Mode Shapes Of Structure Research Articles

Hypersonic Fluid–Thermal–Structural Interaction of Cone–Slice–Ramp: Computations with Experimental Validation

The paper presents an investigation of fluid–thermal–structural interaction (FTSI) on a complex geometry in hypersonic flows. The objective is to assess high-fidelity numerical tools for FTSI by validating two numerical frameworks against wind-tunnel data. We choose a cone–slice–ramp geometry with a wedge angle of 30 deg subjected to a laminar inflow at Mach 8. First, the time-averaged and the time-resolved laminar flow solutions are validated and highlight the mean flow features and their unsteady characteristics, including low-frequency bubble breathing and shear-layer flapping at a higher frequency. The numerical analysis reveals the presence of upstream and downstream legs of streamwise vortices. Next, FTSI analysis is performed at a tractable computational cost by decomposing the numerical frameworks into a quasi-steady FTSI (QS-FTSI) analysis and a transient fluid–structure interaction (FSI) analysis based on the disparity of the characteristic timescales. The QS-FTSI results highlight the shear-layer reattachment as the dominant source heating the structure, with nonuniform spanwise variations due to the streamwise vortices. The temperature increase drives the decrease in the structural modal frequencies. The FSI analysis was performed for an unheated, undeformed structure and a nominal heated and deformed structure. The average error in the predicted FSI frequency of the unheated panel is 2.65% in comparison to the experimental data; however, this value increases to 7.42% for the heated panel. The frequency peaks are associated with the structural mode shapes via dynamic mode decomposition analysis and show a close resemblance to natural modes, indicating weak FSI coupling. The FTSI study concludes that for a cone–slice–ramp configuration under the present inflow conditions, the interaction mostly occurs in a one-way coupled manner, where the flowfield drives the thermal and structural response of the panel.

Nonlinear system identification of a UAV model with distributed aerodynamics and flexible structure

This paper presents the nonlinear system identification of a slightly flexible 25 kg fixed-wing UAV in the time-domain using a computationally efficient distributed aerodynamics model and a linear structural dynamics representation. The equations of motion are formed by making use of the free vibration modes of the structure and the mean axes formulation. The structural modes and mode shapes are determined from ground vibration tests. The distributed aerodynamics, accounting for elastic deformations, are modeled using a quasi-steady stability and control derivative approach and by applying strip theory. Initial distributions for the derivatives are obtained from vortex-lattice-method calculations. For matching the model response to the measured response, parameters for scaling the initial derivative distributions are introduced. The flexible model is subsequently identified based on flight test data using the output error method in the time-domain and maximum-likelihood estimation. A good overall identification result is achieved with a close match of the fast aircraft dynamics. Finally, an evaluation is given on the suitability of the identified model for real-time simulation, loads’ estimation, and active load control law design.

Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation

This article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the structure. The objective of this investigation is to examine how the vibrational frequencies of the Rayleigh beam are affected by the elastic foundation parameter and the rotational inertia. The results obtained from analytical and numerical methods are presented and compared with the configuration of the Euler–Bernoulli beam. The analytic approach employs the technique of separation of variable and root finding, while the numerical approach involves using the Galerkin finite element method to calculate the eigenfrequencies and mode functions. The study explains the dispersive behavior of natural frequencies and mode shapes for the initial modes of frequency. The article provides an accurate and efficient numerical scheme for both Rayleigh and Euler–Bernoulli beams, which demonstrate excellent agreement with analytical results. It is important to note that this scheme has the highest accuracy for eigenfrequencies and eigenmodes compared to other existing tools for these types of problems. The study reveals that Rayleigh beam eigenvalues depend on geometry, rotational inertia minimally affects the fundamental frequency mode, and linear spring stiffness has a more significant impact on vibration frequencies and mode shapes than rotary spring stiffness. Further, the finite element scheme used provides the most accurate results for obtaining mode shapes of beam structures. The numerical scheme developed is suitable for calculating optimal solutions for complex beam structures with multi-parameter foundations.

