Magnitude Of Displacement Research Articles

Modified gravity: gravitationally coupled bodies displace the center of mass of each other

Empirical observations have revealed that Newtonian dynamics do not correspond with the amount of visible matter in galactic scales. This imply that there is a vast amount of unseen matter or failure of the theory of gravity in galactic scales or something else. This paper demonstrates that gravitationally coupled bodies offset the center of mass of each other from either very center. Gravitational interaction among particles composing gravitationally coupled bodies lead to displacement of their (bodies) centers of mass towards each other. The magnitude of displacement of the center of mass of a body depends on its mass density, separation distance between the bodies, and mass of the body exerting the gravitational pull. This phenomenon reduces the separation distance between the bodies, thus increasing the net gravitational force between them (bodies).

Ultrasound rejuvenation for upper facial skin: A randomized blinded prospective study.

Growing demand for facial rejuvenation drives advancements in these therapies, including laser, radiofrequency, and focused ultrasound, alongside thermal stimulation adjuncts. These methods, known for stimulating collagen regeneration, skin tightening, and lifting, have gained popularity due to their minimal side effects, low trauma, and high safety, demonstrating favorable outcomes in clinical practice. We sought to assess the efficacy of ultrasound skin tightening for brow lift within the scope of a procedure addressing facial sagging across the entire face. Our aim was to explore a noninvasive method capable of effectively enhancing mild to moderate brow ptosis by tightening and lifting the skin in the upper facial region. This was a rater-blinded, prospective cohort study. The upper facial region of the participants was treated with the new device, micro-focused ultrasound (MFU), in model D3.0/D2.0/M3.0. Outcomes of brow lift were measured in comparison of pretreatment and posttreatment photographs and three-dimensional (3D) vector analysis. A total of 42 participants (37 females) were enrolled, with 2 participants withdrawing from the trial, resulting in 40 subjects who completed 180-day-follow-up and evaluation. 35 (87.5%) were deemed to have clinically significant brow elevation by two blinded assessors (experienced clinicians) at 180-day posttreatment (p < 0.01). The mean change in brow height after 90-day was 2.16 ± 0.63 mm at the frontal position (straight-ahead gaze) (p < 0.01). The 3D vector analysis reveals varying magnitudes of vector displacement in the upward and outward directions of the skin on the frontal region above the eyebrows. Focused ultrasound appears to be a safe and effective method for upper facial skin rejuvenation. A single focused ultrasound treatment on the forehead and temple areas resulted in an average brow elevation of 2.1 mm.

A Numerical Study of Fault Reactivation Mechanisms in CO2 Storage.

Due to extensive industrialization and ongoing fossil fuel consumption, CO2 emissions have significantly contributed to climate change and rising greenhouse gas levels. The collection and storage of CO2 in subsurface geological formations have been proposed as a feasible alternative. The well-documented In Salah storage site is the subject of the chosen case study. For the numerical analysis, a two-dimensional finite element simulation of fault reactivation processes was conducted in the context of the CO2 storage. The goal of this research is to conduct a mechanistic numerical analysis of a typical CO2 storage condition. The selected analysis domain is 4 km (width) × 2 km (depth) and includes all important domains and formations (overburden, main caprock, lower caprock, and underburden) of the In Salah site. The simulation results indicate that the influence of fault reactivation under 32 MPa of base injection pressure results in peak vertical deformation of 0.044 m in the caprock and a vertical displacement magnitude of 0.015-0.020 m at the surface level (Z = 0 m). The derived vertical deformation findings at the surface level are in agreement with the data obtained from the in situ InSAR monitoring system in 2009. The effects of the changes in the fault dip angle, key caprock mechanical parameters, and in situ stress ratio on the displacement profile are evaluated within the parametric study. In comparison to the benchmark numerical run, the scenario ratio of k = 0.5 led to a significant reduction in the displacement. The simulation in which the fault dip angle was 30° produced a more pessimistic result with a larger displacement field. This could be an indication of heightened fault reactivation risks associated with low-angle faults in storage sites with strong horizontal stress regimes due to the combined effect of increased shear stress and reduced inherent frictional resistance on the fault plane. Considering that a vertical fault dip angle (90°) and an additional three 20 m long vertical fractures above the reservoir produced similar vertical displacement observed with the fault dipping at a 60° angle, this indicated that the vertical faults in the vicinity of the storage site pose limited safety risks to the integrity of the sealing rock.

