Mode Shapes Research Articles

Investigation of dynamic response characteristics of light fixed-wing aircraft

In order to ensure the stability of light fixed-wing aircraft during flight missions, considering the effects of relative airflow velocity and angle of attack, the distribution characteristics of velocity and pressure fields under different conditions, as well as the law of change of dynamic parameters, were derived by using aerodynamic methods. In the free modal condition, the modal truncation method was used to simulate and analyze the low-order modal shapes. Based on the modal analysis results, the sweep frequency range was set to 3-50 Hz, with a step size of 1.6 Hz, for a total of 30 substeps. A harmonic load of 1500 N was applied to the fuselage, and the displacement-frequency response curves and stress-frequency response curves of the fuselage structure and wing structure were extracted after the calculation. The results shows that the maximum lift-drag ratio occurs when the angle of attack is 6°, and the peak displacement deformation of the aircraft occurred around 24 Hz.

Analysis and optimization of the dynamic response characteristics of aircraft cargo rack

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved.

A 3D Statistical Shape Model of the Right Ventricular Outflow Tract in Pulmonary Valve Replacement Patients Post-Surgical Repair.

Assessment of the right ventricular outflow tract and pulmonary arteries (RVOT) for percutaneous pulmonary valve implantation (PPVI) uses discrete measurements (diameters and lengths) from medical images. This multi-centre study identified the 3D RVOT shape features prevalent in patients late after surgical repair of congenital heart disease (CHD). A 3D RVOT statistical shape model (SSM) was computed from 81 retrospectively selected CHD patients (14.7 ± 6.8 years) who required pulmonary valve replacement late after surgical repair. A principal component analysis identified prevalent shape features (modes) within the population which were compared with standard geometric measurements (diameter, length and surface area) and between sub-groups of diagnosis, RVOT type and dysfunction. Shape mode 1 and 2 represented RVOT size and curvature and tapering and length, respectively. Shape modes 3-5 related to branch pulmonary artery calibre, conical vs. bulbous RVOTs and RVOT curvature, respectively. Tetralogy of Fallot, transannular patch type and regurgitant RVOTs were larger and straighter while conduit and stenotic types were longer and more cylindrical than other subgroups. This SSM analysed the main 3D shape features present in a population of RVOTs, exploiting the wide 3D anatomical information provided by routine imaging. This morphological information may have implications for PPVI patient selection and device design.

Computational Analysis of Stiffness Reduction Effects on the Dynamic Behaviour of Floating Offshore Wind Turbine Blades

This paper describes the study of a floating offshore wind turbine (FOWT) blade in terms of its dynamic response due to structural damage and its repercussions on structural health monitoring (SHM) systems. Using a finite element model, natural frequencies and mode shapes were derived for both an undamaged and a damaged blade configuration. A 35% reduction in stiffness at node 1 was applied in order to simulate significant damage. Concretely, the results are that the intact blade has a fundamental frequency of 0.16 Hz, and this does not change when damaged, while higher modes exhibit frequency changes: mode 2 drops from 2.05 Hz to 2.00 Hz and mode 3 from 6.15 Hz to 6.01 Hz. The shifts show a critical loss in the capability of handling vibrational energy due to the damage; higher modes (4, 5, and 6) show larger frequency deviations going down to as low as 18.06 Hz in mode 6. The mode shape change is considerable for the edge-wise and flap-wise deflection of the 2D contour plots, indicating possible coupling effects between modes. These results indicate that lower modes are sensitive to stiffness reductions, and the continuous monitoring of the lower harmonic modes early is required to detect damages. These studies have helped to improve blade design, maintenance, and operational safety for FOWT systems.

Rosen-Morse potential and gravitating kinks

We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation equation is a Schrödinger-like equation with Rosen-Morse potential. For this potential, eigenvalues and wave functions of the bound states, if had any, can be derived by using the standard shape invariance procedure. Depending on the values of the parameters, the stability potential can be reflective or reflectionless. There can be an arbitrary number of shape modes, but the zero mode is always absent.

Modal analysis of the 63 Square Building in Seoul, South Korea and its impact of subsidence and soil-structure interactions (SSI)

We conduct vibration analyses of 63 Building in Seoul, South Korea, using modal analysis and finite element modeling. The building is modeled as a solid structure having the shape of the real structure and with total weight and stiffness consistent with those of the real building. To better understand the fundamental periods of vibration of this structure and the associated mode shapes, we also consider structures with simplified geometry and perform modal analyses of them.

Automatic High-Resolution Operational Modal Identification of Thin-Walled Structures Supported by High-Frequency Optical Dynamic Measurements.

