Mode Shapes Research Articles

Comparison of active and passive vibration control techniques for electric drive power electronic subsystem: Experimental validation

Reducing vibration and noise from power electronics components is vital for enhancing the performance and acceptance of electric vehicles, emphasizing the need for effective mitigation strategies in sustainable transportation. This paper compares passive and active vibration techniques, with a specific focus on utilizing particle damping for passive vibration control. The method achieves vibration reduction through viscoelastic deformation and friction resulting from the movement and collisions of granular material within the cavity. This contribution outlines diverse design strategies for integrating particle dampers into power electronic components. The active control approach, operating typically in the 50 Hz to 1200 Hz frequency range, can concurrently support passive noise treatments. Piezoelectric ceramics serve as both actuators and sensors in active noise reduction. Following the identification of dominant mode shapes, appropriate actuator and sensor positions are chosen. The control problem of the smart system is then addressed, opting for a velocity feedback control algorithm in a real collocated design. This algorithm computes input signals for actuators bonded to the outer surface, achieving significant active damping effects. Lab-tested techniques are validated in real-world conditions with a full-scale electric-drive toolkit, affirming their efficacy in reducing vibration and noise and underscoring their potential for implementation in electric vehicles.

Experiential learning with online vibro-acoustic demonstrators

After 25 years of delivering lecture-based learning at a university with mixed success I now supplement my short courses with online experiential learning demonstrators for visualizing and interacting with vibro-acoustic systems. The demonstrators use simple javascript coding and calls to the plotly free libraries. No special software is required (but stronger computers obviously perform faster). Learners can quickly adjust parameters like stiffnesses, masses, and damping using sliders and immediately visualize changes to vibration response and sound fields. Students may exercise demonstrators for one- and two-dimensional acoustic waves; vibrations and mode shapes of simple oscillators, beams, and plates; and sound radiated by and transmitted through panels. Some of the demonstrators are freely available at hambricacoustics.com (others are only available to my short course students).

Collective coordinate models for 2-vortex shape mode dynamics

Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space M, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on M, modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multibounce structure in vortex-vortex collisions is predicted. Published by the American Physical Society 2024

Polygonal plate element method for free vibration analysis using an efficient alpha (α)-assumed rotations and shear strains

This paper investigates the performance of a recently proposed polygonal plate element with alpha (α)-assumed rotations and shear strains, referred to as αARS-Poly, in free vibration analysis. The αARS-Poly element utilizes a simple and efficient approach involving a scaling factor (α) to enhance the accuracy of assumed rotations and shear strains. To fully explore the advantages of this element, we undertake a comprehensive analysis of free vibration in plate structures using a range of models with complex geometries. Numerical results demonstrate that the αARS-Poly element offers stability and reliability within smooth mode shapes. Furthermore, it significantly outperforms the previous polygonal Reissner-Mindlin plate element with piecewise-linear shape functions (PRMn-PL), achieving frequencies that closely match reference solutions, thereby validating its accuracy and robustness for dynamic applications.

Study on the self-vibration characteristics of non-circular arches with cracks based on the transfer matrix method

As the span of reinforced concrete arch bridges continues to increase, so does the difficulty of construction. The structure is at risk of cracking. Most of the bridges under construction are non-circular arches, and there are few studies on such arches. The current study tried to investigate the self-vibration characteristics of non-circular arches with existing cracks. A computational approach proposed in the original non-circular arch is substituted with multiple infinitesimal arch segments having different radii of curvature, enabling the determination of natural frequencies and mode shapes of the non-circular arches with cracks. Furthermore, a finite element model (FEM) of the reinforced concrete structure with existing cracks is developed to assess the effects of various factors, including axial location, crack depth, and positions within the same cross-section. The results demonstrate the feasibility of the computational method using multiple infinitesimal arc segments with varied radii of curvature, yielding a maximum error of only 1.58 %, which satisfies engineering application standards. An increase in crack depth leads to a reduction in the natural frequencies of specific modes of the structure, while the effect on others is insignificant. For cracks situated at the top or bottom plates within the same cross-section, the impact differs based on the local deformation being convex or concave. If the deformation is convex, the top plate cracks exhibit a higher rate of change in natural frequencies compared to the bottom plate cracks; conversely, with concave deformation, the bottom plate cracks have a greater influence than the top plate cracks.