Construction and validation of a brain magnetic resonance imaging template for normal older Koreans

BackgroundSpatial normalization to a standardized brain template is a crucial step in magnetic resonance imaging (MRI) studies. Brain templates made from sufficient sample size have low brain variability, improving the accuracy of spatial normalization. Using population-specific template improves accuracy of spatial normalization because brain morphology varies according to ethnicity and age.MethodsWe constructed a brain template of normal Korean elderly (KNE200) using MRI scans 100 male and 100 female aged over 60 years old with normal cognition. We compared the deformation after spatial normalization of the KNE200 template to that of the KNE96, constructed from 96 cognitively normal elderly Koreans and to that of the brain template (OCF), constructed from 434 non-demented older Caucasians to examine the effect of sample size and ethnicity on the accuracy of brain template, respectively. We spatially normalized the MRI scans of elderly Koreans and quantified the amount of deformations associated with spatial normalization using the magnitude of displacement and volumetric changes of voxels.ResultsThe KNE200 yielded significantly less displacement and volumetric change in the parahippocampal gyrus, medial and posterior orbital gyrus, fusiform gyrus, gyrus rectus, cerebellum and vermis than the KNE96. The KNE200 also yielded much less displacement in the cerebellum, vermis, hippocampus, parahippocampal gyrus and thalamus and much less volumetric change in the cerebellum, vermis, hippocampus and parahippocampal gyrus than the OCF.ConclusionKNE200 had the better accuracy than the KNE96 due to the larger sample size and was far accurate than the template constructed from elderly Caucasians in elderly Koreans.

Self-powered synchronous asymmetric voltage flip and charge extraction technique for piezoelectric energy harvesting

Abstract This paper presents a nonlinear interface circuit for piezoelectric vibration energy harvester (PEH) with Synchronous Asymmetric Voltage Flipping and Charge Extraction process, denoted as SAFCE. SAFCE flips the PEH voltage polarity at positive peak and completely extracting charge at negative peak through LC resonance. The harvested power is independent of load. In theory, the harvested power is 200 % of SECE and 780 % of best impedance-matched SEH due to the energy injection mechanism, which enhances the electromechanical coupling coefficient of PEH. Moreover, a self-powered SAFCE circuit without rectifier bridge is designed, which reduces power consumption and eliminates the need for external power sources. Experimental measurements are carried out to compare with SEH and SECE circuits under the condition of either constant displacement magnitude (0.5 mm) or constant external excitation acceleration (10 m/s2). The experimental results indicate that the power harvested by the SAFCE technique increased by 171 % compared with the SECE method and by 381 % compared with the best impedance-matched SEH method under the same conditions.

Seismic performance of sheet pile walls in liquefiable soil using centrifuge tests and an assessment of nonlinear effective stress analysis using PM4Sand

Past earthquakes have revealed that damage to sheet-pile walls under saturated conditions is closely linked to excess pore water pressure buildup in the surrounding soil. Nonlinear effective stress analysis (ESA) is commonly employed to assess the seismic performance of sheet-pile walls in liquefiable soils, incorporating constitutive models for liquefaction simulation. However, ESA results are sensitive to uncertainties in input parameters, model calibration, and modeling techniques. Dynamic centrifuge tests conducted in the Liquefaction Experiments and Analysis Project (LEAP) offer valuable insights into important response mechanisms and validate ESA. Seven centrifuge tests on a cantilevered sheet-pile wall model showed that liquefaction did not occur in the backfill near the wall due to net seaward wall displacement but did occur farther away. In addition, the mechanism of wall displacement was mainly due to the shear deformation of the softened backfill, with the displacement magnitude depending on the relative density of soil, peak ground acceleration of base motion, and wall displacement during gravity loading. Nonlinear ESA was performed for three centrifuge tests using FLAC2D and the PM4Sand constitutive model for soil. Gravity analysis captured static wall displacement and initial stress distribution in the soil. Two calibrations of the PM4Sand model were pursued at the element level: C1 calibration for liquefaction strength and C2 calibration for liquefaction strength and the post-liquefaction shear strain accumulation rate. System-level simulations showed similar liquefaction behavior as observed in the tests for both calibrations. However, the C2 calibration provided closer predictions of wall displacements, while the C1 calibration (default for PM4Sand) resulted in larger and more conservative displacements. Overall, the PM4Sand model performed well with minimal calibration, making it suitable for nonlinear ESA of sheet-pile walls.

Effects of jet grouting on adjacent ground through numerical modelling

When using jet grouting for soil stabilisation, effects of the installation process need to be evaluated. This could be particularly important for applications in challenging ground conditions and low initial ground stability. This study investigates such effects in soft marine clays using numerical finite-element (FE) simulations for both flat and sloping terrains. Additionally, an analytical solution using the modified Hagen–Poiseuille equation was developed to (a) assess the pressure induced by the grout at any installed depth and (b) illustrate the importance of maintaining a proper amount of return flow to avoid build-up of excessive pressures in the ground during the jet-grouting process. Combining the analytical and the FE simulations, jet-grouting induced soil displacements, were determined. For flat terrain, the area affected by jet grouting was approximately three to four times the column radius. By contrast, for the studied slope (inclination of 1 : 3), the influenced area increased to about ten times the column radius. The obtained displacement magnitude was also considerably larger for sloping terrain than for flat terrain. The reported findings relate to jet grouting in marine clays (which is not the normal application of this technology) and cannot be extrapolated to other soils.