Numerical simulation of dynamic characteristics of hydrofoil structure under cavitation conditions

In this paper, the effects of different cavitation bubble on the natural frequency, mode shape and hydrodynamic damping of the NACA0009 hydrofoil are investigated by numerical simulation method. The cantilever truncated hydrofoil model is set in a high-speed water tunnel. The dynamic characteristics of the hydrofoil structure is affected by the fluid-structure coupling. Compared to the properties of water, the density of cavitation bubbles decreases, causing an increase in the natural frequency of the structure, and the decrease in the speed of sound also causes a change in the mode shape. The growth rate of frequency under unit chord length cavitation is nonlinear as the cavitation bubble length increases. By defining a modal displacement function to compare the structural mode shapes, cavitation intensifies the bending and torsional deformation of the hydrofoil. Even if the volume of cavitation bubbles is small, the inhomogeneous distribution of acoustic pressure and changes in cavitation bubble properties can cause changes in the structural mode shapes. The one-way FSI numerical method for hydrodynamic damping in cavitating flow is established and the applicability of this method is verified by the calculation of damping in water. For the first bending mode fc1, the hydrodynamic damping with 50% chord length (0.5lc) stably attaching cavitation is simulated. As the length of the cavitation bubble increases to 0.8lc, the damping value becomes smaller. The research in this paper lays the foundation for analysing the dynamic characteristics of hydraulic machinery with cavitation using numerical simulation method.

Review on Design and Analysis of Drill Head of Boring Machine by using Vibration Conditioning Monitoring

Abstract: In terms of both productivity and product quality, machine tools are now held to high standards in the industrial sector. Vibration is a crucial indicator of a product's quality. If the patterns of vibration produced by machine tools during cutting operations are recognised, the structure of the machine tool may be built in a way that separates its frequency response from the imposed frequency. The most effective method for managing all machining operations and maintaining machinery operation is tool condition monitoring. Monitoring tool condition affects production costs, tool life expectancy, tool quality, dimensional accuracy within a given tolerance, and surface polish in a machine shop. Here, the machining process is entirely dependent on the operator's whims and preferences. So, it is more difficult for a novice operator to identify the tool wear point and it is more difficult for the operator to operate the machine. A systematic process is needed for the machining procedure to get around this challenge. Determining the inherent frequency and mode forms of the radial drilling machine construction is the aim of this research as a consequence. Finite element analysis was used to identify the innate frequencies and mode shapes of the radial drilling machine structure.

FLUTTER SPEED LIMITS OF SUBSONIC WINGS

Flutter is a phenomenon resulting from the interaction between aerodynamic and structural dynamic forces and may lead to a destructive instability. The aerodynamic forces on an oscillating airfoil combination of two independent degrees of freedom have been determined. The problem resolves itself into the solution of certain definite integrals, which have been identified as Theodorsen functions. The theory, being based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing-ection theory relating to the steady case. The mechanism of aerodynamic instability has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been analyzed in detail. The solution is of a simple form and is expressed by means of an auxiliary parameter K. The use of finite element modeling technique and unsteady aerodynamic modeling with the V-G method for flutter speed prediction was used on a fixed rectangular and tapered wing to determine the flutter speed boundaries. To build the wing the Ansys 5.4 program was used and the extract values were substituted in the Matlab program which is designed to determine the flutter speed and then predicted the various effects on flutter speed. The program gave us approximately identical results to the results of the referred researches. The following wing design parameters were investigated skin shell thickness, material properties, cross section area for beams, and changing altitude. Results of these calculations indicate that structural mode shape variation plays a significant role in the determination of wing flutter boundary.

Transmission characteristics of train-induced vibration in buildings based on wave propagation analysis

Various studies have focused on predicting, evaluating, and controlling train-induced building vibrations and radiated noise. This study aimed to clarify the theory of building vibration transmission by investigating the transmission characteristics of vibrations in buildings using wave propagation analysis. First, the building was modelled as a periodic structure, as each floor was similar in layout. Based on the wave propagation method, a periodic structure model was established in which the dynamic stiffness matrix of the cell structure could be derived using the spectral element method. Second, a response transfer function (RTF) database of 140 simplified typical residential buildings was established by wave analysis method. Finally, the transmission laws of train-induced vibration were studied. The results indicated that the vibration transmission laws were related to the mode shapes of structures and the participation of modes, which was affected by the spectral characteristics of the input excitation. With an increase in building height, the natural frequency decreased, which influenced the participation of each mode, and this would cause the transmission characteristics of the total vibration energy to change.