Dynamic characteristics of a horizontal rectangular vessel partially or fully filled with a fluid

A theoretical framework is presented for free vibration of a flexible horizontal rectangular vessel, whether it is partially or fully filled with a fluid. The vibrational modal patterns of the vessel, whether dry or wet, are classified into symmetric and antisymmetric modes. The theoretical model conceptualizes the vessel as an unfolded plate with line supports simulating the vessel's corners. The motion of contained fluid is described using displacement potentials that adhere to the Laplace equation and fluid boundary conditions. Importantly, the proposed analytical approach accounts for the dynamic interaction between the vessel and the fluid, ensuring compatibility along their contacting surfaces. The Rayleigh-Ritz method is employed to formulate an eigenvalue problem, considering entire kinetic and strain energies of the fluid-filled vessel. The accuracy of the theoretical approach is checked by conducting finite element analyses. Remarkably, the natural frequencies obtained through commercial software align closely with the theoretical predictions for both dry and fluid-filled vessels. In instances of fully fluid-filled vessels, we can discern the presence of fluid contact at the vessel's upper plate by examining the natural frequencies and mode shapes. The proposed method offers applicability in dynamically analyzing water-filled spent fuel casks, enhancing safety during transportation.

Dynamic characteristics of a flexible rotor supported on surface textured journal bearings

Abstract This paper presents the dynamic characteristics of a flexible rotor supported on surface textured journal bearings. Oil lubricated journal bearings exhibit the self-exited whirling of rotor, leading to instability. Understanding the threshold speed of instability is crucial in mitigating excessive vibration in rotating machinery. In this work, a simple model of a flexible rotor with central disc is studied. Modal analysis is carried out to obtain the whirl frequencies of the system, mode shapes, and stability limit speed. The addition of surface textures to the journal bearing stands out as a significant modification aimed at improving performance. Fully textured and partially textured bearing surfaces are considered in the investigation and compared with the performance of smooth journal bearings. Notably, fully textured bearings enhance stability limits. This study offers insights essential for optimizing machinery performance and minimizing operational risks.

Study on the dynamic characteristics of the head cover-bolts-stay ring of a variable-speed pump-turbine

Abstract The design and operation of variable-speed pump-turbine units is more difficult than that of conventional units due to their adjustable speed, frequent start stop, and forward and reverse operation. Due to the development of variable-speed pump-turbines towards variable-speed, high head, and large capacity, the vibration instability caused by frequent switching between turbine and pump operating conditions is more prominent. The study on the dynamic characteristics of the head cover-bolts-stay ring system is an important guarantee for the long-term safe and stable operation of the units. This article uses the finite element method to conduct modal analysis on the head cover-bolts-stay ring system of a variable-speed pump-turbine. The natural frequency and mode shape are analyzed, and resonance analysis is carried out in combination with the dynamic and static interference characteristics of the variable-speed unit. The research results show that the dynamic and static interference frequency of the unit during the variable-speed process may be close to the natural frequency of the head cover-bolts-stay ring system, which needs to be paid attention to during operation. The results and findings in this article provide theory and practical basis for the research and design of high head, large capacity, and variable-speed pump-turbine units.

Flexural edge waves and customizable local modes of circular plates with metasurface

In this research, we study the propagation of flexural edge waves of circular plates (also known as circular-edge waves), present design strategies of metasurfaces for manipulating these waves, and realize customizable edge modes on the basis of edge wave manipulations. Theoretical frameworks are presented to solve the dispersion relationship of circular-edge waves propagating along different boundaries, including a free edge, a strip with a weakness stiffness, and a metasurface with a slot array. On the basis of these frameworks, the propagation characteristics of circular-edge waves are revealed, and the rainbow reflection and topological interface state are realized by constructing metasurfaces. Furthermore, the modal frequency prediction, the robustness to structural parameters, and the effective excitation position for circular-edge modes are explored. Finally, based on the above analysis, the customizable local modes are presented, which means that the position of high energy regions in mode shapes can be designed without changing the corresponding modal frequency. Our work provides a new idea for the manipulation of flexural waves in circular plates and find a potential correlation between flexural waves and vibrations, which may exhibit wide applications in vibration control and acoustic device development.

