The research, carried out by Onur Onat of the Department of Civil Engineering at Inonu University in Malatya, rests on a deceptively simple idea. Every structure, from a guitar string to a skyscraper, has a set of natural frequencies at which it prefers to oscillate. These frequencies depend on the structure’s mass and stiffness, so when an earthquake cracks masonry, opens bed joints, or otherwise softens a building, the natural frequencies drop. By measuring the minarets’ vibration signatures before and after the Kahramanmaraş sequence, engineers can effectively ask the towers themselves how much damage they sustained, even in places the eye cannot see.

Ambient vibration measurement, the technique at the heart of the study, requires no artificial shaking. Wind, distant traffic, and micro-tremors in the ground provide a continuous, gentle excitation that is more than enough to coax a tall minaret into swaying at its natural frequencies. Sensitive seismometers recorded these barely perceptible motions at both towers, and signal processing identified the natural frequencies, damping ratios, and mode shapes, the characteristic patterns of deformation associated with each frequency, for the first four vibration modes of each minaret. The pre-earthquake and post-earthquake modal vectors were then compared using the Modal Assurance Criterion, a standard statistical measure of how similar two vibration patterns are.

The results tell a consistent story of measurable but not catastrophic degradation. The first four identified frequencies decreased by an average of 5.46 percent for the Yusuf Ziya Pasha minaret and 5.98 percent for the Sunullah Melik minaret. A frequency drop of roughly six percent may sound modest, but in structural terms it corresponds to a meaningful loss of lateral stiffness, the property that allows a slender tower to resist horizontal earthquake forces. Intriguingly, the damping ratios, which describe how quickly vibrations die away, showed no uniform trend, a reminder that energy dissipation in cracked masonry is a far messier phenomenon than stiffness loss.

Field inspections corroborated what the vibration data implied. At the Yusuf Ziya Pasha minaret, observers documented bending-induced tensile cracking in the lower body of the tower, exactly where the flexural demands of earthquake shaking would be expected to concentrate in a cantilever-like masonry shaft. At the Sunullah Melik minaret, the damage took a different form: sliding and separation along the bed joints, the horizontal mortar lines between stone courses, around the pulpit region. These distinct crack patterns illustrate a crucial point about masonry behavior, namely that the same earthquake can produce qualitatively different failure mechanisms in structurally similar towers depending on their geometry, construction details, and local ground conditions.

To translate these observations into a quantitative assessment of seismic performance, the study employed finite element models, numerical representations of each minaret built from thousands of interconnected elements. Rather than assuming material properties from textbooks, the researcher independently calibrated separate pre-earthquake and post-earthquake models using the measured fundamental frequencies of each tower. The models were then verified against the higher-mode frequencies and the modal vectors, ensuring that the numerical replicas matched reality not just in their simplest vibration pattern but across the full measured spectrum. This two-stage approach, calibration followed by independent verification, guards against the common pitfall of a model that fits one number by accident while being wrong everywhere else.

With trustworthy models in hand, the study moved from diagnosis to prognosis. Nonlinear time-domain analyses subjected both the pre-earthquake and post-earthquake models to five unscaled ground-motion records, letting the computer simulate how the towers would respond to real earthquake shaking in their intact and damaged states. Nonlinear analysis is essential here because masonry does not behave elastically under strong shaking; cracks open and close, joints slide, and stiffness degrades progressively as the motion intensifies. The models incorporated material behavior consistent with established plasticity formulations for masonry, allowing the simulations to capture the initiation and propagation of the very cracking patterns observed in the field.

The comparison between intact and damaged simulations produced one of the study’s most consequential findings. The post-earthquake stiffness reductions were reflected far more clearly in the deformation demands than in the global force responses, particularly under the stronger ground motions. In other words, a damaged minaret may carry roughly similar peak forces as an intact one, yet it must bend, sway, and distort substantially more to do so. Since deformation, not force, is what ultimately tears masonry apart, this result carries a sobering implication for heritage managers: towers that appear to have weathered an earthquake without collapse may nonetheless have crossed into a regime where the next strong event produces disproportionately larger displacements and more severe cracking.