High-frequency optical dynamic measurement can realize multiple measurement points covering the whole surface of the thin-walled structure, which is very useful for obtaining high-resolution spatial information for damage localization. However, the noise and low calculation efficiency seriously hinder its application to real-time, online structural health monitoring. To this end, this paper proposes a novel high-resolution frequency domain decomposition (HRFDD) modal identification method, combining an optical system with an accelerometer for measuring high-accuracy vibration response and introducing a clustering algorithm for automated identification to improve efficiency. The experiments on the cantilever aluminum plate were carried out to evaluate the effectiveness of the proposed approach. Natural frequency and damping ratios were obtained by the least-squares complex frequency domain (LSCF) method to process the acceleration responses; the high-resolution mode shapes were acquired by the singular value decomposition (SVD) processing of global displacement data collected by high-speed cameras. Finally, the complete set of the first nine order modal parameters for the plate within the frequency range of 0 to 500 Hz has been determined, which is closely consistent with the results obtained from both experimental modal analysis and finite element analysis; the modal parameters could be automatically picked up by the DBSCAN algorithm. It provides an effective method for applying optical dynamic technology to real-time, online structural health monitoring, especially for obtaining high-resolution mode shapes.

Evaluation of Static Displacement Based on Ambient Vibration for Bridge Safety Management.

The evaluation of bridge safety is closely related to structural stiffness, with dynamic characteristics and displacement being key indicators. Displacement is a significant factor as it is a physical phenomenon that bridge users can directly perceive. However, accurately measuring displacement generally necessitates the installation of displacement meters within the bridge substructure and conducting load tests that require traffic closure, which can be cumbersome. This paper proposes a novel method that uses wireless accelerometers to measure ambient vibration data from bridges, extracts mode shapes and natural frequencies through the time domain decomposition (TDD) technique, and estimates static displacement under specific loads using the flexibility matrix. A field test on a 442.0 m cable-stayed bridge was conducted to verify the proposed method. The estimated displacement was compared with the actual displacement measured by a laser displacement sensor, resulting in an error rate of 3.58%. Additionally, an analysis of the accuracy of displacement estimation based on the number of measurement points indicated that securing at least seven measurement points keeps the error rate within 5%. This study could be effective for evaluating the safety of bridges in environments where load testing is difficult or for bridges that require periodic dynamic characteristics and displacement analysis due to repetitive vibrations, and it is expected to be applicable to various types of bridge structures.

Generation of a virtual cohort of TAVI patients for in silico trials: a statistical shape and machine learning analysis.

In silico trials using computational modeling and simulations can complement clinical trials to improve the time-to-market of complex cardiovascular devices in humans. This study aims to investigate the significance of synthetic data in developing in silico trials for assessing the safety and efficacy of cardiovascular devices, focusing on bioprostheses designed for transcatheter aortic valve implantation (TAVI). A statistical shape model (SSM) was employed to extract uncorrelated shape features from TAVI patients, enabling the augmentation of the original patient population into a clinically validated synthetic cohort. Machine learning techniques were utilized not only for risk stratification and classification but also for predicting the physiological variability within the original patient population. By randomly varying the statistical shape modes within a range of ± 2σ, a hundred virtual patients were generated, forming the synthetic cohort. Validation against the original patient population was conducted using morphological measurements. Support vector machine regression, based on selected shape modes (principal component scores), effectively predicted the peak pressure gradient across the stenosis (R-squared of 0.551 and RMSE of 11.67mmHg). Multilayer perceptron neural network accurately predicted the optimal device size for implantation with high sensitivity and specificity (AUC = 0.98). The study highlights the potential of integrating computational predictions, advanced machine learning techniques, and synthetic data generation to improve predictive accuracy and assess TAVI-related outcomes through in silico trials.

Vibro-acoustic characterization of Functionally Graded Multiwalled Carbon Nanotube composite cylindrical panels: An experimental approach

This study experimentally investigates the vibro-acoustic properties of Functionally Graded Multiwalled Carbon Nanotubes (FG-V MWCNT) Glass Fiber Reinforced Polymer composite cylindrical panels, a topic often explored through numerical methods. A novel process methodology is introduced to realize FG-V MWCNT composites, and the results are compared with those of uniformly distributed and conventional composites. Using an in-house developed experimental setup, the natural frequencies, mode shapes, acceleration, and Sound Pressure Levels (SPL) are measured. The FG-V MWCNT composites demonstrate a notable enhancement in fundamental frequency (21.13%) and a reduction in SPL in the lower frequency range compared to conventional composites. The proposed material composition and process methodology show potential for creating lightweight, structurally efficient large airframe components.

