Modal Response Research Articles

Modal analysis and optimization design of ultra-high acceleration platform rail frame

The ultra-high acceleration macro and micro motion platform has the advantages of high positioning accuracy and small error, and the key mechanism rail frame of the ultra-high acceleration macro and micro motion platform is optimized based on modal analysis to achieve the performance optimization of the platform. SolidWorks software was used to build the rail frame model, and ANSYS Workbench software was used to carry out modal analysis, topology optimization and response surface optimization, etc., so as to reduce the quality of the rail frame as much as possible under the premise of maintaining the stability of the first-order natural frequency. The results show that the optimization of the response surface meets the expected goal, the first-order natural frequency of the guide rail frame increases by 0.7 %, the mass decreases from 6.165 kg to 5.592 kg, and the change rate is 9.2 %, which achieves the purpose of lightweight.

Study on Dynamic Characteristics of Resilient Mount Under Preload.

Resilient mounts are essential for anti-vibration and shock absorption applications, making accurate predictions of their static and dynamic behaviors critical for effective design and mechanical performance. This study investigates static and dynamic characteristics of resilient mounts to predict their effects. Tension, compression, and shear tests were performed under quasi-static loading conditions to obtain stress-strain cycle curves. This study includes a review of the Yeoh hyperelastic model, which consists of three parameters, and discusses the calibration of these parameters to describe the hyperelastic material behavior. The parameters were validated through numerical analysis by comparing them with experimental results from quasi-static tests on the resilient mount. The dynamic behavior was further analyzed using modal analysis and frequency response simulations under various preload conditions. Results show that increasing preload significantly shifts the transmissibility curves and resonance peaks to lower frequencies. This study offers valuable insights into static and dynamic characteristics of resilient mounts, contributing to the design and optimization of vibration isolation systems for naval applications.

De-mixing variational mode decomposition and its application on operational modal analysis in the presence of closely spaced modes

Variational mode decomposition (VMD), and its derivative methods have been demonstrated to be promising signal decomposition tools and widely utilized in modal analysis. However, they inevitably suffer from mode mixing sometimes, greatly impairing the quality of decomposition. This paper proposes a pair of novel VMD-based methods for univariate signal and multivariate signal respectively, referred to as de-mixing VMD (D-VMD) and de-mixing multivariate VMD (D-MVMD), which can greatly alleviate mode mixing in decomposition. The ensemble correlation coefficient is defined to evaluate the correlatedness between one mode and others and then involved in the variational formulation as an additional Lagrangian multiplier item to enhance the constraint in terms of mode mixing. Additionally, a new scheme is proposed to robustly identify modal parameters from the decomposed modal responses. Numerical simulations and a pedestrian bridge were investigated to validate the effectiveness of the proposed methods in identifying closely spaced modes.

Updated Static Influential Factor Analysis for Unidirectional Carbon-Based Composites.

The orientation of carbon fibers significantly affects the dynamic properties of unidirectional carbon-based composites (UCBCs), with variations under different static loads. A previous study analyzed changes in the modal parameters of UCBC structures by using the static load influential factor (SLIF). This study introduces a revised SLIF, derived from a simplified formulation that accounts for shifts in resonance frequency and the in-phase relationship between static load and modal response. The revised SLIF is theoretically linked to the modal participation factor in UCBC structures. The dynamic behavior of UCBCs was studied across six modes-four bending and two torsional-using specimens with five carbon fiber orientations, from 0 to 90 degrees. The revised SLIF showed significant effects in two robust specimens, #1 and #2, and an isotropic SUS304 specimen subjected to uniaxial pre-static load, with resonance frequency variations under 0.16%. In contrast, the original SLIF gave negligible results in the fifth mode due to a damping term, which, when multiplied by the resonance frequency, led to an undetectable indicator. Therefore, the revised SLIF more effectively captures the static load's impact on UCBC dynamic behavior compared with the original method.