Vision-Based Dynamic Response Extraction and Modal Identification of Simple Structures Subject to Ambient Excitation

Vision-based modal analysis has gained popularity in the field of structural health monitoring due to significant advancements in optics and computer science. For long term monitoring, the structures are subjected to ambient excitation, so that their vibration amplitudes are quite small. Hence, although natural frequencies can be usually identified from the extracted displacements by vision-based techniques, it is still difficult to evaluate the corresponding mode shapes accurately due to limited resolution. In this study, a novel signal reconstruction algorithm is proposed to reconstruct the dynamic response extracted by the vision-based approach to identify the mode shapes of structures with low amplitude vibration due to environmental excitation. The experimental test of a cantilever beam shows that even if the vibration amplitude is as low as 0.01 mm, the first two mode shapes can be accurately identified if the proposed signal reconstruction algorithm is implemented, while without the proposed algorithm, they can only be identified when the vibration amplitude is at least 0.06 mm. The proposed algorithm can also perform well with various camera settings, indicating great potential to be used for vision-based structural health monitoring.

Investigation of potential benefits and functionality of a vibroacoustic camera by combining results of a common beamforming and nearfield holography acoustic camera and a highspeed camera, allowing to visualize structural vibration (optical flow tracking

In this paper potential benefits and functionality of a vibroacoustic camera are investigated by combining results of a common beamforming and nearfield holography acoustic camera using the software NoiseImage and a highspeed camera, allowing to visualize structural vibration (optical flow tracking) using the software WaveImage. Both results can be used to calculate color maps - mapped parameters are sound pressure, vibration displacement and its derivatives. The authors will investigate how the combination of methods might enhance understanding and interpretation of the vibroacoustic behavior of specimens in the overlapping frequency range. At low frequencies, the beamforming approach is limited due to main lobe width and array size. While the limits for source localization can be offset employing nearfield acoustic holography, those methods can be time consuming and might fail for complex 3-dimensional structures. It was also previously shown that mode shapes of 2-dimensional structures can be reproduced using nearfield acoustic holography (SONAH). The highspeed camera results present a way to provide positions of local vibration maxima and operating deflection shapes without accessing the acoustic nearfield. Accordingly, the approach could be viewed as a potential extension of the frequency range in which meaningful visualization of vibroacoustic data can be achieved from a single far field measurement from 0 Hz to the ultrasound frequency regime.

Full-Field Mode Shape Identification Based on Subpixel Edge Detection and Tracking

Most research on computer vision (CV)-based vibration measurement is limited to the determination of discrete or coarse mode shapes of the structure. The continuous edge of the structure in images has rich optical features, and thus, by identifying and tracking the movement of the structure’s edge, it is possible to determine high-resolution full-field mode shapes of the structure without a preset target. The present study proposes a CV-based method of full-field mode shape identification using the subpixel edge detection and tracking techniques. Firstly, the Canny operator is applied on each frame of the structure vibration video to extract the pixel-level edges, and the improved Zernike orthogonal moment (ZOM) subpixel edge detection technique is adopted to relocate the precise structure edges. Then, all the detected edge points are tracked to obtain the full-field dense displacement time history that is subsequently used to determine the structure frequencies and compute full-field mode shapes by combining the covariance driven stochastic subspace identification (SSI-COV) with the hierarchical cluster analysis. Finally, the proposed method is verified on the aluminum cantilever beam in the laboratory and the Humen Bridge in the field. The results show that the proposed method is able to detect more precise structure edges and identify the full-field displacement and mode shapes of structures without the need for installing artificial targets on the structure in advance, which provides valuable information for the structural condition assessment, especially for structures with small-amplitude vibrations.

Effect of Soil Type on Dynamic Behavior of Reinforced Concrete Industry Chimneys

Industrial structures built with different materials and methods play an important role in the sector with development of industry and increase in energy need. Many parameters are considered in the design and application phase of industrial structures to provide service for many years. The aim of this study is to examine dynamic behavior of reinforced concrete industrial chimneys depending on soil-structure interaction (SSI). For this reason, a reinforced concrete industrial chimney, which was exposed to the 1999 Kocaeli Earthquake, was chosen as a sample. The effect of soils with different properties (hard, medium and soft) on the dynamic behavior of the selected structure was investigated numerically by linear time history analysis in ANSYS finite element program. The horizontal component of the Kocaeli Earthquake (1999) was used in analyses. As a result of the studies, besides the mode shape and frequency of structure, stress, strain and displacements were also obtained. It has been observed that as the hardness of the soil environment decreases (transition from hard soil to soft soil), chimney apex displacements and stresses on the edge of the voids increase.