Perhaps the most methodologically valuable conclusion concerns what vibration monitoring can and cannot detect. The combined measurement and modeling framework demonstrated that mode-dependent dynamic changes, the frequency shifts distributed across the first four modes, can identify earthquake-related stiffness loss even when the principal global mode shapes remain broadly preserved. This is good news for the growing field of structural health monitoring of cultural heritage, because mode shapes are notoriously difficult to measure accurately in the field, while frequencies can be tracked reliably with modest instrumentation. The study suggests that a monitoring program need not capture perfectly resolved shape changes to flag damage; a careful reading of frequency trends across multiple modes, interpreted through a calibrated model, suffices.

The implications extend well beyond two minarets in Malatya. Türkiye holds an extraordinary inventory of historical masonry minarets, and the 2023 Kahramanmaraş sequence damaged or destroyed many mosques and their towers across the affected region, prompting widespread post-earthquake assessments. The approach demonstrated here, pairing ambient vibration surveys with independently calibrated nonlinear finite element models, offers a repeatable template for triaging that inventory: identifying which towers have silently lost stiffness, quantifying how much seismic reserve remains, and prioritizing retrofit resources accordingly. As climate extremes and seismic activity continue to threaten unreinforced masonry heritage worldwide, the quiet hum of a minaret vibrating in the wind may prove to be one of the most eloquent damage reports a historic structure can give.

Subject of Research: Structural health monitoring and seismic performance assessment of historical masonry minarets damaged by the 2023 Kahramanmaraş earthquake sequence

Article Title: Structural health monitoring and seismic performance assessment of two historical masonry minarets before and after the 2023 kahramanmaraş earthquake sequence

Article References: Onat, O. (2026). Structural health monitoring and seismic performance assessment of two historical masonry minarets before and after the 2023 kahramanmaraş earthquake sequence. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02721-4

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02721-4

Keywords: structural health monitoring, masonry minarets, Kahramanmaraş earthquakes, ambient vibration, modal analysis, finite element model updating, nonlinear seismic analysis, natural frequencies, damage assessment, cultural heritage, earthquake engineering, Türkiye

The research team set out to answer a deceptively simple question: what happens to the oil films at all four supports of a multi-bearing rotor when a load is applied at just one end? The answer required solving a coupled problem that most earlier studies avoided. Previous work on misaligned journal bearings, stretching back to Sun and Gui’s foundational lubrication analyses in 2004 and confirmed experimentally in 2005, established that shaft deformation distorts the convergent wedge of oil, thins the minimum film thickness, and reshapes the pressure field. But those studies largely examined single bearings or prescribed the misalignment in advance. In a real multi-support system, the four journal attitudes are not independent quantities. The deformation of the shared shaft and the hydrodynamic reaction forces generated at all supports collectively determine the global equilibrium, so strengthening one oil film can weaken, shift, or redistribute the constraints at its neighbors.

To capture this system-level coupling, the researchers modeled a three-disk, four-support bearing-rotor system resembling a camshaft under asymmetric loading. The shaft was represented with a Timoshenko beam formulation, which accounts for both bending and shear deformation, while each bearing’s lubricant was described by the Reynolds equation for a finite-length journal bearing under laminar, incompressible, isoviscous assumptions. Crucially, the eccentricity and inclination of all four journals were solved simultaneously through a fluid-structure equilibrium iteration: the shaft deformation determines each journal’s displacement and tilt, the resulting oil-film pressures generate reaction forces, and those forces feed back into the global structural balance until the two fields become mutually consistent. The team also introduced a compact descriptor, a flexible-deformation index denoted M_r, that combines the journal’s eccentricity ratio with a dimensionless measure of its inclination, allowing the coupled eccentricity-inclination state at each support to be summarized in a single number.

The numerical campaign was ambitious. The team built an offline database spanning end loads from 0 to 30 newtons and speeds from 1000 to 8000 rpm, sampling 211,001 load-speed states, of which 200,304, or 94.93 percent, returned valid directly converged fluid-structure solutions. At each converged state, the full oil-film stiffness and damping matrices were extracted by differential perturbation of the journal position and velocity, then stored for interpolation into a finite-element rotordynamic model. Validation was layered: the predicted maximum oil-film pressures under journal inclination agreed closely with the established results of Sun and Gui and of Lv and colleagues, with deviations of roughly 9 to 11 percent only at the most extreme inclination of 0.010 degrees, where the exact peak is known to be sensitive to cavitation treatment and thermal effects. The dynamic coefficients matched the classic calculations of Lund and Orcutt, and the computed bending mode shapes near 53 and 89 hertz agreed well with an independent ANSYS three-dimensional finite-element model.