Investigation on typhoon-induced aero-elastic response of membrane structures by wind tunnel test and numerical simulation

Extreme winds, such as typhoons, can lead to serious vibration and damage for flexible membrane roofs. An understanding of the aeroelastic behavior experienced by membrane structures during typhoons is therefore significant to allow well designed in practice. This paper investigates the aeroelastic response of umbrella shaped membrane structures under typhoon experimentally and numerically. The flexible scaled model is tested in typhoon field simulated in wind tunnel to investigate the aeroelastic characteristics varying with wind velocities and wind directions, including displacement response, non-Gaussian characteristics, frequency, modal shape and damping ratios et al. The full coupled fluid-structure interaction numerical model proposed is benchmarked and expanded in parameter discussions. The results indicate that non-Gaussian characteristics appear significant with positive skewness in pressure region and negative skewness in suction region. The probabilistic distribution proves leptokurtic type with kurtosis beyond three. The displacement response in statistics increases almost linearly with wind velocity while the non-Gaussian characteristics remain robust. The high-order mode shapes can be excited in typhoon, and their frequencies and damping ratios vary with wind velocities. The effects of both wind velocity and membrane pretension are proved to be more remarkable than rise-span ratio. This study can address the deficiency of current studies and provisions on the dynamic response of membrane structures in typhoons.

Nonlinear normal modes and response to random inputs of systems with bilinear stiffness

This work seeks to provide a comprehensive review of the effects that stiffness bilinearity can have on the nonlinear modes of a system, its response in a random vibration environment, and the connection between the two. Stiffness bilinearity here refers to a continuous piecewise linear force vs displacement function that is composed of two linear regions. This work focuses on a bilinear stiffness function that is regularized so there is a smooth transition at the point where the two linear regions meet. A single-degree-of-freedom system (SDOF) and a two-degree-of-freedom (2DOF) system are explored and several interesting behaviors are shown. The SDOF bilinear spring model is characterized by four parameters: the low amplitude frequency, the ratio of the linear stiffnesses on either side of the transition, the displacement at which the transition occurs, and the rate or sharpness of the transition. The effect of each parameter on the shape of the NNM is described. In a 2DOF system, these parameters have similar effects, but modal coupling is found to play a significant role. When a bilinear system is subjected to random excitation, many harmonics appear in the response for both the SDOF and 2DOF cases. The root-mean-square (RMS) response of the bilinear system can be larger or smaller than the corresponding linear case depending on the values of the parameters and the type of forcing (broadband, bandlimited, in the shape of a vibration mode, etc.). However, many cases were observed in which the RMS response of the bilinear system was almost the same as that of a linear system, and hence the response could be predicted well using linear analysis. It is hoped that the results presented herein can assist engineers in helping to determine when linear analysis would be adequate to predict the failure of a system, when a rigorous nonlinear analysis is required, and what phenomena are likely to be observed in the latter case.

Investigating work commuters mode choice behavior in Dalian city during pandemic: a hybrid choice model approach

ABSTRACT This study examined commuters' mode choice behavior during the COVID-19 pandemic, focusing on the impact of both tangibles and intangibles factors. To do so, the authors developed a Hybrid Choice Model (HCM) which investigated the effects of sociodemographic characteristics, travel attributes, and intangible factors such as satisfaction, safety, and discomfort, on travel behavior. The model was tested using Stated Preference data collected from commuters in Dalian City (China) via wenjuanxing, an online survey platform. The results indicate that individual characteristics played a significant role in shaping people's perceptions and mode choice behavior was influenced by sociodemographic factors, travel characteristics, and the aforementioned intangible factors. More specifically, individuals, who perceived a higher level of safety, measured in terms of worries about robbery, accidents, and pandemic concerns, were less likely to choose cars. People with a stronger perception of discomfort favored metro over bus. Private car users reported higher satisfaction. The findings will be useful to policymakers for establishing more resilient transport solutions.