Nonlinear characteristics and radial-bending-torsional vibration of a blade with breathing crack

Rotor failures due to cracked blades are frequently observed in rotating machinery. The identification of cracking state of rotating blade based on vibration characteristics has garnered a lot of attention. However, nonlinear characteristics and vibration combining in radial, bending and torsional directions of a rotating blade induced by the crack breathing is yet not clear. This paper proposes a radial-bending-torsional dynamic model of rotating blade with breathing crack. A time-varying integration method is proposed for determining the crack state based on the strain energy release rate. The crack breathing behavior is described by Boolean operation and the numerical integration are applied to open or close the crack. The model is validated through modal analysis, vibration responses and contact state of crack surface. Frequency veering is changed between the 2nd flap and 1st edgewise frequency due to the existence of crack. Strong nonlinear behaviors are found in the radial and torsional vibrations because of the crack breathing. Nonlinearities are also found in the combined vibrations between the radial-bending and the bending-torsional directions. Radial and torsional vibration amplitude levels can be used as an indication of blade crack failure, but the applicability depends on the absolute response decided by the aerodynamic excitation and resonant vibration. These findings can serve as guidance in crack identification and cracking state monitoring of rotating blades.

Conceptual design of a prestressed precast UHPC-steel hybrid tower to support a 15 MW offshore wind turbine

Ultra-high-performance-concrete (UHPC) possesses favorable mechanical properties and economy efficiencies and has the potential to be used as the main material to construct tower structures of offshore wind turbines (OWTs). Then the shortages of widely used pure steel OWT towers such as relatively small lateral stiffness, weak fatigue behavior and corrosion resistance can be avoided. In this work, a new type of hybrid tower structure combining a prestressed UHPC tube at the bottom and an upper steel tube is proposed to support a large-size 15 MW OWT. Detailed and carefully refined finite element (FE) analysis by ABAQUS was conducted to explore the dynamic performance of the proposed hybrid tower. The modal properties, dynamic responses, ultimate strength, fatigue strength, and economy performance of the hybrid tower were comprehensively evaluated. It shows that with a similar lateral stiffness but greatly reduced material and maintenance costs compared to a reference steel tower, the hybrid tower has enough ultimate and fatigue strength to resist huge environmental loads caused by extreme winds, waves and earthquakes.

A kind of single-phase full bandgaps phononic crystals and experimental evidence

The exceptional performance of locally resonant phononic crystals (PCs) in vibration attenuation and noise reduction within nuclear power plants has garnered widespread attention in scholarly circles. To address the need for improved predictive accuracy in substrate structures characterized by significant flexibility, a one-dimensional mechanical model rooted in the mass-spring chain paradigm has been established. This model offers a straightforward and accurate means of predicting the lower and upper frequencies of the initial bandgap within locally resonant phononic crystals. Moreover, the dynamic model elucidates modal characteristics and vibrational responses inherent to locally resonant phononic crystals. Utilizing the proposed model, a singular-phase phononic crystal structure boasting full bandgaps has been devised. This structure facilitates the omnidirectional acquisition of locally resonant bandgaps across an exceedingly low-frequency spectrum through the incorporation of cantilever beam elements. Such a design holds immense promise within the realm of large-scale mechanical vibration isolation. As a means of validation, steel samples embodying this phononic crystal model were fabricated. Experimental results demonstrated an insertion loss of approximately 18.67 dB, affirming the vibration isolation efficacy of the singular-phase phononic crystal configuration.

Equivalent static wind load based on displacement mode and load combination for high‐rise buildings

AbstractUnder the action of the fluctuating wind load, the low frequency part produces background response to the structures, while the high frequency part produces resonance response to the structures. In structural design, equivalent static wind load is usually used to equate the fluctuating wind load. Although there are various methods of evaluating the equivalent static wind load, they did not consider the correlation between modal responses or considered them insufficiently. Therefore, in this paper, the correlation between modal response is considered to evaluate the equivalent static wind load, the displacement response is decomposed by proper orthogonal decomposition (POD) method, the correlation between modal displacement is removed, the equivalent static wind load is expressed in the form of displacement mode, and then the correlation between modal response is fully considered in the extreme value combination. This paper combines the equivalent static wind loads in order to make the wind resistance design more reasonable for high‐rise buildings. First, the formulas of equivalent static wind loads expressed by displacement modes of background and resonant response are deduced based on modal decomposition and POD method. Second, the combination formulas of square‐root‐of‐sum‐square (SRSS) and complete‐quadratic‐combination (CQC) rules for the equivalent static wind loads considering the mean wind loads are proposed. Both the linear combination formula of SRSS for the equivalent static wind load and the weighting factor expressions of background and resonance equivalent static wind load are given. Third, the accuracy and validity of the formulas of equivalent static wind load are verified by a wind tunnel pressure test of a high‐rise building. Finally, the simplified combination coefficient formulas for the equivalent static wind loads are proposed, and the combination of the high‐rise building base's fluctuating equivalent static wind loads of along‐wind direction, across‐wind direction, and torsional direction is analyzed.

