Natural Frequencies Research Articles

Vibration-based structural damage detection using FRF and modal constant curvature

ABSTRACT This paper presents a new method for locating and quantifying damage in beam-like structures based on the modal constant curvatures and natural frequency extracted from the measurements of the Frequency Response Function (FRF). The modal constant curvature is very effective for localising the damage due to the discontinuity created near the damaged zone. However, in classical vibrational measurement techniques, the discontinuity is confounded by measurement noise. To overcome these limitations, a new index is developed by normalising the curvature of the first fourth vibration mode. The new index gives a value of 1 in the damage location with the elimination of all the values that can distort the results. In order to make the index sensitive for damage depth, quantification charts are developed based on natural frequency ratios. Numerical simulations on a cantilever beam demonstrated the high sensitivity of the proposed method, with errors of under 0.4%. Experimental tests on a cantilever beam confirmed its reliability, with errors of under 3.6%. The method’s low sensitivity to disturbance makes it a robust method for locating and quantifying damage in mechanical structures.

Optimized harmonic PWM implementation in a reduced switch count MLI with quadruple boosting using PSO for solar PV applications

Abstract The reduced switch multilevel inverters are used in many applications specially in renewable energy system. They have a smaller number of semiconductor devices, complexity and thus lower cost and power losses. A reduced-switch multilevel inverters (MLIs) with quadruple boosting capability have been investigated in this study by implementing an optimized harmonic pulse width modulation (OPWM) technique. As an example, a nine-level quadruple boosting inverter, operating at fundamental frequency, is analysed to reduce the dominant lower order harmonics such as third, fifth, and seventh-order harmonics in the output voltage along with control on fundamental component. The particle swarm optimization (PSO) algorithm is employed to obtain the optimize the switching angles using a constrained nonlinear objective function. The computational results have been used to simulate the nine-level quadruple boost inverter and results shows a significant reduction in lower order harmonics. The simulation results have been verified on a prototype of nine-level quadruple boost inverter.

Complete classification and additional saddle-point solutions for high-order above-threshold ionization induced by a strong laser field

Ionization of atoms by a strong laser field can be described using the improved strong-field approximation. The corresponding transition amplitude of high-order above-threshold ionization is presented in the form of a two-dimensional integral over the electron ionization time t0 and the rescattering time t. This integral can be solved using the saddle-point (SP) method and the resulting T-matrix element is expressed as a sum (over the SP times t0 and t) of the partial transition amplitudes. We address the problem of finding the solutions of the system of SP equations for the times t0 and t. For a bichromatic linearly polarized laser field with the frequencies rω and sω (r and s are integers, s>r, and ω is the fundamental frequency) we found that there are 8s2 SP solutions per optical cycle. For one half of them the velocity of the electron emitted in the laser field polarization direction changes the sign at the rescattering time (we call such solutions backward-scattering solutions), while for the other half this velocity remains unchanged (these solutions we call forward-scattering SP solutions). For very short (or even negative) electron travel time we call these solutions backward-like and forward-like scattering SP solutions. For these solutions the imaginary parts of the times t0 and t become large so that the concept of real electron trajectories becomes questionable. Having such a classification, we found additional SP solutions even for the simplest case of a monochromatic linearly polarized laser field. For a bichromatic linearly polarized laser field with s=2 and equal component intensities we presented a detailed analysis of all 32 solutions per optical cycle, showing how the SP times t0 and t and the corresponding differential ionization rates depend on the photoelectron energy. We have also analyzed the case where the intensity of the second component decreases while the sum of the component intensities remains fixed. Published by the American Physical Society 2025

Students’ performance and typical errors in filling empty probabilistic visualizations with probabilities or frequencies