The headline finding concerns how violently the support conditions redistribute under end loading. At rest, the journal attitudes are nearly symmetric, with the outer pair of bearings mirroring each other. Apply a modest end load, and that symmetry collapses. Within the 0 to 25 newton range, the flexible-deformation index at the loaded-end bearing, labeled J4, surges by 266.5 to 402.2 percent, while the inner supports J1 and J3 actually decrease and J2 barely moves. At 25 newtons, the index at J4 reaches 4.19 to 6.02 times that of J1 and 1.76 to 2.33 times that of J3. The physical picture is one of concentration: shaft flexibility funnels the eccentricity-inclination coupling into the loaded-end bearing while the inner supports respond mainly through load redistribution.

The consequences for the oil films themselves are even more striking. At 3000 rpm, the non-dimensional stiffness trace of the loaded-end support increases by 4298.0 percent and its damping trace by 293.6 percent. At 2884 rpm, the direct-stiffness trace of J4 climbs from 2.66 million to 125 million newtons per meter, roughly 47 times its initial value. Meanwhile the neighboring support J3 weakens markedly, its stiffness and damping traces falling by 62.4 and 36.8 percent, and J1 and J2 change only modestly. The cross-coupled stiffness term at the loaded end even reverses sign near a deformation index of 0.96, signaling a strongly asymmetric pressure field at high tilt. In short, the four-bearing boundary evolves from a comparatively shared support distribution into a strongly nonuniform, loaded-end-dominated one. The authors are careful to note that the exact extreme pressure peaks and coefficient amplitudes near the limiting thin-film state remain model-dependent, since the formulation is isothermal with a non-mass-conserving half-Sommerfeld cavitation treatment, but the direction and ordering of the redistribution proved robust across sensitivity checks.

Here is where the story takes its most counterintuitive turn. One might expect that a support suddenly 47 times stiffer would dramatically shift the rotor’s critical speeds, the rotation rates at which synchronous vibration resonates. It barely does. By continuously tracking the synchronous modal branches with a mass-weighted complex modal assurance criterion, which prevents closely spaced modes from being confused with one another, the team found that the two low-order forward and backward whirl branches near 2884 and 2895 rpm shift by only minus 0.00037 percent and plus 0.00039 percent respectively, essentially nothing. The higher-order branches H1 and H2 move a bit more, by plus 0.0140 and plus 0.1477 percent, and an additional high-order synchronous intersection appears at 5843.2 rpm in the highly deformed state. Yet even these larger shifts are tiny compared with the local stiffness explosion, and the global mode shapes themselves remain almost unchanged.

The resolution of this paradox lies in modal participation. The bearing locations are simply not very important players in the low-order bending modes: the shaft flexes between the supports in ways that barely engage the oil films, so even a massive local stiffness change barely registers. In the higher-order modes, and especially H2, the bearings matter far more. The generalized bearing-stiffness participation and the bearing-location displacement participation for H2 reach 1.449 percent and 0.0568 percent in the low-deformation state, approximately 23.6 and 22.1 times the corresponding forward-whirl values, and its critical-speed sensitivity rises in the same order. The support redistribution acts as a filter: the same local hydrodynamic change is transmitted into the global dynamics only in proportion to how strongly each modal branch involves the bearing locations. This explains why the first bending mode is reshaped more clearly in character than the main low-order critical speeds are shifted in frequency.

For engineers designing camshafts, compressors, and any flexible rotor carried on multiple oil-film bearings, the message is practical and profound. Local bearing coefficients measured or assumed in isolation cannot predict system behavior, because the four supports form a single coupled hydrodynamic network whose state emerges from shared shaft deformation. A designer who hardens one bearing without accounting for the induced weakening of its neighbors may misjudge both the lubrication regime and the vibration margin. The study’s framework, linking shaft flexibility, journal attitude redistribution, oil-film coefficient evolution, and branch-dependent modal sensitivity in one coherent chain, extends misaligned-bearing research from local lubrication analysis to the evolution of dynamic boundaries in whole multi-support systems. The authors note that conditions involving mixed lubrication, mass-conserving cavitation dynamics, or large-amplitude transient squeeze would require extended formulations, but within the converged hydrodynamic regime they examined, the mechanism is clear: the global dynamic consequence of local oil-film strengthening is governed not by the magnitude of the local change alone, but by how the redistributed support couples into each mode of the spinning shaft.

