Steady-state Response Research Articles

Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) systems subjected to harmonic excitation. Utilizing a classical spring–mass–damper model, Fourier decomposition is applied to derive transient and steady-state responses, highlighting the effects of damping, resonance, and excitation frequency. To overcome the uncertainties and limitations of traditional models, Extended Kalman Filters (EKFs) and Physics-Informed Neural Networks (PINNs) are incorporated, enabling precise parameter estimation even with sparse and noisy measurements. This paper uses Adam followed by LBFGS to improve accuracy while limiting runtime. Numerical experiments using 1000 time samples with a 0.01 s sampling interval demonstrate that the proposed PINN model achieves a displacement MSE of 0.0328, while the Eurocode 8 response-spectrum estimation yields 0.047, illustrating improved predictive performance under noisy conditions and biased initial guesses. Although the present study focuses on a linear SDOF system under harmonic excitation, it establishes a conceptual foundation for adaptive dynamic modeling that can be extended to performance-based seismic design and to future calibration of Eurocode 8. The harmonic framework isolates the fundamental mechanisms of amplitude modulation and damping adaptation, providing a controlled environment for validating the proposed PINN–EKF approach before its application to transient seismic inputs. Controlled-variable analyses further demonstrate that key dynamic parameters can be estimated with relative errors below 1%—specifically 0.985% for damping, 0.391% for excitation amplitude, and 0.692% for excitation frequency—highlighting suitability for real-time diagnostics, vibration-sensitive infrastructure, and data-driven design optimization. This research deepens our understanding of vibratory behavior and supports future developments in smart monitoring, adaptive control, resilient design, and structural code modernization.

Second-order RLC series circuits serve as fundamental models for analyzing electrical transients and steady-state sinusoidal responses in power systems, communications, and control applications. This review summarizes the use of linear differential-equation methods to describe and solve the governing second-order ordinary differential equation derived from Kirchhoff’s voltage law. We examine the three classical damping regimes underdamped, critically damped, and overdamped and show how characteristic roots and natural frequencies determine current and voltage evolution following a step or impulse excitation. Analytical solutions employing homogeneous and particular components, Laplace transforms, and phasor techniques are compared, highlighting their roles in predicting transient decay, steady-state sinusoidal behavior, and resonance phenomena. Extensions to forced inputs, quality factor evaluation, and frequency-domain interpretation are discussed, along with representative case studies illustrating the impact of component tolerances and energy loss. By consolidating fundamental theory, solution strategies, and practical considerations, this review provides a unified framework for applying linear differential-equation methods to the transient and steady-state analysis of second-order RLC series circuits.

Do cognitive and neurophysiological effects of acute memantine "challenge" predict its clinical benefits in Alzheimer's Disease?

Parameter identification of lap-type joints based on Bouc–Wen–Bilinear model and event-driven steady-state response sensitivity method

Abstract This study investigates the mechanisms of friction-induced vibration under periodic stress distribution variations using an improved fretting friction model. A fretting friction test system integrated with a total reflection method was developed to analyze interfacial contact behavior under dynamic loading conditions. An improved fretting friction model was established, incorporating three critical nonlinear parameters: hysteretic friction coefficient, tangential stiffness fluctuations, and stress distribution. Through systematic validation, the model demonstrates high-fidelity replication of experimental steady-state amplitude-frequency responses. Key findings reveal that stress distribution non-uniformity governs vibration response irregularity, and increased uniformity intensifies stick-slip instabilities. Near the stick-slip transition threshold, distinct vibration anomalies emerge due to the coupled effects of stress heterogeneity, friction hysteresis, and stiffness variations during state transitions. Furthermore, the magnitude of the normal contact force systematically alters the dominant interfacial contact mechanism. The different interfacial contact states at various frequencies lead to distinct steady-state responses. This shift elevates resonance frequencies and amplifies higher-order resonant peaks. The fretting friction model provides a predictive framework for vibration control under dynamic interfacial loading.