Abstract It has been established that, in Bayesian tasks, performance and typical errors in reading information from filled visualizations depend both on the type of the provided visualization and information format. However, apart from reading visualizations, students should also be able to create visualizations on their own and successfully use them as heuristic tools in modeling tasks. In this paper, we first want to broaden the view on Bayesian reasoning to probabilistic tasks with two binary events in general and embed the whole process of solving these tasks using probabilistic visualizations in a modified modeling framework. Thereby, it becomes apparent that most of the steps remained untouched by existing research. Second, in the present empirical study, we focused on one part of the largely unexplored creation process and examined entering statistical information into empty visualizations as heuristic tools. N = 172 participants had to enter conditional and joint probabilities or the corresponding frequencies into empty visualizations in a paper-and-pencil test. We analyze (a) students’ performance when entering information in visualizations and (b) typical errors, both dependent on the information format (probabilities vs. natural frequencies), which empty visualization structure (2⨯2 table, double tree, net diagram) was provided, and type of information (conditional vs. joint information). The well-known positive effect of natural frequencies on participants’ performance was evident when entering conditional information into 2⨯2 tables and net diagrams. However, with respect to joint information, no superior effect of frequencies was observed. Furthermore, the theoretical implementation of our research in a modeling cycle allows us to identify desiderata for future research.

Numerical Modal Analysis of Foams with Different Types and Configurations

Thanks to the perfect combination of mechanical properties like high strength and rigidity with functional properties like thermo-acoustic insulation and vibration damping, foam structures are becoming increasingly attractive in engineering applications. Most of the research done so far has been focused on the mechanical properties of foams. On the other hand, understanding the vibration behavior of foams is vital since most failures in engineering applications are associated with violent vibrations. In this research, it is focused on the vibration analysis of foams with different types and configurations. In the context of vibration, modal analysis is a highly preferred method for fully understanding the structural behavior of materials. The Finite Element Method is commonly employed for numerical modal analysis to reveal the vibration characteristics of structures, including natural frequencies and corresponding mode shapes. With this objective, the natural frequencies and mode shapes of these foams were defined under both clamped-free and free-free boundary conditions. Subsequently, the effects of material application and boundary conditions were examined. The findings and results obtained can provide valuable insights to researchers and engineers for design applications.

Insights on the Influence of the Central-Cut Width of the Box Assembly with Removable Component on Its Dynamical Responses

This investigation focuses on the dynamical effects caused by varying the central-cut width within the Box Assembly with Removable Component (BARC) system. The central-cut widths included in this study are a 0.5″ cut, a 0.25″ cut, a thin 0.1″ cut, and a structure that did not have a cut at all. Finite element analysis was conducted to determine the mode shapes and natural frequencies of each of the BARC structures. Structural dynamics experiments were run to examine the effects of the central-cut width on the dynamical responses and nonlinear characteristics of the BARC system. Free vibration testing with an impact hammer was carried out to excite the system and extract the dominant frequencies and directions of the significant responses. A pseudorandom vibration test that allows for the qualitative determination of any nonlinear behavior within the system was performed. This type of behavior can include nonlinear softening, nonlinear hardening, and the most common, nonlinear damping due to the presence of several bolted-joint connections and the possible activation of geometric and inertia nonlinearities. To quantitatively investigate the impacts of the central-cut width on the dynamics of the system, swept sinusoidal testing was conducted. It is determined that almost all systems with central cuts demonstrate the presence of nonlinear softening, but at times, nonlinear hardening trends are seen, particularly in the 0.1″ cut and no-cut systems when testing harmonically. Each of the central-cut systems displays nonlinear damping, with the amount of damping generally increasing as the central cut decreases in size. The effect of the central cut of the BARC system on the mode-switching ability of the system is negligible; however, mode switching takes place when comparing the central-cut configurations to the no-cut one. These results show the significance of accurately measuring the central-cut width and how geometric uncertainty may change the dynamical responses and nonlinear properties of the system.

Design and analysis of a linear astigmatism-free confocal off-axis reflective collimator for aerial applications

This paper presents the design and analysis of a linear astigmatism-free confocal off-axis reflective collimator for line-of-sight alignment in multi-wavelength/multi-field-of-view optical sensor modules. Comprising two off-axis mirrors and one flat mirror, the collimator has a 73 mm entrance pupil diameter and a 1200 mm focal length. Sensitivity analysis and Monte Carlo simulations using Optic Studio (ZEMAX) confirmed that the design meets all specified requirements. Stray light analysis shows that stray light is effectively blocked by the optomechanical structures only, eliminating the need for additional baffle structures. A semi-kinematic mount ensures assembly precision, while modal analysis indicates a fundamental frequency of 232.55 Hz, ensuring durability in aerial operations.

Dynamics of pitch perception in the auditory cortex.