Subject of Research: Hydrodynamic support redistribution and modal response in flexible multi-support bearing-rotor systems

Article Title: Shaft-flexibility-induced hydrodynamic support redistribution and modal response in a multi-support bearing-rotor system

Article References: Zhang, Y., Li, B., Xu, W., Guo, H., & Yuan, Y. (2026). Shaft-flexibility-induced hydrodynamic support redistribution and modal response in a multi-support bearing-rotor system. Mechanical Sciences, 17(2), 857-871. https://doi.org/10.5194/ms-17-857-2026

Image Credits: AI Generated

DOI: 10.5194/ms-17-857-2026

Keywords: journal bearings, rotor dynamics, shaft flexibility, hydrodynamic lubrication, journal misalignment, oil-film stiffness, critical speeds, modal analysis, fluid-structure interaction, Timoshenko beam, Reynolds equation, camshaft

The study, published in Energy Reports by Xiangxu Wang, Junjie Sun, Xinwei Li, Xiaoheng Zhang, Shubo Hu, Jifeng Cheng, Chao Wang, and Qiang Zhang, addresses a fundamental gap in how engineers assess frequency security. Frequency is one of the key indicators for monitoring and operating alternating-current power systems, and dispatching agencies must accurately assess frequency conditions and develop adequate control measures to keep fluctuations within the nominal range. Several large-scale power incidents in recent years, including major blackouts, have demonstrated that wide-range frequency fluctuations are a primary cause of cascading failures. Frequency response, the collective reaction of generation and load to a sudden power imbalance, serves as the first line of defense, working alongside automatic generation control to arrest frequency decline before protective relays begin shedding load.

Existing analytical approaches to frequency response analysis trace back to a landmark low-order System Frequency Response model that assumed frequency behaves identically everywhere in the grid, an assumption reasonable when synchronous machines dominate. But modern grids violate that assumption in two profound ways. First, the resources providing frequency response have diversified. Renewable generators and aggregated virtual power plants now offer so-called fast frequency response through virtual inertia and droop control implemented in power-electronic converters, while battery storage, flywheels, and industrial interruptible loads such as electrolytic aluminum plants inject power in rapid step changes. Second, because these resources are geographically uneven, the frequency spatial distribution characteristics across interconnected regions have become pronounced, meaning each region experiences a distinct rate of change of frequency, a distinct frequency nadir, and a distinct recovery trajectory after a disturbance.

Ignoring this spatial variation, the authors argue, can lead to misjudgments of frequency stability and inaccurate control, causing local frequency instability even when the system-wide average appears secure. The problem with capturing it is mathematical: once the transmission network is retained in the model, power angle coupling between generators causes the model order to balloon exponentially, making analytical solutions infeasible for realistic systems. Earlier regional frequency response models either worked only for two regions, required Taylor series expansions running to ninety-first order, relied on empirical parameter estimation, or omitted fast frequency response resources altogether. None of the previous closed-form regional models, the researchers note, simultaneously captured the frequency spatial distribution characteristics, incorporated fast frequency response resources, and achieved a rigorous closed-form solution.

The new model does all three for a three-region interconnection, which the authors consider a fundamental and representative form sufficient for engineering practice. Each region is modeled as an equivalent generator obeying a simplified swing equation, with three categories of frequency response resources represented: synchronous generators with their dominant reheat governor dynamics retained and faster time constants discarded; proportional or derivative response resources such as wind, photovoltaic, and virtual power plants that respond to both frequency deviation and its rate of change; and step response resources such as batteries and flywheels that inject a preset power increment for a specified duration. Between regions, a DC power flow approximation, which linearizes the nonlinear power flow equations by neglecting reactive power and voltage dynamics, describes how power transfers across tie lines in response to rotor angle differences, preserving the crucial network coupling while keeping the equations tractable.