The response amplified friction damper (RAFD) can serve as a high-performance friction damper or a frictional inerter to reduce the vibration of a structure. Since the RAFD is highly nonlinear, the performance of RAFD under external forces is still affected by the axial stiffness, gap, and stick condition. To obtain the key aspects that determine the performance of RAFD, in this study, a theoretical model considering the axial deformability and gap of the RAFD under harmonic loads is established by the equivalent linearization of the friction behavior. The effectiveness of the RAFD on reducing the vibration and the key parameters that determine the effectiveness are investigated. The results show that the proposed model can accurately estimate the steady-state response amplitude of the structure equipped with the RAFD under harmonic excitations. Besides, axial stiffness is the key parameter that determines the effectiveness of the RAFD. A large axial stiffness, and the corresponding large preload, both help to improve the effectiveness of the RAFD and expand the frequency range of external excitations that make the RAFD slide. The gap can enlarge the peak displacement response of the SDOF system. Further, as it is easy to design a RAFD with large inertial mass, this study proposes a design instance to adjust friction and inertial forces, which can expand the applicability of this device in engineering aspects.

Background: Gamma-range auditory steady-state responses (ASSRs) are emerging as promising translational biomarkers of neural network function. While extensively studied in human neuropsychiatric and neurodevelopmental research, their application in animal models has expanded in recent years, providing mechanistic insights into disease-related neural dynamics. However, methodological approaches vary widely, findings remain fragmented, and outcomes are not easily generalized. Methods: A literature search was conducted in March 2025 across PubMed and Scopus to identify studies investigating gamma-range ASSRs (30–100 Hz) in animal models with relevance to psychiatric and developmental conditions. Results: Most studies employed rodents, with a smaller number involving non-human primates, and used pharmacological, genetic, lesion-based, or developmental manipulations relevant to schizophrenia, autism spectrum disorder, and related conditions. ASSRs were highly sensitive to NMDA receptor antagonism, state- and trait-related factors, and exhibited region- and layer-specific generation patterns centered on the auditory cortex. Less common paradigms, such as chirps and gap-in-noise, also demonstrated translational potential. Conclusions: Animal research confirms that gamma-range ASSRs provide a sensitive, cross-species readout of circuit dysfunctions observed in psychiatric and neurodevelopmental disorders. To maximize their translational utility, future work should prioritize methodological harmonization, systematic inclusion of sex and behavioral state factors, and replication across laboratories. Strengthening these aspects will enhance the value of ASSRs as biomarkers for early detection, patient stratification, and treatment monitoring in clinical psychiatry.

To address pressure control inaccuracy caused by nonlinearity (master cylinder piston position-pressure relationship) and uncertainty disturbances (temperature-induced changes in system parameters and brake pad wear) in an electro-hydraulic brake system (EHB), this paper suggests a cascaded adaptive control strategy consisting of a pressure outer loop and a position inner loop to improve pressure control performance. Firstly, the master cylinder pressure tracking adaptive control technology is used in the pressure outer loop. This technology uses the master cylinder piston position-pressure nonlinear relationship as the pressure feed-forward and combines fuzzy PI feedback control to enhance the dynamic compensation ability of feedback control for position-pressure relationship, improving the pressure tracking accuracy of the EHB system. Then, for the position inner loop, a linear active disturbance rejection controller (LADRC) is designed based on the EHB dynamic model. This controller has the capability of observing and compensating for uncertain disturbances, thereby guaranteeing the robustness of pressure control. Finally, sinusoidal and step pressure tracking experiments are performed on a hardware-in-the-loop bench. The results indicate that the proposed control strategy can significantly improve the steady-state accuracy and dynamic response characteristics of pressure tracking.