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Structural damage detection for spatial frame structures with semi-rigid joints using multiple set wireless measurements

Damage detection of a complex spatial frame structure with semi-rigid joints is a challenging task. Most existing damage detection methods consider the joint as rigid and the nonuniform cross section of the member is not considered. This assumption results to a large error in the structural damage identification. A novel generic element is proposed for the nonuniform cross-section member with semi-rigid joints at both ends in this study. The finite element model of spatial structures with semi-rigid joints is established using the proposed element. The modal strain energy-based damage index is defined and its sensitivity to the member and joint damage has been investigated using numerical and experimental study. An 8-m long bridge model with the bolted connection at joints is built in the laboratory. Dynamic responses of the bridge under random excitations are monitored using 13 wireless tri-axis accelerometers. The spatial mode shapes of the bridge are extracted using the reference-based stochastic subspace identification from multiple set wireless measurements. The numerical model is validated using experimental results. Dynamic responses of the bridge with different damage scenarios have been simulated using the validated model and the corresponding damage indices are obtained. The results show that the proposed method is reliable and accurate to analyze dynamic behavior of the spatial structure with semi-rigid joints, and structural damage can be identified accurately using the modal strain energy-based damage index.

A framework for three-dimensional statistical shape modeling of the proximal femur in Legg-Calvé-Perthes disease.

The pathomorphology of Legg-Calvé-Perthes disease (LCPD) is a key contributor to poor long-term outcomes such as hip pain, femoroacetabular impingement, and early-onset osteoarthritis. Plain radiographs, commonly used for research and in the clinic, cannot accurately represent the full extent of LCPD deformity. The purpose of this study was to develop and evaluate a methodological framework for three-dimensional (3D) statistical shape modeling (SSM) of the proximal femur in LCPD. We developed a framework consisting of three core steps: segmentation, surface mesh preparation, and particle-based correspondence. The framework aims to address challenges in modeling this rare condition, characterized by highly heterogeneous deformities across a wide age range and small sample sizes. We evaluated this framework by producing a SSM from clinical magnetic resonance images of 13 proximal femurs with LCPD deformity from 11 patients between the ages of six and 12 years. After removing differences in scale and pose, the dominant shape modes described morphological features characteristic of LCPD, including a broad and flat femoral head, high-riding greater trochanter, and reduced neck-shaft angle. The first four shape modes were chosen for the evaluation of the model's performance, together describing 87.5% of the overall cohort variance. The SSM was generalizable to unfamiliar examples with an average point-to-point reconstruction error below 1mm. We observed strong Spearman rank correlations (up to 0.79) between some shape modes, 3D measurements of femoral head asphericity, and clinical radiographic metrics. In this study, we present a framework, based on SSM, for the objective description of LCPD deformity in three dimensions. Our methods can accurately describe overall shape variation using a small number of parameters, and are a step toward a widely accepted, objective 3D quantification of LCPD deformity.

Analysis on stall mechanism of axial flow compressor with rotating inlet distortion by dynamic mode decomposition

To study the impact of rotating inlet distortion on stall mechanism of an axial compressor, the full-annulus unsteady simulation results are analysed using dynamic mode decomposition (DMD). Firstly, the frequency and energy ratio of each mode at near stall condition for the compressor with uniform inflow are obtained. A dominating frequency band 0.3–0.6 BPF regarded as the characteristic frequency of unsteady tip leakage flow is observed. The distribution of eigenvalues further confirms that there are a few critical unstable modes in the flow field. With further throttling, four large-scale disturbance structures are captured by the second-order mode, whose frequency is twice as the rotor frequency. The circumferential propagation velocity of the stall cell is thus deduced to be about 50% of the rotor speed. Further, when the compressor is subjected to rotating inlet distortion, the change of stalling process is related to the relative position of distortion plate and stall cell according to the DMD mode frequency and shape. The addition of rotating distortion does not change the stall type of the compressor, but the unstable modes indicate that the number and shape of the stall cells have been varied.