Machine tool cross beam design, fabrication, and testing using metal big area additive manufacturing

This paper describes the application of metal Big Area Additive Manufacturing (mBAAM) to the fabrication of a machine tool cross beam. The replacement of a traditional box design weldment with a new design printed by wire arc additive manufacturing using the MedUSA system at Oak Ridge National Laboratory (ORNL) is detailed. This requires a new design strategy based on the unique mBAAM capabilities. The intent of the new design is to reduce mass, while maintaining the dynamic stiffness. To compare the two designs, the natural frequencies and mode shapes are measured using impact testing and predicted using finite element analysis. It is confirmed that the printed structure dynamics agreed with the numerical model predictions, which demonstrates that it is feasible to model a large-scale mBAAM part and understand its behavior prior to printing. Another notable outcome of this study is that the significant residual stress and distortion in the print indicate that knowledge gaps remain for widespread implementation of mBAAM.

Full-Field Measurement of Lightweight Nonlinear Structures Using Three-Dimensional Scanning Laser Doppler Vibrometry

Modern noncontact measurement techniques such as the three-dimensional scanning laser Doppler vibrometry (3D SLDV) are advantageous in measuring vibrations of lightweight, thin-walled aerospace structures, which were conventionally deemed as difficult or not feasible to apply using attached transducers. Nevertheless, the full-field measurements using 3D SLDV are still limited to extracting modal properties of linear structures, while measurements of complex nonlinear structures are rarely reported. This paper aims to extend the full-field measurement capability of 3D SLDV and combines it with a multiple-input–single-output vibration controller to deal with nonlinear structures. An advanced test strategy is introduced, which is capable of obtaining amplitude-dependent resonant frequencies, modal damping ratios, and full-field, multiharmonic mode shapes of nonlinear normal modes (NNMs). Conflicting parameters such as the frequency resolution and measurement time are optimized by combining phase separation and phase resonance testing techniques in a coherent strategy. The capabilities of the proposed nonlinear modal testing strategy are demonstrated on a realistic, large-scale fan blade that exhibits softening behaviors. Two of its NNMs were investigated at larger vibration amplitudes. Its nonlinear modal parameters were successfully extracted and validated, highlighting the time efficiency and data accuracy of the proposed strategy for measuring industrial-scale, lightweight nonlinear structures.

A novel solution for dynamic behaviors of multi-span bridge plates

The present paper draws a comprehensive analysis of the free vibration characteristics and discusses modal localization phenomena of multi-span bridge plate structures through an analytical method, numerical simulations, and experimental measurements. A novel analytical solution using the generalized superposition segment method (GSSM) is first proposed to investigate the transverse vibration of a multi-span bridge, which offers complete flexibility in describing arbitrarily classical boundary conditions. Furthermore, a new experimental setup achieves precisely simply supported boundary conditions, and scaled physical models of two- and three-span bridge plates are employed to validate the analytical solution. The effect of span length mismatch is studied by analyzing the resonant frequencies and mode shapes of a multi-span bridge plate with varying span lengths. The good consistency of results by theoretical analysis, numerical simulation, and experimental measurements indicate that the proposed analytical solution can solve the vibration problem of the multi-span bridge plate efficiently and reflect the real-world boundary condition. Finally, the two modal localization behaviors are observed in theoretical analysis and experimental measurement. Through analytical solutions, numerical simulations, and experimental measurements, this study enhances the understanding of the dynamic behavior of multi-span bridges. It provides a new theoretical benchmark for predicting vibrations of multi-span bridge systems and useful insights into the transient behavior of multi-span bridge plates, suggesting several fruitful avenues for future research, including exploring passive and active control systems and vibration suppression techniques.