The ability to perceive pitch allows human listeners to experience music, recognize the identity and emotion conveyed by conversational partners, and make sense of their auditory environment. A pitch percept is formed by weighting different acoustic cues (e.g., signal fundamental frequency and inter-harmonic spacing) and contextual cues (expectation). How and when such cues are neurally encoded and integrated remains debated. In this study, twenty-eight participants (16 female) listened to tone sequences with different acoustic cues (pure tones, complex missing fundamental tones, and tones with an ambiguous mixture), placed in predictable and less predictable sequences, while magnetoencephalography was recorded. Decoding analyses revealed that pitch was encoded in neural responses to all three tone types, in the low-to-mid auditory cortex and sensorimotor cortex bilaterally, with right-hemisphere dominance. The pattern of activity generalized across cue-types, offset in time: pitch was neurally encoded earlier for harmonic tones (∼85ms) than pure tones (∼95ms). For ambiguous tones, pitch emerged significantly earlier in predictable contexts than unpredictable. The results suggest that a unified neural representation of pitch emerges by integrating independent pitch cues, and that context alters the dynamics of pitch generation when acoustic cues are ambiguous.Significance Statement Pitch enables humans to enjoy music, understand the emotional intent of a conversational partner, distinguish lexical items in tonal languages, and make sense of the acoustic environment. The study of pitch has lasted over a century, with conflicting accounts of how and when the brain integrates spectrotemporal information to map different sound sources onto a single and stable pitch percept. Our results answer crucial questions about the emergence of perceptual pitch in the brain: namely, that place and temporal cues to pitch seem to be accounted for by early auditory cortex, that a common representation of perceptual pitch emerges early in the right hemisphere, and that the temporal dynamics of pitch representations are modulated by expectation.

Comparing Gaussian process enhanced grey-box approaches to detect damage in unknown environmental conditions due to climate change

In vibration-based structural health monitoring (SHM), it is well known that environmental and operational variations (EOVs) affect the dynamic response of the structure of interest. This fact makes it difficult to distinguish between structural changes caused by damage and those caused by EOVs. In SHM, this issue is addressed by data normalisation, whereby machine learning techniques are commonly applied. However, ensuring their accuracy necessitates capturing a comprehensive range of EOVs within the training data. Collecting these is inherently challenging for real-world applications, especially with new EOV states emerging due to climate change. This study’s unique contribution is applying and comparing two grey-box models based on Gaussian process (GP) regression to remove EOVs with low data coverage and demonstrate their efficiency for damage detection with an open-access benchmark dataset. To this end, the first two bending mode natural frequencies – used as damage-sensitive features – of the Leibniz University Test Structure for Monitoring (LUMO), an outdoor lattice tower, are mapped. Two approaches to embedding physical knowledge in the GP are investigated. The first approach incorporates knowledge through the mean function, while the second involves the selection or design of a kernel. Subsequently, the two approaches are compared with a black-box and a white-box model. For long-term SHM, the repair of a damage mechanism is accounted for by the normal-condition alignment scheme, and damage detection is performed using the Mahalanobis distance. The study demonstrates that applying grey-box models contributes to a more reliable representation of the variations caused by unknown EOVs than pure black-box models, thereby improving damage detectability with sparse and incomplete training data due to climate change. However, as the dependencies modelled for LUMO are primarily linear, further research is required to assess the applicability of these findings to structures where dependencies are expected to be non-linear.

Nonlinear vibrations of graphene nanoplates with arbitrarily orientated crack located in magnetic field using nonlocal elasticity theory

