and Structural Health Monitoring (SHM) have sought to address these concerns. On the other hand, the burgeoning application of machine learning (ML) techniques across diverse domains has been noteworthy. This research proposes the combination of ML techniques with SHM to bridge the gap between high-cost and affordable measurement devices. A significant challenge associated with low-cost instruments lies in the heightened noise introduced into recorded data, particularly obscuring structural responses in ambient vibration (AV) measurements. Consequently, the obscured signal within the noise poses challenges for engineers in identifying the eigenfrequencies of structures. This article concentrates on eliminating additive noise, particularly electronic noise stemming from sensor circuitry and components, in AV measurements. The proposed MLDAR (Machine Learning-based Denoising of Ambient Response) model employs a neural network architecture, featuring a denoising autoencoder with convolutional and upsampling layers. The MLDAR model undergoes training using AV response signals from various Single-Degree-of-Freedom (SDOF) oscillators. These SDOFs span the 1–10 Hz frequency band, encompassing low, medium, and high eigenfrequencies, with their accuracy forming an integral part of the model's evaluation. The results are promising, as AV measurements in an image format after being submitted to the trained model become free of additive noise. This with the aid of upscaling enables the possibility of deriving target eigenfrequencies without altering or deforming of them. Comparisons in various terms, both qualitative and quantitative, such as the mean magnitude-squared coherence, mean phase difference, and Signal-to-Noise Ratio (SNR), showed great performance. [ABSTRACT FROM AUTHOR]

Object: The dynamic behavior of sandwich cylindrical shell with fused deposition processed of flexible honeycomb core and carbon nanotube reinforced composite faces sheets is analyzed. Method: The every layer of the sandwich cylindrical shell is described by three displacements projections and two rotations angles of the normal to the middle surface. The faces sheets displacements projections are expanded up to the quadratic terms with respect to transverse coordinates. The honeycomb core displacements projections are expanded up to the cubic terms with respect to a transverse coordinate. The compatibility conditions for layers are used. The Rayleigh–Ritz method is applied to analyze linear vibrations of sandwich cylindrical shell. Results: The properties of the eigenfrequencies and eigenmodes of the structure vibrations are analyzed in detail. [ABSTRACT FROM AUTHOR]

Non-reciprocal interactions of discrete or continuous systems may induce surprising responses such as flutter instabilities. It is shown in this paper that a finite one-dimensional lattice under non-symmetrical elastic interactions may flutter for sufficiently strong unsymmetrical interactions. An exact solution is presented for the vibration of such one-dimensional lattices with direct and non-symmetrical elastic interactions. An internal force controlling the interactions is included in the model as an additional force for each mass, which acts proportionally to the elongation of a spring at its position. This non-conservative problem due to this circulatory interaction is solved from the resolution of a linear difference equation for this unsymmetrical repetitive lattice. It is possible to derive the exact eigenfrequency dependence with respect to the unsymmetrical interaction parameter, which plays the role of a bifurcation parameter. Divergence and flutter instabilities of this fixed–fixed non-conservative axial lattice under non-Hermitian interactions are theoretically predicted, from a direct approach or by solving the difference equation whatever the number of masses of the lattice. It is shown that the system may flutter for sufficiently strong unsymmetrical interactions, whatever the size of the system, for even or odd number of masses. However, divergence instability may arise in such a system only for even number of masses. The drastic change of response of the present system for odd or even number of particles is specific of the discrete nature of the dynamic system. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to analyzing the components of centrifuge rotor vibrograms using a 2D trajectory fractal analysis based on the Detrended Moving Average method. The method identifies the different noise oscillatory behavior of the rotor depending on the rotation frequencies, ranging from non-stationary unbounded and 1/f pink noise to correlated and uncorrelated noise. Fractal characteristics of the vibrograms were computed for the first time and demonstrated differences for rotation frequencies close to the eigenfrequencies and far from them. This paper also discusses the influence of gyroscopic effects on the natural frequencies of centrifuge oscillations and the excitation of second harmonics when the centrifuge rotates at higher frequencies. The main cause of rotor vibration is identified as the mass imbalance of the rotors, and this paper proposes a vibration classification according to source nodes to diagnose serviceable and faulty technical systems. Finally, the possibility of anisotropy of the vibrogram is discussed, and the oriented fractal scaling components analysis method is applied to pave the way for further investigation. [ABSTRACT FROM AUTHOR]