Trajectories of posttraumatic stress symptoms following collective violence: A systematic review and meta-analyses.

Although collective violence represents a significant public health concern, a limited number of longitudinal studies have addressed this topic, with no systematic reviews focusing on posttraumatic stress symptom (PTSS) trajectories. The present systematic review and meta-analyses examined PTSS prevalence and trajectories after exposure to collective violence. A systematic literature search across six databases (APA PsycInfo, APA PsycArticles, PSYINDEX, MEDLINE, ERIC, and PubMed) identified 771 studies that were screened for the following eligibility criteria: exposure to collective violence, adult sample, longitudinal design, PTSS assessment using validated measures, PTSS trajectories estimated using latent growth modeling, and report sample prevalence rate for each trajectory. Ten studies met the criteria, and five meta-analyses were performed to assess the overall prevalence of each trajectory. Most included studies (63.6%) identified four trajectories, characterized as low-stable, high-stable, decreasing, and delayed-worsening. The low-stable trajectory was the modal response, with a pooled prevalence of 58.0%, 95% CI [51.0, 65.0]. The high-stable prevalence was 7.0%, 95% CI [4.0, 19.0]; the decreasing trajectory was 13%, 95% CI [9.0, 17.0]; and the delayed-worsening trajectory was 8.0%, 95% CI [5.0, 10.0]. A fifth trajectory, moderately stable, had a prevalence of 19.0%, 95% CI [9.0, 29.0]. The trajectory models robustly identified clinically relevant patterns of response to collective violence, offering a contribution to the literature and a starting point for future research. Further studies are needed, as a better comprehension of symptom trajectories after collective violence events has important clinical and public health implications.

Investigation on the propagation of uncertainties of a timber floor under human excitation

Due to the characteristics of high stiffness-weight ratio, timber floors are prone to annoying vibrations under human excitation. Given the natural origin of timber, its mechanical properties exhibit significant variability. The randomness inherent in human excitation cannot be overlooked during structural dynamic analysis. Consequently, the adoption of a stochastic approach is imperative for attaining reliable serviceability evaluation results. However, current research on human-induced vibrations in the timber floor, accounting for this randomness, remains inadequate. In this paper, an experimental investigation is conducted on the dynamic properties and human-induced responses of a timber floor composed of glued laminated timber and oriented strand board. A finite element model is developed and subsequently validated for accuracy in terms of modal properties and dynamic responses. The probability density evolution method is introduced for stochastic analysis, which demonstrates that both the natural frequency and dynamic responses of the floor exhibit considerable variability when uncertainty factors are considered. The Kullback–Leibler divergence indices are used to assess the impact of each uncertain variable quantitatively. The results indicate that the longitudinal elastic modulus has the greatest influence on the natural frequency, while the first dynamic load factor, αz1, exerts the most significant impact on dynamic responses. Notably, both material mechanical properties and load model parameters contribute to the uncertainty of dynamic responses, with the influence of the load model parameters being significantly greater than that of material mechanical properties.

A simplified approach for judging and evaluating the contribution of higher-order modes to the wind-induced acceleration of high-rise buildings

Acceleration is the control parameter for the occupant comfort, often solved in the frequency domain with modal decomposition. In general, the first-order mode response is adopted to represent the total acceleration in practice. However, considering only the first-order mode has been demonstrated to yield underestimated results up to 20 %, while no exact criterion exists to determine whether higher-order modes require to be considered or not. Hence, underlying factors, like the structural natural frequencies, the excitation dominant frequencies, and the distributions of building masses/stiffness, which may significantly affect the contribution of higher-order modes to the acceleration, are analyzed first. Notably, the ratio of the natural frequency of the higher-order mode to that of the first-order mode plays a decisive role in the contribution of the higher-order mode's acceleration. Moreover, the third-order and beyond modes can be largely disregarded. Subsequently, an empirical approach is introduced to determine the need for considering high-order modes. Finally, a simplified formula for estimating acceleration response in the frequency domain is derived to consider second-order modal response. This study provides a method for determining the contribution of higher-order vibration modes to acceleration and a simplified formula to consider the higher-order modal response.