PurposeThe study explores frequency curves and natural frequencies as functions of crack length, crack angle, magnetic field strength and small size effects under the three boundary conditions.Design/methodology/approachThis study investigates the nonlinear dynamics of a single-layered graphene nanoplate with an arbitrarily oriented crack under the influence of a magnetic field. The research focuses on three boundary conditions: simply supported, clamped and clamped-simply supported. The crack effect is modeled by incorporating membrane forces and additional flexural moments created by the crack into the equation of motion.FindingsResults reveal that increasing the crack length, small size effects and magnetic field intensity reduces the flexural stiffness of the nanoplate, increases the compressive load and lowers its natural frequency. Additionally, excessive magnetic field intensity may lead to static buckling. The critical dimensionless magnetic fields are found to be 33.6, 95.1 and 72.3 for All edges of the nanoplate are simply supported (SSSS), fully clamped edges (CCCC) and two opposite edges are clamped and the other are simply supported (CSCS) nanoplates, respectively. Furthermore, for SSSS and CCCC boundary conditions, an increase in the crack angle results in a softening behavior of the hard spring. In contrast, the SCSC boundary condition exhibits the opposite behavior. These findings emphasize the importance of considering the effects of angled cracks and electromagnetic loads in the analysis and design of graphene-based nanostructures.Originality/valueNovel equations are derived to account for the applied loads induced by the magnetic field. The nonlinear equation of motion is discretized using the Galerkin technique, and its analytical response is obtained via the multiple time-scales perturbation technique.

Investigation of Free Vibration Behavior for Composite Sandwich Beams with a Composite Honeycomb Core

The purpose of the current research is to determine the effect of fiber type, volume ratio, and matrix type on the vibration properties of sandwich beams made of composite face sheet and core. The typical sandwich structure consists of three layers: face sheets, core, and adhesive bonding, and in this research, the adhesive layer between the face sheets and core was abolished by preparing the overall mold with fibers inside and casting the resin to fill the face sheet and core parts. The face sheets of the composite beams are made from a polyester or epoxy matrix reinforced with glass fiber, carbon fiber, and hybrid fiber, and the core is a honeycomb consisting of random glass fibers immersed in a resin matrix (polyester or epoxy). 22 composite sandwich beams were constructed to conduct vibration testing. The vibration results obtained experimentally were compared to the ANSYS R1 2022 software, and the results were in very good agreement. Hybrid fibers and polyester matrix achieved the highest values of natural frequency for (clamped-clamped) boundary conditions, where the natural frequency value of the hybrid fiber and polyester matrix reached (2037 Hz) at a volume fraction of (23.14%) experimentally and the natural frequency reached (1804.5 Hz) at a volume fraction of (21.95%) experimentally for the simply supported boundary condition.

Ecological Validity of Self-Perceived Voice Quality and Acoustic Measures During Voice Assessments: An Observational Study on Faculty Teachers.

This study investigated the ecological validity of conventional voice assessments by comparing the self-perceived voice quality and acoustic characteristics of voice production during these assessments to those in a simulated environment with varying distracting conditions and noise levels. Forty-two university professors (26 women) participated in the study, where they were asked to produce loud connected speech by reading a 100-word text under four different conditions: a conventional assessment and three virtual classroom simulations created with 360° videos, each with different noise levels, played through a virtual reality headset and headphones. The first video depicted students paying attention in class (40 dB classroom noise); the second showed some students talking, generating moderate conversational noise (60 dB); and the third depicted students talking loudly and not paying attention (70 dB). The entire experiment was conducted in a sound-treated room, and the voice of each participant was recorded for acoustic analysis. In each condition, self-perception of voice quality (vocal effort and vocal ease), SPL, fundamental frequency, long-term average spectrum (L1-L0 ratio, alpha ratio, and the 1/5-5/8 ratio), and smooth cepstral peak prominence were measured. Visual distraction and noise level significantly impacted both subjective and acoustic measures of voice production, as shown by numerous statistically significant differences across almost all conditions and variables examined. Specifically, all measures increased with higher levels of distraction and noise, except for the 1/5-5/8 ratio, which showed a decreasing trend. These findings indicate that visual distraction and noise level significantly influence self-perceived and acoustic vocal characteristics and suggest that conventional assessments, typically conducted in silence and without visual distractors, may not accurately represent real-world performance, thus limiting their ecological validity.