Effects of Aeroelastic Walls on the Aeroacoustics in Transonic Cavity Flow

The effects of elastic cavity walls on noise generation at transonic speed are investigated for the generic M219 cavity. The flow is simulated with the Spalart–Allmaras (SA) improved delayed detached-eddy simulation (IDDES) turbulence model in combination with a wall function. The structural analysis software uses a modal formulation. The first 50 structural normal mode shapes are included in the simulation, spanning frequencies of 468–2280 Hz. Results are compared with those from a reference simulation with rigid cavity walls. A spectral analysis of pressure fluctuations from a microphone array above the cavity evinces a distinct tone at 816 Hz, which is absent in the reference simulation. Furthermore, the power of the 4th Rossiter mode at 852 Hz is depleted, implying a significant energy transfer from the fluid to the structure. Spectral proper orthogonal decomposition (SPOD) is employed for analyses of cavity wall pressure fluctuations and wall displacements. The SPOD mode energy spectra show results consistent with the spectra of the microphone array with respect to the tone at 816 Hz and the depletion of the energy at the 4th Rossiter mode. Furthermore, the SPOD mode energy spectra show energy spikes at additional frequencies, which coincide with structural eigenfrequencies.

Damage Identification Method and Uncertainty Analysis of Beam Structures Based on SVM and Swarm Intelligence Algorithm

A two-stage damage identification method for beam structures based on support vector machine and swarm intelligence optimization algorithms is proposed. First, the frequencies and mode shapes of the beam structure are obtained using the smooth orthogonal decomposition method, and the normalized modal curvature is calculated as the input of a pre-trained support vector machine to determine the damage location. Then, the stiffness loss at the damaged location of the structure is calculated using swarm intelligence algorithms. The fitness function is the sum of the residual squares of the frequencies of the damaged structure identified by the smooth orthogonal decomposition method and the frequencies calculated for each iteration of the intelligent optimization algorithm. Numerical examples of a damaged simply supported beam structure are used to verify the damage identification performance of the two-stage method. The accuracy of the support vector machine model under different damage degrees and noise levels is studied using the Monte-Carlo method, and an uncertainty of the damage degree prediction value is studied by comparing the particle swarm optimization algorithm, moth-fire algorithm, and mayfly algorithm.

Lateral vibration mitigation of monopile offshore wind turbines with a spring pendulum pounding tuned mass damper

Lateral vibration of monopile offshore wind turbines (MOWT) is often lightly damped, inducing the apparent vibration under environmental loads. In this paper, a spring pendulum pounding tuned mass damper (SPPTMD) is developed to mitigate the lateral response of MOWT. First, the mathematical model of the controlled MOWT with SPPTMD is established based on the Euler–Lagrange equation. Compared to the referenced model, some improvements are made to enhance the numerical accuracy, where the aerodynamic damping, the bending moment effect, and the 1st mode shape of support structure calculated by Abaqus are considered. In addition, simulations of environmental loads are also introduced. In that regard, a 14 degree-of-freedom (DOF) model for the controlled MOWT with SPPTMD is obtained and compared with FAST. Then, the parameters of SPPTMD are first optimized. On this basis, the parametric analyses and verifications under complicated environmental loads of the proposed SPPTMD are carried out. The results indicate that the SPPTMD has better control effects than the conventional TMD in the low frequency detuning region due to the better energy dissipation capacity in this region. In that regard, the proposed SPPTMD has certain robustness and effectiveness for lateral vibration mitigation for MOWT.

Influence of frost and local stiffness variations on the strain mode shapes of a steel arch bridge

Natural frequencies are probably the most widely used modal characteristics in vibration-based monitoring. However, they can be highly influenced by temperature and this influence can completely mask the effect of even severe damage. This translates into a necessity for time-consuming data-normalization techniques to remove the influence of temperature and identify damage. Displacement mode shapes of homogeneous material structures are less influenced by temperature, but obtaining them in a dense grid, which is required for damage localization, is cumbersome due to the large number of sensors needed. Strain mode shapes on the other hand can be insensitive to temperature variations, while obtaining them in a dense grid is possible when fiber-optic sensors such as fiber-Bragg gratings (FBG) are used. This work presents the results of the continuous monitoring of a steel railway bridge for a period of almost two years, where modal data were collected for a wide temperature range. The bridge is instrumented with eighty FBG strain sensors, multiplexed in four fibers. The natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, on an hourly basis. A clear influence of temperature on the natural frequency of most modes is identified, especially during frost periods. On the contrary, the strain mode shapes are mostly insensitive to temperature changes and only these of some higher-order modes are slightly and uniformly influenced when frost occurs. This behavior is confirmed also by a finite element model (FE) of the bridge. Furthermore, the FE model is used to investigate the influence of local stiffness changes on the modal characteristics. A clear and local change of the modal strain amplitude is observed at the location of the reduced stiffness, especially when information from all modes is combined in a sensitive damage index.