Research on design thinking of pleated clothing inspired by fractal geometry

PurposeThis paper summarizes the design thinking of pleated clothing, uses virtual software to simulate the pleated clothing process and clothing effect and applies the fractal geometry principle to conduct relevant experiments, which verifies the possibility of simulation software assisting pleated clothing design, improves research and development efficiency, lays a foundation for future process parameter collection to upgrade the pleated clothing database and realizes the diversity of digital innovative design of pleated clothing.Design/methodology/approachAccording to the principle of self-similarity and fractal dimension in fractal geometry, the design thinking of pleated clothing is put forward and the simulation folding of 3D digital technology is expanded. The design method takes traditional craft and digital technology as an example. The two-dimensional design thinking of pleated clothing is geometric crease thinking of fabric swatch and geometric expansion of basic clothing pattern. Three-dimensional modeling design thinking, such as based on the human body shape, geometric shape and folding mode. As well as digital design thinking, such as the angle of the fabric element and the perspective of garment pattern change.FindingsThis paper analyzes the Y structure of the similar shape “binary tree” in origami art, the principle of infinite folding with 45? As the unit and the point set capacity theory of Cantor concentric circles in the fractal dimension principle expands the design thinking of pleated clothing, applies a large number of experimental cases of design thinking inspired by the fractal geometry of pleated clothing and validates the possibility of simulation software assisting pleated clothing design.Research limitations/implicationsWe argue here that digital technology should continue to be used in a similar way for research and development in other clothing design-related processes in the future. When it comes to the possibilities for digital innovation in relation to pleated clothing, there is a lack of data for modeling the characteristics of such clothing and establishing the processing requirements. Thus, there is scope here for innovation breakthroughs in terms of both the art and the technology associated with clothing design, not to mention how the two are integrated. This paper has laid some potential foundations for this through its elaboration of fractal-inspired design in the context of pleated garments.Practical implicationsNumerous experiments were undertaken and digital simulation software was used to explore various potential designs in the paper. This confirmed the possibility of using simulation software to assist in the design of pleated clothing, which offers the scope for improved research and more efficient development. However, if the processing parameters for changes in the pleated fabric are not set in the software, it is impossible to automatically generate auxiliary clothes. The collection of processing parameters and the creation of a more comprehensive pleated clothing database should therefore be the focus of future research.Social implicationsThe paper is oriented toward future clothing design. There is some impact on research, practice and/or society. This opens up the possibility of using fractal geometry in the design of the folds and dimensional energy in pleated clothing. On the whole, the innovation point is clear and the idea is novel. By seeking the principles of science and technology, sensing the infinite possibilities, improving the design efficiency and inspiring innovative design thinking methods, in order to meet the diversity and personality needs of the external shape of the human body.Originality/valueThe concave and convex texture of pleated fabric is geometric and decorative. It has a direct reference value for pleated clothing design by using the concepts of partial and whole in fractal geometry and the quantity and energy conversion in fractal dimension space. Due to the influence of clothing intelligent manufacturing policy, there is a lack of data sorting for the modeling characteristics and process requirements of pleated clothing, and there is innovative design thinking that needs to be integrated with technology and art, which lays a foundation for the future collection of process parameters to upgrade the pleated clothing database.

Initial monitoring of a six-story lightweight timber frame building under different environmental conditions

AbstractThis study presents a comprehensive investigation of the dynamic behavior of a six-story lightweight timber frame building through periodic and continuous ambient vibration tests. Seasonal changes in temperature and relative humidity can influence the dynamic response of timber buildings, by affecting stiffness, strength, and connection properties due to changes in moisture content. Systematic tests were performed from October 2022 until May 2024 to identify natural frequencies, damping ratios, and mode shapes of the building using five battery-driven data acquisition units equipped with 15 uni-axial accelerometers. Two different only-output frequency and time domain Operational Modal Analysis (OMA) methods were used to evaluate the dynamic properties of the building. Additionally, the building has been continuously monitored with temperature and humidity sensors since its construction. Results obtained from the periodic measurements highlighted the need for a permanent system to capture the transient changes in the modal parameters. A complementary permanent system to record the accelerations at the roof level was installed in May 2024. The modal parameters from in situ measurements were compared with those obtained from the Finite Element (FE) model of the structure. The FE model, calibrated through a multi-stage approach, incorporating non-structural elements, and varying imposed loads, showed good agreement with experimental data. Comparative analysis of the results obtained under different temperature and humidity conditions showed the effect of the environmental conditions on the building dynamics properties, for both periodic and permanent measurements. This study highlights the importance of continuous monitoring and detailed FE modeling in understanding the dynamic properties and long-term structural behavior under varying conditions. This information can be used to ensure that the building meets safety and performance requirements and to identify potential issues that may need to be addressed during the design and maintenance phases.

Modal and harmonic analysis of femur bone using different boundary conditions by Finite Element Analysis.

The longest and largest bone in the human body is the femur. Pelvic bone sustains the weight of the body to which the femur bone is connected. Many researches have been carried out to identify the behaviour of the femur bone. The study aimed to explore the natural frequencies and mode shapes of vibrating devices to gain insights into the dynamic behavior of the femur bone during various physical activities. Examining the impact of patient-specific bone shape and density on bone natural frequencies is crucial. The primary goals of femur bone analysis involve employing computer simulations for fracture detection and employing Finite Element (FE) models to determine natural frequencies and vibration modes. To obtain the natural frequency of the femur bone, different boundary conditions such as free-fixed and fixed-fixed are applied. Avoiding the coincidence of the natural frequency with external excitation frequencies is crucial to prevent femur bone fractures. Also, for different magnitude of loads, femur bone is involved in harmonic analysis is to identify the amplitude and stress against acceleration.