Abstract Cross-modal neuroplasticity is a well-studied phenomenon whereby in the absence of sensory input (e.g., in individuals who are deaf or blind), the sensory cortices of the affected modality are “taken over” by the unaffected sensory systems. This neuroplasticity is often coupled with changes in the dynamics of the unaffected primary sensory cortices themselves. Nonetheless, whether these cross-modal changes extend to those with mild-to-severe sensory loss where sensory input is degraded but not absent, as is the case for children who are hard-of-hearing (CHH), remains poorly understood. Visual entrainment, sometimes referred to as the visual steady-state response, is the process by which the primary visual cortices entrain to the frequency of a rhythmic exogenous visual stimulus. Importantly, visual entrainment dynamics are thought to serve as an important proxy for how visual stimuli are processed in the brain. The current study sought to identify the impact of mild-to-severe hearing loss and individual differences in auditory experience on visual entrainment dynamics in youth. To this end, CHH and an age- and sex-matched group of children with normal hearing (CNH) were presented with a visual entrainment stimulus that flickered at 15 Hz during magnetoencephalography. Neural responses to the fundamental (15 Hz) and first harmonic (30 Hz) were imaged using beamforming, and the power envelope of the peak responses were extracted as a function of time and submitted to linear mixed effects modelling. We found a significant group-by-time interaction, whereby CHH exhibited a stronger increase in power during entrainment compared to CNH, suggesting altered entrainment dynamics. We also ran whole-brain correlations between 15 Hz and 30 Hz neural responses and hearing aid use in CHH, controlling for degree of hearing loss. We found a significant negative relationship between hearing aid use and activity in the left primary auditory cortex and left lateral parietal cortex, such that CHH who consistently wore their hearing aids showed the smallest amount of cross-modal neuroplasticity in these regions. Crucially, reductions in cross-modal neuroplasticity in the left lateral parietal cortex were related to better verbal outcomes. These data provide important new information regarding how consistent auditory experience may serve to normalize the neural dynamics serving sensory processing, and how these changes may cascade into improvements in verbal ability in CHH.

Abstract Vibration mitigation remains a critical challenge in mechanical and structural systems under resonant and broadband excitation. While conventional tuned mass dampers (TMDs) are widely used, their effectiveness is constrained by substantial mass requirements and narrow operational bandwidths. This study introduces two inertial amplification mechanism (IAM)-based absorbers designed to overcome these limitations, the tuned inertial amplified mass damper (TIAMD) and the tuned inertial amplified viscous mass damper (TIAVMD). The TIAMD integrates an IAM into a Voigt-type TMD, while the TIAVMD embeds the IAM within a grounded viscous-TMD configuration. Mathematical models of both systems, coupled with a single-degree-of-freedom primary system, are derived using Lagrange’s equations and solved using an adaptive step-size Runge–Kutta method. Numerical optimization using pattern search algorithms identifies optimal frequency and damping ratios to minimize peak steady-state response under harmonic excitation. The influence of key design parameters including Mass ratio, Mass distribution ratio, and IAM angle on dynamic performance is investigated, and comprehensive design charts for optimal tuning are presented. Results demonstrate that both configurations significantly outperform conventional TMDs, with the TIAVMD achieving 40.4% greater vibration suppression, 75.5% wider bandwidth, and 68.2% lower absorber displacement. The TIAMD shows comparable improvements, including 31.2% enhanced attenuation and 58% bandwidth expansion. These IAM-based absorbers offer superior vibration control without mass penalties, providing efficient and compact solutions for diverse engineering applications.

Abstract Background Sensorineural hearing loss (SNHL) poses a significant public health burden globally, with a disproportionately higher prevalence in developing regions like Africa. The consequences of SNHL in early childhood can be devastating, impacting speech, language, cognitive, and psychosocial development, ultimately affecting educational attainment and quality of life. The etiology of SNHL is multifactorial, encompassing genetic predispositions, prenatal and perinatal complications, infections, ototoxic insults, and environmental factors. In the African context, preventable causes such as congenital rubella, meningitis, mumps, and ototoxic medications play a significant role. Additionally, the high prevalence of consanguineous marriages and the lack of universal newborn hearing screening programs contribute to delayed diagnosis and interventions. Early and accurate diagnosis of SNHL is crucial for timely and appropriate medical, surgical, or audiological (re)habilitative measures. Main body However, the diagnosis of SNHL, particularly in children, can be challenging, necessitating a combination of audiological and radiological evaluations. Audiological assessments; behavioral measures (pure-tone audiometry [PTA]), electroacoustic measures (immittance audiometry and otoacoustic emissions), and electrophysiologic measures (auditory brainstem response and auditory steady-state response) are comprehensive audiological assessments which remain the cornerstone for identifying the site, degree, and laterality of hearing loss. They cannot localize or detect the underlying pathology, and this may affect the determination of appropriate interventions such as hearing aids, cochlear implants, other amplification devices, and other management options. Radiological imaging techniques, particularly computed tomography and magnetic resonance imaging, have revolutionized the evaluation of SNHL by providing detailed visualization of the intricate anatomy and pathologies of the bony and membranous labyrinths, respectively. Conclusion SNHL poses a significant challenge in the African context, with a higher burden and unique etiological patterns. Early and accurate diagnosis, facilitated by the integration of audiological and radiological evaluations, is crucial for timely interventions and optimal outcomes.