An Open Database of the Internal and Surface Temperatures of a Reinforced-Concrete Slab-on-I-Beam Section

Due to climate change, the temperature monitoring of reinforced-concrete (RC) structures is becoming critical for preventive maintenance and extending their lifespan. Significant temperature variations in RC elements can affect their natural frequencies and modulus of elasticity or generate abnormal stress levels, potentially leading to structural damage. Data from thermal monitoring systems are invaluable for testing and validating numerical methodologies for estimating internal thermal responses and aiding in prevention/maintenance decision making. Despite its importance, few experimental outdoor data on the internal and external temperatures of concrete structures are available. This study presents a comprehensive dataset from a 120-day temperature-monitoring campaign on a 1.2 m long reinforced-concrete slab-on-I-beam model under tropical conditions in Bucaramanga, Colombia. The monitoring system measured the internal temperatures at 40 points using embedded thermocouples, while the surface temperatures were recorded with handheld and drone-mounted thermal cameras. Simultaneously, the ambient temperature, solar radiation, rainfall, wind velocity, and other parameters were monitored using a weather station. The instrumentation ensured the synchronization and high spatial resolution of the thermal data. The data, collected at 30 min intervals, are openly available in CSV format, offering valuable resources for validating numerical models, studying thermal gradients, and enhancing structural health-monitoring frameworks.

Vocal and Facial Behavior During Affect Production in Autism Spectrum Disorder.

We investigate the extent to which automated audiovisual metrics extracted during an affect production task show statistically significant differences between a cohort of children diagnosed with autism spectrum disorder (ASD) and typically developing controls. Forty children with ASD and 21 neurotypical controls interacted with a multimodal conversational platform with a virtual agent, Tina, who guided them through tasks prompting facial and vocal communication of four emotions-happy, angry, sad, and afraid-under conditions of high and low verbal and social cognitive task demands. Individuals with ASD exhibited greater standard deviation of the fundamental frequency of the voice with the minima and maxima of the pitch contour occurring at an earlier time point as compared to controls. The intensity and voice quality of emotional speech were also different between the two cohorts in certain conditions. Additionally, facial metrics capturing the acceleration of the lower lip, lip width, eye opening, and vertical displacement of the eyebrows were also important markers to distinguish between children with ASD and neurotypical controls. Both facial and speech metrics performed well above chance in group classification accuracy. Speech acoustic and facial metrics associated with affect production were effective in distinguishing between children with ASD and neurotypical controls. https://doi.org/10.23641/asha.28027796.

FREE VIBRATION ANALYSIS IN INNOVATIVE 3D PRINTING SANDWICH PANAELS FOR AIRCRAFT STRUCTURE

Sandwich panel structures are composed of three layers: core and two facings. The configuration of the core deeply influences the mechanical properties of the sandwich panel. Numerous innovative core shapes have been proposed to enhance these properties; however, many have not been implemented due to manufacturing difficulties, particularly spherical shapes. This research aims to address this manufacturing challenge by utilizing 3D printing technology to produce sandwich panels with a spherical core. Additionally, the study investigates the effects of varying design parameters like sphere diameter, offset distance and face thickness on the free vibration features of the sandwich panels experimentally and numerically. Experimental tests validated the finite element models with an error margin below 12%. The key parameters explored were spherical diameter (3-12mm), offset distance (10-33mm), and face thickness (1-5mm). The results demonstrate a direct correlation between these parameters and the sandwich beam natural frequency.

On quantifying dynamic behavior of architected metal/polymer TPMS/lattices-based interpenetrating phase composites.

This article presents the numerical analysis of architected metal/polymer-based interpenetrating phase composites (IPCs) to study their effective mechanical properties and dynamic behavior using finite element (FE) simulation. In this, we considered four types of Triply periodic minimal surfaces (TPMS) and lattice architectures, including gyroid, primitive, cubic, and octet, to form architected IPCs. The aluminum alloy is used for the TPMS/lattice reinforcing phase, and epoxy as a reinforced phase. The periodic boundary conditions were applied using FE analysis to compute the effective properties, while these properties were utilized to investigate the dynamic analysis of composite structures considering free vibration, wherein actual and homogenized models are compared. Our results reveal that the effective properties of IPCs increase with respect to the volume fraction of respective architectures in conjunction with enhanced natural frequency and less deformation. Moreover, we conducted a comparative study between these newly architected metal/polymer IPCs and conventional composites.

Exact and Approximate Analysis of Structural Models with Linear Viscous or Viscoelastic Dampers and Singular Mass Matrices

This research is concerned with model reduction methods in analysis of structural models with viscous or viscoelastic damping and singular mass matrices. These types of models are commonly used in the preliminary design of building structures containing supplemental damping devices to define locations and parameters of the energy dissipaters. In this paper we develop an exact reduced-order technique for the modal analysis of models with singular mass matrices and viscous or viscoelastic supplemental dampers. Using static condensation of generalized coordinates without mass and no damper connection, and using a transformation using the eigenvectors of the damping matrix, an exact state-space formulation with non-singular mass matrix is developed. The above-mentioned alternative model-reduction strategies are revisited and the accuracy of these methods in the estimation of poles (natural frequencies and damping ratios) and frequency response functions is compared with the exact model. To compare the accuracy of the alternative models developed a simple benchmark structural model with singular mass matrix is used.