Sloshing eigenvalues and eigenfunctions are studied for vertical cylinders of constant, finite depth occupied by a two-layer fluid. Two families of eigenfrequencies are obtained in the form expressing them explicitly via the eigenvalues of the Neumann Laplacian in the two-dimensional domain—the cylinder's cross section. Eigenfrequencies belonging to one of the families behave similar to those that describe sloshing in a homogeneous fluid, whereas the other family includes a large number of sufficiently small frequencies, provided the ratio of densities is close to unity. Various properties of eigenfrequencies are investigated for cylinders of arbitrary cross section; they include the dependence on the interface depth and the ratio of densities, and the asymptotics of the eigenvalue counting function. The behavior of eigenvalues and the corresponding eigenmodes is illustrated by numerical examples for circular cylinders without and with a radial baffle. [ABSTRACT FROM AUTHOR]

The study analyzed the influence of periodic and aperiodic stiffness distribution for the four-element Bernoulli-Euler beam on the first two eigenfrequencies and the dynamic stability of the system. The influence of increasing the ratio of cross-sections of the analyzed elements was also analyzed. Significant differences were found in eigenfrequencies and dynamic stability. Using the variational Hamilton principle, the equation of motion was derived, on the basis of which the values of the eigenfrequencies were determined, and the transformation into the form of the Mathieu equation made it possible to determine the dynamic stability for the analyzed structures. [ABSTRACT FROM AUTHOR]

Within planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT systems undergo vibration or oscillation upon exposure to external forces or disruptions. This research paper presents a comprehensive investigation into the dynamic behavior of a three-stage PGT utilized in medium and heavy trucks. This study introduces the Rayleigh energy method to assess system dynamics, revealing a bounded Rayleigh quotient related to the highest related eigenvalue. Then, this study delves into eigenfrequencies and the mode shape behavior of the adopted PGT model. The eigenfrequencies are identified as encompassing diverse vibrational modes of central components and planet gears. Moreover, a multi-scale analysis of the adopted PGT model is presented by deriving matrices for mass, bearing stiffness, and mesh stiffness. Comparisons with the Rayleigh energy method demonstrate the new approach's efficiency, exhibiting a low margin of error in the determination of eigenfrequencies. This investigation also highlights the alignment of identified mode shapes with the established literature, detailing the multi-scale approach's minor deviation in mode shape determination compared to the Rayleigh energy method. [ABSTRACT FROM AUTHOR]

In this paper, it is proposed a systematic presentation of the known methods for determining the elastic constants of a composite material using the vibration response. For a series of bodies with a simple shape, the value of the eigenfrequencies for different boundary conditions can be calculated with the standard formula (for example for beams, plates, or cylinders). These values depend on the elastic constants of the materials through simple formulas. So, if we know the eigenfrequencies for a certain particular shape of bodies made of a certain material, the elastic constants (or some of them) can be easily determined. The most accurate methods to determine these values of eigenfrequencies are, obviously, experimental methods. However, these methods are generally expensive in terms of time and resources. As a result, especially if we are in the design phase, it is very advantageous if we can determine these values from the calculations. For this, the Finite Element Method (FEM) is used in the paper. Cases are presented in which these values can be calculated with relative ease and therefore the values of the elastic constants can be obtained with less effort. [ABSTRACT FROM AUTHOR]

The lattice dynamics of face-centered square and edge-centered square lattice structures is classically examined using the harmonic approximation between atoms. The dynamical matrices and dispersion relations for the two lattice structures are derived. The eigenfrequencies are presented numerically. At long wavelengths, the acoustic branches and corresponding group and phase velocities are obtained. [ABSTRACT FROM AUTHOR]

In this work, we propose a method to optimize the material thickness distribution of partition panels for maximized sound insulation while constraining material usage. A framework is developed to couple structural optimization with diffuse field sound transmission loss (STL) predictions based on deterministic-statistical energy analysis (Det-SEA). The methodology can handle the design of both single panels, including a single mechanical plate, and double panels, in which two mechanical plates are separated by an air cavity. Three formulations of the optimization problem are developed and compared in terms of final obtained performance and computational cost. In the first formulation, the resonance dips in the STL are suppressed by pushing the panel eigenfrequencies as far away as possible from the target frequency. In the second and the third formulations, the diffuse STL of the panel is directly maximized respectively at the target frequency and in a frequency band around the target frequency. The practical advantages of the method are investigated for different target frequencies in the audible range and for relevant design cases, such as the suppression of the STL dip located around the critical frequency of single panels and around the mass–spring–mass resonance frequency of double panels. For single panels, all three different formulations lead to significant insulation improvements, with no big differences in the final obtained performance. For double panels instead, we show that simply suppressing the resonance dips with the first formulation does not lead to adequate insulation improvements, but a direct maximization of STL is needed. [ABSTRACT FROM AUTHOR]