Numerical analysis of energy dissipation due to eddy currents in a vibrating beam

Vibration attenuation is a key aspect of mechanical engineering. One method to achieve this is through eddy currents, which can be generated in a vibrating system when a magnetic field is present, creating forces that oppose motion. This study examines a mechanical system consisting of a thin cantilever beam vibrating in a uniform and time-invariant magnetic field under steady-state conditions to understand the nature of energy dissipation and the relationship between motion, eddy currents, and damping forces. The calculation of eddy currents generally requires the use of complex numerical procedures. However, for systems with simple geometry, such as a cantilever beam, a recent numerical procedure based on the finite difference method, known for its simplicity in implementation, has been adapted and expanded to determine eddy currents under motional induction. A numerical application has been developed in which the vibration of a specific beam is characterised by its bending or torsional mode shapes, and the nature of the corresponding dissipative forces is analysed. Results indicate that the eddy currents are an effective means of dissipating energy at lower-order modes. Additionally, the direction of the applied magnetic field can induce coupling between bending and torsional vibrations.

Analysis and mitigation of uncertainties in damage identification by modal-curvature based methods

The objective of this paper is to address and reduce the uncertainties associated with measurement noise and discretization in damage identification methods based on modal curvature analysis. The experimental case study considers the local reduction in the bending stiffness of a slender beam under free-free and simply supported boundary conditions. First, the analysis of error sources and their propagation is theoretically set up. Second, the mitigation of uncertainties in damage localization is pursued using a two-stage approach based on multiple hypothesis testing relative to the normalized indices and the definition of a combined macro-index. Finally, the Monte Carlo method is exploited to obtain the statistical error distribution of the experimental damage position and severity predictions by randomizing the numerical displacement mode shapes with the identified noise. The present analysis allows us to find the optimal number of sensors that minimizes the combination of bias and truncation errors, to highlight how sensor spacing and data noise affect damage localization, and to determine the uncertainty bounds of the predicted damage severity. The two-stage approach, enhanced by selecting thresholds related to real noise levels and tuned on SHM objectives, appears to improve identification accuracy compared to the separate use of damage indices based on absolute confidence levels.

Limit Cycle Oscillation of Elastic Plate in Supersonic Flow

Fluid–structure interaction of an elastic plate with piezoelectric elements, turbulent freestream flow at Mach 2.5, and a pressurized cavity is investigated computationally and correlated with a recent experiment. The pressure field on the plate is measured using pressure-sensitive paint, and the structural response is observed using the measured voltage of a piezoelectric patch. The measurements show a dominant frequency of oscillation which indicates the likely onset of flutter and a postflutter limit cycle oscillation (LCO). A computational investigation is conducted to study the effects of static pressure differential, temperature differential, cavity pressure coupling, and plate boundary conditions on the linear flutter onset condition and the nonlinear postflutter LCO characteristics. Rivets that connect the plate to the supporting structure are modeled as local constraint in the in-plane direction, and their effect is investigated. Computations show that the coupling between the cavity acoustic and plate structural modes is necessary for flutter onset in the wind-tunnel conditions. Correlation between computed and measured aerodynamic pressure shows reasonable agreement in amplitude and frequency. Computational results are obtained using Piston Theory and also potential flow aerodynamics. Computed and measured pressure LCO mode shapes are extracted and correlated.

A novel damage index for crack identification of a drilling riser during deployment based on the modal vibration energy flow

Early detection of structural damage especially small cracks in marine deepwater drilling risers is of paramount importance. Small cracks are always hard to detect because of weak vibration signals if using traditional damage indices, such as natural frequencies and mode shapes including modal displacements, cross-section slopes, and curvatures. Especially when the deepwater riser is during deployment, the variable suspension riser length and strong sea environment noise make the small crack identification more difficult. To address this problem, this study formulates a new concept of damage detection by integrating the vibration energy flow theory into the vibration-based damage detection (VDD) technique. A novel damage-sensitive feature (DSF) named modal vibration energy flow (MVEF) is established for detecting and locating the small cracks in deepwater drilling risers. The capability of the approach is verified by using the same riser model and the numerical results in the literature. The sensitivities versus crack positions and depths, variable suspension riser length, and sea noise are studied in detail. Results show that the proposed index MVEF is more sensitive than the classic traditional DSFs, i.e., modal slope, modal strain (or curvature), and modal strain energy. In total, the MVEF approach can accurately identify the small cracks and is robust against noise interference, suitable for detecting and locating small cracks in the deepwater drilling riser during deployment.

Development and testing of a novel vibratory compaction instrument considering its natural frequency.