A Survey of Aero-Engine Blade Modeling and Dynamic Characteristics Analyses

The rotating blade is a key component of an aero-engine, and its vibration characteristics have an important impact on the performance of the engine and are vital for condition monitoring. This paper reviews the research progress of blade dynamics, including three main aspects: modeling of blades, solution methods, and vibration characteristics. Firstly, three popular structural dynamics models for blades are reviewed, namely lumped-mass model, finite element model, and semi-analytical model. Then, the solution methods for the blade dynamics are comprehensively described. The advantages and limitations of these methods are summarized. In the third part, this review summarizes the properties of the modal and vibration responses of aero-engine blades and discusses the typical forms and mechanisms of blade vibration. Finally, the deficiencies and limitations in the current research on blade modeling and vibration analysis are summarized, and the directions for future efforts are pointed out. The purpose of this review is to provide meaningful insights to researchers and engineers in the field of aero-engine blade modeling and dynamic characteristics analysis.

Research on vibration response distorted similitude of cylindrical shells under modal distribution disorder

Similitude theory enables local-scale models to reflect the dynamic characteristics of full-scale models and is widely employed in engineering experimentation. However, shell structures, constrained by wall thickness, cannot undergo experiments through proportional downsizing. Existing similitude studies with retained wall thickness exhibit only minimal distortion, and accurate prediction of vibration responses is hindered by modal distribution disorder. To address these challenges, a method based on modified frequency response functions of natural frequencies and mode shapes is proposed. Scaling laws for natural frequencies and mode shapes of cylindrical shells with retained wall thickness are established. This method yields a maximum prediction error of 4.29 % for prototype natural frequencies, compared to 50.57 % for existing methods. Predicted prototype vibration acceleration responses correspond well with theoretical calculations in both frequency and amplitude, while existing methods fail entirely. The phenomenon of modal distribution disorder and the effectiveness of the proposed method in mitigating it are verified by modal experiments and response tests. Research reveals that the sensitivity of different modal frequencies to the wall thickness scaling factor varies, serving as the cause of modal distribution disorder. The modal distribution with the same circumferential wave number is unaffected by wall thickness. Modes above the bending frequency, with axial half-wavelength consistent with bending modes, are prone to disorder due to wall thickness distortion. During wall thickness distortion, a mode originally with the lowest frequency is surpassed towards lower frequency by the mode with larger circumferential wave number and the same axial half-wave number, leading to disorder. The proposed method addresses the challenge of minimal distortion in structural vibration response and poor performance, advancing the development of distorted similitude.

Variation in the Modal Response of Retrofitted Unreinforced Masonry Walls at Different Levels of Damage

Variation in the Modal Response of Retrofitted Unreinforced Masonry Walls at Different Levels of Damage

Identification of modal parameters of soil specimen based on impact force

This study used vibration testing signals of soil samples under external loading to identify modal parameters (including natural frequencies and damping ratios) with different compaction degrees. Based on these parameters, a novel approach was proposed for reliable roadbed vibration compaction control and compaction process optimization. The experimental section utilized six soil samples with varying compaction degrees as experimental subjects, using the hammering method as the excitation mode. Subsequently, the frequency response function and modal parameters of the sample system were obtained through the acquisition, analysis, and parameter identification of samples’ acceleration signals. Firstly, samples with compaction degrees ranging from 88 % to 97 % primarily exhibited three modes, with the second modal frequency response displaying the weakest amplitude, and the fundamental mode being the dominant one. Additionally, parameter identification results revealed that the fundamental modal frequency exhibited a significant negative exponential growth with increasing compaction degree, while the second and third modal frequencies showed significant linear growth. Furthermore, the average damping ratio also demonstrated a tendency toward linear change with increasing compaction degree. Finally, the feasibility of modal parameters being actively used in practical engineering is discussed. Consequently, this study aimed to propose an indicator system for accurately assessing the bearing level of compacted soils from a modal dynamics perspective and to integrate modal dynamic indicators with density-class indicators into further optimization design work on road compaction processes.