ASSR and ABR tests in early diagnosis of hearing loss: A STROBE observational study.

The study first experimentally investigates the effects of CO₂ filling-ratios, cooling fluid flowrate, and temperature on steady-state performance and thermal resistances in different zones of the system. Subsequently, a time-dependent model of the transient thermal response of various key parameters—heat transfer rate, temperatures, and thermal resistances—in different zones of the system was developed to characterize the first-order system. The thermal response of each zone is represented by an exponential function, establishing a relationship between the response time, the geometry, and the heat transfer phenomena specific to each zone. Each zone has its own time constant, defined as the time required for the average temperature of that zone to reach 63.2% of its steady-state value. Any deviation from this reference value, during operation, indicates anomalies such as fouling, frost formation, or component failures in the system. Results show that total thermal resistance of the GT is 2 to 4 times higher than that of the active condenser (HX). The active condenser’s resistance exceeds the evaporator and CO2-side-condenser sections by up to 3 and 7 times, respectively. Reducing the thermal resistance of the active condenser and the interface between the evaporator and the ground is crucial for enhancing GT performance. The study also provides a detailed insight into the transient regime of the thermosyphon, which is not available for real-scale systems in the literature. These findings not only identify the critical components influencing performance but also introduce a novel diagnostic method for detecting anomalies in GT-HRV systems based on deviations in zone-specific time constants.

This article takes the linear inclined vibrating screen (TLIVS) as the research object, establishes a spatial 6-degree-of-freedom dynamic model of TLIVS, and verifies the correctness of the established model through comparison between real experiments and simulation experiments. Steady-state response of TLIVS is solved by numerical analysis method, The influence of each degree of freedom acting separately on the screening process of TLIVS was explored using the discrete element method. The results indicate that x-direction translation movement mainly promotes the dispersion of the mixture, and y-direction translation movement mainly increases the velocity of the mixture towards the outlet. z-direction translation movement mainly causes the mixture to stratify. Rotation in the x-direction accumulates the mixture in the middle of the screen surface, rotation in the y-direction helps to disperse the material at the inlet, and rotation in the z-direction may cause blockage of the mixture.

Auditory processing underlies phonological representation and presents neural oscillation lateralization in the brain. Atypical lateralization in auditory processing has been widely accepted as associated with impaired reading skills in alphabetic languages. However, whether Chinese adults with a reading difficulty (RD) history present atypical lateralization in auditory processing similar to that in alphabetic languages remains unknown. The purpose of this study was to investigate whether Chinese adults with poor reading would show atypical lateralization of neural oscillations during auditory sampling. Thirty-two adults with self-reported RD history and 44 adults without RD history were screened using the Chinese Adult Reading History Questionnaire. Reading accuracy, phonological accuracy, and rapid automatized naming (RAN) were assessed in all the participants. Auditory steady-state responses modulated at 10 to 80 Hz were recorded during a 5.4-sec white noise. Time-frequency power and phase synchrony indices were used to measure induced oscillatory power and synchrony of beta and gamma oscillations related to phonemic processing. Adults with a RD history performed worse than adults without RD history in reading accuracy and phonological accuracy. Adults with a RD history showed atypical rightward lateralization in the gamma band oscillation, whereas the adults without a RD history showed leftward lateralization. Adults with a RD history also demostrated reduced left-hemisphere oscillatory power and weaker bilateral synchrony. Event-related spectral perturbation in the left hemisphere correlated with reading accuracy in adults with RD history, while left-hemisphere lateralization of event-related spectral perturbation correlated with phonological accuracy in adults without RD history. In adults with RD history, the inter-trial phase synchrony in the left hemisphere correlated with RAN, and inter-trial phase synchrony in the right hemisphere correlated with reading accuracy and RAN, respectively. Adults with RD history demonstrated atypical rightward gamma band lateralization compared with adults without RD history, alongside reduced left-hemisphere oscillatory power and weaker bilateral synchrony. These neural patterns correlated with reading accuracy and phonological skills, supporting the hypothesis that auditory lateralization deficits underlie phonological processing challenges in Chinese, mirroring mechanisms observed in alphabetic languages.