The mathematical centerpiece of the paper is a striking analogy: the regional frequency response problem is shown to be isomorphic to the forced vibration of a three-degree-of-freedom mass-damper-spring system. The inertia matrix of the power system plays the role of mass, the damping coefficients play the role of the vibration damper, the network admittance plays the role of stiffness, and the power deficit plays the role of external excitation. This correspondence allows the researchers to import the well-established modal analysis method from vibration mechanics. Solving the eigenvalue problem of the undamped free vibration equation reveals that a three-region grid possesses three modes. The first, with a zero eigenvalue and a uniform eigenvector, represents the rigid-body motion of the whole system, which corresponds exactly to the frequency of the system’s center of inertia, the weighted average frequency that all regions eventually converge toward. The remaining two modes describe damped inter-regional oscillations, the relative swinging of one region’s frequency against the others.

The resulting closed-form solution for any region’s frequency is therefore the linear superposition of three terms: the identical center-of-inertia component shared by all regions, and two proportional damped-sinusoidal oscillation components driven by the other two regions. Because the three regional systems are weakly interconnected, a forced decoupling approximation renders the modal equations independent, allowing each to be solved analytically and transformed back through the inverse Laplace transform. The final expressions are concise, symmetric, and require no iteration: frequency at any instant in any region can be computed directly from grid parameters and disturbance data, with the computational load equivalent to a single step of a conventional iterative solver.

The validation is where the model proves its worth. On a modified IEEE Western System Coordinating Council nine-bus test system, reconfigured with 120 megawatts of wind power and 70 megawatts of energy storage so that fast frequency response resources hold 30 percent of capacity, a sudden 100-megawatt load increase exposed dramatic discrepancies in the older system-wide model. In one region the true maximum rate of change of frequency was 1.926 hertz per second, while the single-frequency model predicted minus 0.988, and the time to frequency nadir in another region was off by nearly a full second, deviations that could lead to drastically different control strategies. The new three-region model tracked the reference curves closely.

More compelling still is the test against a real provincial power system in China: 48 buses, 123 transmission lines, 313 loads, 44 synchronous generators across nine conventional plants, and 73 doubly fed induction generators across five wind farms, with renewables supplying 24 percent of generation. Benchmarked against PSASP, a commercial full time-domain simulation package using sixth-order generator models, the new analytical model computed all frequency response indicators in 23 milliseconds, roughly 480 times faster than the 11-second simulation, with mean absolute percentage errors of just 3.06 percent for maximum rate of change of frequency, 6.26 percent for maximum frequency deviation, and 15.73 percent for time to nadir. The older system-average model, by contrast, posted errors as high as 38 and 152 percent and took no less time. The study also mapped the model’s boundaries: as long as spinning reserve stays within the standard engineering range of 6 to 12 percent of load, generator output saturation never activates and accuracy holds; only under abnormally thin reserves, where generators hit output limits during transients, do the linear assumptions break down.

The practical implications reach well beyond a faster calculator. Millisecond-scale analytical frequency assessment makes online situational awareness, emergency control, economic dispatch, reserve planning, and unit commitment with explicit frequency constraints genuinely feasible on modern, low-inertia grids, letting operators coordinate scarce conventional frequency response with rapidly growing fast frequency response from renewables and storage. The authors acknowledge the model’s simplifications, including neglected dead zones, limiters, and reactive power coupling, and propose piecewise linearization, superposition of active and reactive components, and hybrid data-physics methods as remedies. Future work will incorporate the uncertainties of renewable output, customer behavior, and weather to capture the probabilistic distribution of frequency, an essential step as grids worldwide race toward decarbonization without sacrificing the split-second stability that modern life depends on.

Subject of Research: Analytical modeling of regional frequency response in three-region interconnected power systems with fast frequency response resources

Article Title: Regional frequency response analytical model for three-region interconnected power systems considering fast frequency response resources

Article References: Wang, X., Sun, J., Li, X., Zhang, X., Hu, S., Cheng, J., Wang, C., & Zhang, Q. (2026). Regional frequency response analytical model for three-region interconnected power systems considering fast frequency response resources. Energy Reports, 16, Article 109670. https://doi.org/10.1016/j.egyr.2026.109670

Image Credits: AI Generated

DOI: 10.1016/j.egyr.2026.109670

Keywords: frequency response, fast frequency response, interconnected power systems, frequency spatial distribution, low-inertia grids, modal analysis, closed-form solution, renewable energy, RoCoF, frequency nadir, power system stability, Energy Reports