High-Resolution Photoelectron Spectroscopy of NO3- Vibrationally Excited Along Its ν3 Mode.

The nitrate (NO3) radical has long been the subject of both experimental and theoretical studies due to its complex electronic structure resulting from vibronic interactions between its X̃2A2' and B̃2E' states. In particular, the definite assignment of the fundamental of its degenerate stretching vibration (ν3) is still under debate. Here, we report high-resolution photoelectron spectra of vibrationally pre-excited NO3- using the recently developed IR-cryo-SEVI technique. The anions are excited through infrared (IR) excitation near 1350 cm-1, accessing the ν3 and 2ν3(e') vibrational levels with band centers at 1350.5 and ∼2700 cm-1, respectively. The IR-cryo-SEVI spectrum for 2ν3 pre-excitation shows clear evidence for an intense 321 transition. From the position of this feature (30031 cm-1), the electron affinity of NO3 also determined in this work (31680 cm-1), and the IR excitation energy, we obtain a fundamental frequency of 1051 cm-1 for the ν3 fundamental of the NO3 radical. This assignment and other features in the IR-cryo-SEVI spectra are supported by spectral simulations based on a vibronic Köppel-Domcke-Cederbaum Hamiltonian. The simulations also show that nearly all features in the IR-cryo-SEVI spectra arise because of pseudo-Jahn-Teller coupling between the X̃ and B̃ states of NO3. The results and analysis presented here settle a long-standing controversy regarding the ν3 frequency of NO3.

Evolution characteristics and mechanism of coal fracture under resonance excitation based on computed tomography scanning

AbstractThe resonance of coal reservoir induced by external excitation is a kind of environment‐friendly stimulation technology. In this work, an experimental system was established to carry out the coal resonance fracturing experiments, and the change trend of fracture structure was investigated by computed tomography scanning. The results showed that under the excitation of vibration within the resonance frequency band range, the coal fracture will gradually expand to failure. There are three forms of coal fracture expansion under the condition of resonant, which are the formation of slip zones in coal, the formation of fracture at phase interface and the formation of ‘void’. When the excitation frequency is constant, the natural frequency of coal decreases gradually with the expansion of fractures, resulting in the vibration frequency gradually deviating from the natural frequency of coal, and the fracture propagation behaviour of vibrating coal gradually changes from divergence to convergence.

Multiple TMDS Coupled with Viscous Dampers to Improve Acceleration Performance and Robustness of Buildings Subject to Wind-Induced Vibrations

The performance of a novel configuration of multiple tuned mass damper (MTMD) proposed by the author for floor acceleration reduction of linear elastic buildings subjected to broad-band wind force excitation is studied. To improve efficiency and robustness under variations or uncertainties of main-structure dynamic parameters, three single degree of freedom mass dampers in parallel are tuned to different frequencies close to the natural frequency of the target mode of vibration of the main structure and the classical viscous damping elements that connect the TMDs to the main structure are replaced by dampers that connect the masses of the TMDs. This special coupling between parallel TMDs is called viscous-coupling multiple tuned mass dampers (VCMTMD). The effectiveness of the proposed technique is evaluated and compared with conventional TMD and uncoupled MTMD configurations for the same total mass of the TMDs. The reduction of root mean square acceleration and deformations of the main structural system subjected to broad-band excitation is analyzed and compared with those of a conventional optimal TMD and of a parallel MTMD without coupling. The VCMTMD outperforms both the conventional TMD and parallel MTMDs in terms of deformation and acceleration reduction of the structure with the proposed TMD viscous coupling. The VCMTMD shows high robustness to changes or uncertainties in main-structure parameters (mass or stiffness). The proposed TMD configuration can find practical applications in wind-induced acceleration reduction in high-rise buildings and vibration reduction in different structures subjected to broad-band loading.