This study aims to develop a novel vibratory compaction instrument designed for the preparation of large triaxial soil specimens, offering an efficient alternative to the traditional manual specimen preparation process. However, when the motor frequency closely aligns with the natural frequency of the structure, severe resonance phenomena may occur. This paper employed finite element modal analysis, experimental modal analysis, and operational modal analysis techniques to conduct a multi-objective optimization of the structure, aiming to improve the dynamic characteristics. First, the natural frequency and mode shapes of the vibratory compaction instrument were determined via finite element technology. Subsequently, the optimization of this instrument was conducted by integrating the Kriging surrogate model with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Finally, the steel column underwent a modal test using impulse stimulation to ascertain its natural frequency, and the stochastic subspace identification (SSI) approach was employed to conduct an operational modal analysis of the vibratory compaction instrument to determine its modal characteristics. The experimental findings corroborated the conclusions obtained from the finite element analysis, validating the precision of the finite element modal analysis and the rationality of the optimized structure. The research results are of significant importance for improving the preparation efficiency of large triaxial specimen, contributing to advancements in soil mechanics testing.

Operating modal parameter identification of railway vehicle bogie based on k-value optimization variational mode decomposition and second-order blind identification method

Due to the variable operating conditions and strong background noise, the accuracy of modal parameter identification of the railway vehicle bogie is low. This paper proposes a method for identifying operational modal parameters by combining the K-value optimization variational mode decomposition (KVMD) and second-order blind identification (SOBI) method (KVMD–SOBI method). Firstly, the variational mode decomposition (VMD) algorithm is used to adaptively decompose a single-channel vibration signal into intrinsic mode function (IMF) components with different scale characteristics. The feature IMF components are selected through the K-value optimization method based on energy ratio and stability graph. Then, the SOBI algorithm is used to separate the matrix composed of the feature IMF components. And the mode shape and single-mode signal are obtained. Finally, the natural frequency and damping ratio of each order mode are extracted by the single-mode parameter recognition method. Through simulation and experimental verification, it is shown that the proposed method has good noise robustness and can effectively identify the first three modal parameters of railway vehicle bogies in variable-speed operation. At the same time, the feature IMF components extracted by KVMD algorithm eliminate the sensitivity of sensor installation positions and operating conditions to detection results. Therefore, this method is an excellent operational mode identification method based on a single-channel signal with good noise and working condition robustness.

20 years of monitoring of a steel jacket offshore platform: variability of environmental and modal parameters

The fixed steel offshore platform VEGA-A has been operating in the Sicily channel since 1988. The platform, one of the largest in the Mediterranean Sea, is equipped with a monitoring system that collects environmental (by means of a current meter, a depth gauge, and a system for detecting wind speed and direction) and structural (by means of nine accelerometers) data. After a description of the recording system, this paper provides a statistical interpretation of the structural response of the platform over the last 20 years. The structural monitoring system is aimed at performing dynamic identification (i.e., evaluating main frequencies and mode shapes), and part of the acquired data is directly processed on the platform in order to constantly check their representativeness in relation to the structural control of the platform. The possible variation of main frequencies and mode shapes over time may be due to both changes in environmental loads/conditions and/or structural damage; in this respect, a data-driven approach capable of recognizing anomalies in the dynamic behavior was adopted here to assess the performances of the platform over the 20 years monitoring period.

Damage identification in composite structures using high-speed 3D digital image correlation and wavelet analysis of mode shapes

ABSTRACT In this study, the damage identification procedure combining the advantages of high-speed 3D digital image correlation (DIC) that is used for modal analysis and wavelet-based processing algorithm is presented. The proposed procedure has been successfully validated on sandwich composite structures with internal damage of a core and impact damage, and its performance was demonstrated by detection, localisation, and identification of shapes of damage in tested structures, comparable to the results from scanning laser Doppler vibrometry (SLDV). The effectiveness in damage identification was achieved by the development of processing algorithm of acquired mode shapes, which uses a 2D double-density directional wavelet transform with increased sensitivity with entropic weights allowing to automatically select those wavelet coefficients and mode shapes, which are most sensitive to damage. The procedure presented in this paper demonstrates the performance of 3D DIC for damage identification as a cost-effective alternative to the procedures based on SLDV measurements.