Abstract A steady-state linear response matrix (L) characterizes the time-mean responses (〈Δx〉) of a dynamical system to weak, time-invariant forcings (f), as 〈Δx〉 = Lf. For the Lorenz-63 system, direct simulations give We find lzz = −0.00111±0.00014 to be a negative eigenvalue of L, which is incompatible with the linear Markov assumption or the linear inverse modeling approach for calculating L. Such negative eigenvalue arises not from numerical errors nor reduction of prognostic variables, as previously suggested. We also review a few direct applications of L and discuss the prospect of using the Lorenz-63 L as a benchmark in a unified testbed. In this framework, other linearization methods can be examined and refined to enable faster and more accurate computation of the steady-state linear response matrix L for more realistic atmospheric systems.

SNRENN: A Transformer-Based Neural Network with Self-Supervised Learning for Auditory Steady State Response Signal SNR Enhancement

For fourth-generation synchrotron light sources, the triple rf system has been proposed to achieve further bunch lengthening compared to the commonly used double rf system, as well as to meet specific requirements for longitudinal injection. In a previous study for the double rf system [T. He , Periodic transient beam loading effect with passive harmonic cavities in electron storage rings, ], it was shown that the periodic transient beam loading (PTBL) effect, also referred to as mode 1 instability, could limit the maximum bunch lengthening. Intuitively, in the triple rf system, the harmonic cavity (HC) operating at a higher harmonic of the fundamental rf frequency is expected to help mitigate the mode 1 instability driven by the lower-order HC, as the two HCs are tuned in opposite directions. However, contrary to this intuition, both tracking simulations and semianalytical calculations presented in this paper show that the two HCs of the triple rf system together actually strengthen the PTBL effect. To better understand this unexpected behavior, we introduce a novel concept of steady-state response matrix of cavity voltage, which simplifies the semianalytical algorithm and directly links cavity voltage perturbations to the complex bunch form factor perturbations. Additionally, we propose a modified semianalytical method that efficiently and accurately determines the PTBL threshold for the triple rf system. Using the parameters of the Hefei Advanced Light Facility storage ring as a case study, we apply this modified method to explore the relationship between the threshold R/Q values of the two HCs under different bunch lengthening scenarios. All results are well validated through tracking simulations. Our findings show that the R/Q values of the two HCs must be sufficiently low to avoid the PTBL effect under the desired optimum bunch lengthening condition. This result provides valuable guidance for the design of the triple rf system.

Broadband neural oscillatory dynamics at stimulus onset and offset during 40-Hz auditory stimulation.

We investigated how early human visual cortex processes color by analyzing individual variability in steady-state visual evoked potentials (SSVEPs). Sixteen participants viewed a flickering checkerboard that swept around the isoluminant hue circle at three chromatic contrasts. The current study analyzed the individual variability in the SSVEP data from the study to elucidate the hue-selective mechanisms in the early visual areas using a factor-analytic approach. The initial analyses of the correlations revealed that the responses to the nearby hues correlated highly, which is consistent with multiple overlapping color channels. Also, the correlational pattern showed consistent peaks and troughs at specific hue angles: 0° (+L–M), 30°, 120°, 180° (−L+M), 240°, and 300°. We further performed nonmetric multidimensional scaling, identifying four significant hue dimensions. Peaks and troughs of the dimension components were consistent with the hue angles revealed in the correlational pattern. Additional four hues also appeared in the last dimension: 90° (+S), 150°, 270° (−S), and 330°. The 10 (six plus four) hues suggested in these analyses may subserve the basis of early cortical color processing, including classical cone opponency and the mechanisms tuned to the intermediate hues.