A one-dimensional model of the near wake produced by a pair of not-too-close cylinders in a viscous incompressible fluid is developed on the basis of the Stuart–Landau model and perturbation theory. The whole wake is considered as two interacting partial von Kàrmàn vortex streets or two coupled Stuart–Landau oscillators, when the nonlinear nature of the interaction of these streets is taken into account. The observable spectrum of the global modes of the wake is obtained, the calculated and experimental eigenfrequencies of the oscillation modes being in agreement with respect to the modes. [ABSTRACT FROM AUTHOR]

The free vibrations of elastic circular arches made of a nano- material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch. [ABSTRACT FROM AUTHOR]

The assessment of infrastructure integrity is considered paramount to verify its structural health and to build its resilience. In this study, a monitoring strategy, consisting of a pre-developed microcontroller-based data acquisition system (DAQ) hardware and a software program for post processing built on LabVIEW platform, was conducted to assess the structural behavior of an arch-and-tie pedestrian bridge located in Haidari, Greece, following its construction phase. This endeavor aimed to delineate its systemic state and to verify the fulfillment of comfort criteria stated by EN1990, HIVOSS and SETRA guidelines. To this end, four trademark Bridge Diagnostic Inc. (BDI) triaxial accelerometers were meticulously deployed along the bridge expanse to scrutinize the structure's response toward a spectrum of induced perturbations. The established framework effectively compiled the acquired acceleration time domain then employed a Butterworth bandpass filter to derive the bridge eigenfrequencies, eigenmodes, and damping ratios. The resultant findings conclusively indicate that the bridge response towards pedestrian crossing conforms to the established specifications and thus does not necessitate the installation of dampers. The bridge maintains comfortable structural integrity for pedestrian traversal up to an upper frequency limit of 3.67 Hz, substantiating its ability to absorb the dissipated energy generated by pedestrian movement. [ABSTRACT FROM AUTHOR]

The design of timber floors is often governed by the fulfilment of serviceability requirements concerning human-induced vibrations. The stiffness and modal properties (eigenfrequency and damping ratio) are essential parameters for the design verification of timber floors against vibrations. In the present paper, a series of experimental tests (static tests, impact hammer modal tests, forced resonant vibrations and free vibrations) on a long-span, stressed-skin, timber floor are presented, together with predictions using a Finite Element model. Moreover, the effect of additional mass was investigated by adding extra weight in the mid-span. The modal properties obtained by different methods were in good agreement. The measured damping ratios were low, especially for the first two modes (of the order of 0.7% for the first mode and 0.8-1.0% for the second mode). The FE predictions were in good agreement with the experimental results regarding stiffness and the first two eigenfrequencies. However, the FE model overestimated the third eigenfrequency and underestimated the steady state accelerations observed under forced vibrations. A stiffness-proportional Rayleigh damping was found to describe best the energy dissipation. [ABSTRACT FROM AUTHOR]

Noise is increasingly recognised as a serious, worldwide public health concern. Noise is a type of occupational hazard that can cause damage to hearing and other health effects in workers who are exposed to high levels of noise in their work environment. Traditionally, noise can be controlled and suppressed but recently, noise can be useful and converted into electrical energy. The process of converting noise or acoustic waves into electrical energy by using a quarter wavelength resonator tube embedded with a flexible piezoelectric backplate was used in this study. The results show the maximum output voltage of 1.41 V/Pa at 112 Hz and 0.44 V/Pa at 225 Hz in the experiment, and 1.44 V/Pa at 106 Hz and 0.41 V/Pa at 226.5 Hz with incident sound waves at 90 dB. A parametric study was then performed by adjusting the lumped pointed mass at the piezoelectric backplate to tune the resonant frequencies of the system and the optimal power output. The point mass has given significant change in the acoustic properties. The maximum output power increased from 20.4 µW/Pa² at 112 Hz using a flexible back plate to 711 µW/Pa² at 119.75 Hz. Various small power applications can benefit from the approach by reducing and absorbing specific low-frequency bandwidths of continuous noise in the environment. [ABSTRACT FROM AUTHOR]