Free Vibration Analysis of Tapered Composite Aircraft Wing via the Finite Element Method

The responses of the structures used in engineering applications under the effects of static and dynamic forces are significant in the design phase. Determination of the response of dynamic forces for a structure is initially performed by the evaluation of free vibration characteristics that are mode shape of the structure and vibration frequencies. This paper presents modal analyses of tapered aircraft wing structures that consist of NACA4415 design and different common materials used in the aviation industry. Furthermore, the effect of winglets on natural frequencies is examined. The main wing structures as ribs and shells are drawn using CATIA and imported to ANSYS Workbench. Analyses have been carried out considering the aircraft wing as a three-dimensional cantilever beam by fixing one end (root chord) of the aircraft wing while the other end (tip chord) is free. The first ten modes of free vibration with their respective natural frequencies and mode shapes of the wing structures of the aircrafts are obtained. The results show that the winglets decrease the natural frequency noticeably and the shell material as Carbon Epoxy UD has been observed to have higher natural frequency compared with Kevlar Epoxy.

A comparative study of the directional characteristics of two gamelan gongs

While previous research on the structural modes of gamelan gongs has revealed important insight into its unique acoustics, little attention has been dedicated to study the directionality of their acoustic radiation. This study compares high-angular resolution spherical directivity measurements of two Balinese gamelan gongs of different sizes. The directional characteristics are usually closely connected with measured structural modes at both low and high frequencies. However, the directivities of the large and small gong for the same structural mode shape are not always consistent, particularly at higher frequencies. Thus, changes in modal frequencies due to the scaling of the gongs do not always indicate similar acoustical radiation patterns.

Low-frequency directional characteristics of a gamelan gong

The structural modes of gamelan gongs often have clear impacts on their far-field directivity patterns with the number of directional lobes corresponding to the associated structural mode shapes. Many of the lowest modes produce dipole-like radiation with the dipole moment determined by the positions of the nodal and antinodal regions. Spherical harmonic and multipole expansions facilitate further understanding of the gongs' low-frequency directional characteristics. The expansions also yield practical simplifications to model their radiation.

Structural damage quantification in shear buildings using mode shape slope ratio

Mode shape-based techniques are very popular among researchers since the last two decades and varying levels of success have been achieved towards identifying damage using structural mode shapes. This study presents a novel formulation to establish the expression of damage severity in the form of mode shape slope. The derived closed-form solution directly correlates the percentage damage intensity with the derivatives of the changes in mode shapes in shear buildings, the most common class of civil structures. Numerical experimentation involving a 16-storey two-dimensional shear building has been performed to show the applicability of the proposition in damage quantification. First three mode shapes are used for this purpose. A detailed parametric study comprising of location as well as noise sensitivity has also been carried out to test the robustness of the proposition. Further, the derived expression has been applied to quantify damages in multiple locations. A relatively shorter structure of eight-storey shear building has also been considered to check the efficiency of the proposed algorithm in structural damage quantification. However, if any mode depicts a very low slope value at the damage location, that particular mode could not be used for damage quantification. Finally, an extensive experimental program on a three-dimensional six-storey miniature model of a shear building ensures its practical applicability under real measurement condition in a laboratory environment. Therefore, this novel mode shape slope-based damage quantification technique can be widely applicable to be appropriate for various circumstances.

Non-destructive performance assessment of bonded surface connections by changes in curvature mode shape

Joining processes have gained increasing relevance and their effectiveness appears as a necessity in the production of lightweight structures. Many researchers have been investigating affordable testing solutions to assess joint performance. Herein, an easy-to-apply non-destructive technique, based on vibration analysis, is presented and evaluated by a purely numerical approach. Changes in the curvature mode shape of beam-like structures are measured and related to the extension of bonded areas of the connected parts. The preliminary results, achieved by modal analysis, provide a first proof-of-concept of the proposed technique and of its increased sensitivity compared to techniques based on frequency response functions.