Study on rigid-flexible coupling modeling of planetary gear systems: Incorporation of the pass effect and random excitations

A rigid-flexible coupling model for the planetary gear system is developed, in which the flexibility of the ring gear, input shaft, and carrier are considered. Subsequently, rotational modal projection is proposed to simulate the meshing of the flexible ring gear at any angle of planet gear revolution, and the coordinate transformation equations are presented to establish the coupling between rigid body and rotating flexible body. These two approaches incorporate the pass effect into the coupling model. Additionally, a method employing pre-emphasized noise to simulate random excitations is introduced. The model is validated by comparing computed modal frequencies and dynamic responses with those from ANSYS software and experiment, respectively. Results indicate that the proposed method accurately simulates the modulation signal observed in the experiment. Closely matched resonances excited by random excitations are apparent in experimental and simulated acceleration spectra, highlighting the validity of the proposed method and aiding in the determination of operational system modes. In addition, analyses of parameter influences are conducted, which further reveal the dynamic characteristics of the system.

Efficient Vibration Measurement and Modal Shape Visualization Based on Dynamic Deviations of Structural Edge Profiles.

As a non-contact method, vision-based measurement for vibration extraction and modal parameter identification has attracted much attention. In most cases, artificial textures are crucial elements for visual tracking, and this feature limits the application of vision-based vibration measurement on textureless targets. As a computation technique for visualizing subtle variations in videos, the video magnification technique can analyze modal responses and visualize modal shapes, but the efficiency is low, and the processing results contain clipping artifacts. This paper proposes a novel method for the application of a modal test. In contrast to the deviation magnification that exaggerates subtle geometric deviations from only a single image, the proposed method extracts vibration signals with sub-pixel accuracy on edge positions by changing the perspective of deviations from space to timeline. Then, modal shapes are visualized by decoupling all spatial vibrations following the vibration theory of continuous linear systems. Without relying on artificial textures and motion magnification, the proposed method achieves high operating efficiency and avoids clipping artifacts. Finally, the effectiveness and practical value of the proposed method are validated by two laboratory experiments on a cantilever beam and an arch dam model.

Modal response of sandwich plate having carbon-epoxy faceplate with different honeycomb core material and geometry considerations

Modal response of sandwich plate having carbon-epoxy faceplate with different honeycomb core material and geometry considerations

Influence of muscle soft tissue and lower limbs on the vibration behavior of the entire spine inside the seated human body: A finite element study.

The objective of the study is to investigate the vibration behavior of the entire spine inside the human body and the influence of muscle soft tissue and lower limbs on spinal response under vertical whole-body vibration. This study conducted modal and random response analyses to simulate the modal displacements and stress of all intervertebral discs in the vertical principal mode in the skeleton, upper, and whole body. Additionally, the acceleration response of intervertebral discs under vertical random excitation was investigated. The results revealed that removing muscle soft tissue and lower limbs significantly changed the resonant frequency, modal displacement, and stress. Particularly, there was a rapid increase in vertical displacement of the lumbar spine in the skeleton model. The reason for that was due to the lack of soft tissue to provide stability, leading to significant lumbar spine bending. Under random excitation, the fore-aft acceleration of intervertebral discs in the skeleton model was considerably larger than that in the whole body, especially in the lumbar spine where it can reach up to four times higher. Conversely, the vertical response of the intervertebral discs inside the human body model was 1.4-2.4 times larger than that of the skeleton model. Muscle soft tissue contributes to the strength of the spine, reducing fore-aft response. The muscle soft tissue in the gluteal region, connected below the spine, can lower the vertical natural frequency and attenuate spinal impact. Although the lower limbs enhance spinal stability, stimulation from the feet can superimpose vibrational responses in the spine.

Application of Modal Strain Energy Analysis to Localize an Added Mass on an Aluminium Plate.

The modal strain energy method is a vibration-based damage detection method that allows the use of passive measurements. The method is based on the measurement and analysis of the modal response of the structure under investigation. The aim of this work is to investigate the application of this method to detect and localise a local change in a structure using acoustic measurements in a fluid around the structure. Firstly, the modal strain energy is presented. The technique is based on the analysis of the modal shapes of undamaged and damaged samples obtained by operational modal analysis. The application of modal strain energy to off-contact acoustic measurements is then discussed. The method is used to detect and locate a local change (an additional mass) in an aluminium plate subjected to a mechanical force. The study begins with numerical simulation using finite element models, followed by experiments on the aluminium plate.