Multi-Story Volumetric Blocks Buildings with Lower Frame Floors

This article presents the results of experimental studies of the stress–strain state of volumetric blocks based on the underlying frame structures. The aim of the research is to evaluate the stress–strain state and the nature of damage development as a result of an increase in the load up to a critical level. Based on the analysis of the nature of the damage, recommendations have been developed to strengthen the destruction zone. Data were collected on the redistribution of stresses and deformations, the formation of cracks and joint openings, the magnitude of horizontal displacements, and the failure mode of volumetric blocks and floor frames. Five full-scale volumetric blocks were tested under the loading of hydraulic jacks, differing in concrete type, reinforcement, presence of doors, and dimensions of the stylobate beams. When the volumetric modules were supported by a frame floor the results revealed that the maximum destructive load of 10,462 kN was observed in the first specimen; the horizontal displacements of the walls decreased by 13–18 mm, and there was a decrease in the crack opening width to 0.5 mm. The cracks decreased the strength of the walls, leading to a redistribution of the compressive stresses and their increase in the support zone. The most significant compressive strains in concrete in the corner parts of longitudinal walls were in the range of (600–620) × 10−6, and in the middle part of the walls, 370 × 10−6 were observed. Furthermore, the largest cracks caused significant horizontal displacements (deplanation) of the walls, which decreased the stiffness of the conjunction of longitudinal walls with the floor slab and created an additional eccentricity of the vertical force. Based on the findings, the correlation between the measured parameters of each specimen at all stages of vertical load increase is demonstrated and illustrated in graphs of the measured parameters. The importance of quantity compliance with the initial rigid connection between the longitudinal wall and ceiling plate has been estimated.

Evaluating the Use of Seasonal Surface Displacements and Time‐Variable Gravity to Constrain the Interior of Mars

AbstractThe mass transport of volatiles on Mars represents a seasonally changing load on the surface of the planet. Like on Earth, as mass is redistributed across the planet, the surface responds in a complex manner becoming displaced downwards or upwards. The magnitude and extent of displacement depend on the properties of the load and mechanical properties of the planetary interior. Based on new estimates of the height variation of the seasonal polar caps (SPCs), we predict local surface displacements of up to tens of millimeters with a strong degree 1 signal throughout the Martian year. The long‐wavelength portion of the displacement is potentially observable, with a magnitude of a few millimeters, located away from the SPC where one could realistically measure it with a landed or orbital mission. We also model the direct contribution of this process to observable time variable gravity, where we find the zonal coefficients to be in line with previous measurements, although with a smaller magnitude. Future measurements of this displacement could be used to help elucidate the composition of the interior of Mars using this process as a probe into the Martian interior. Furthermore, more refined measurements of time‐variable gravity would be a powerful tool in constraining the pole‐to‐pole volatile cycle present on Mars.

Deformation of the Gruithuisen region lava tube under compressional stress on the Moon

The lava tube in the Gruithuisen region on the Moon is intriguing because it is characterized by a distinctive chain of collapsed pits and raised features, providing an opportunity to understand the potential morphologic deformation of lunar lava tubes under compressional stress. This study aimed to understand the morphological deformation in the Gruithuisen region’s lava tube when subjected to compressional stress. A combination of numerical simulations and morphometric analysis was employed to achieve this objective. The morphometric analysis of different collapsed and raised features associated with a lava tube in the study area revealed eight characteristic morphologies ranging from curvilinear channel-like to elliptical shape. Notably, average normal stress and strain values derived from a wrinkle ridge were found to be ∼70 MPa and 2 × 10−3, respectively, and wrinkle ridges exhibited a northward orientation. These quantified parameters were utilized as the foundation for initializing three-dimensional models. Furthermore, the outcomes of the models closely replicated the deformation in the Gruithuisen region, emphasizing the significant role of compressional stress in the deformation of the lava tube. These models suggest that the observed eight unique features associated with the lava tube arise from disparities in displacement magnitude and direction along three axes (x, y, z). Our research sheds light on the structural transformations of lava tubes when subjected to varying compressional stress and enhances understanding of the ways in which the interplay between compressional tectonic activity and lava tube features has shaped the Moon’s surface.

An Optical Sensor for Measuring Displacement between Parallel Surfaces.

An optoelectronic sensor was developed to measure the in-plane displacement between two parallel surfaces. This sensor used a photodetector, which was placed on one of the parallel surfaces, to measure the intensity of the red (R), green (G), blue (B), and white/clear (C) light spectra of a broad-spectrum light that was reflected off a color grid on the opposing surface. The in-plane displacement between these two surfaces caused a change in the reflected RGB and C light intensity, allowing the prediction of the displacement direction and magnitude by using a polynomial regression prediction algorithm to convert the RGB and C light intensity to in-plane displacement. Results from benchtop experiments showed that the sensor can achieve accurate displacement predictions with a coefficient of determination R2 > 0.97, a root mean squared error (RMSE) < 0.3 mm, and a mean absolute error (MAE) < 0.36 mm. By measuring the in-plane displacement between two surfaces, this sensor can be applied to measure the shear of a flexible layer, such as a shoe's insole or the lining of a limb prosthesis. This sensor would allow slippage detection in wearable devices such as orthotics, prostheses, and footwear to quantify the overfitting or underfitting of these devices.

Effect of geometrical design variables on implantation configuration and fixation stiffness of titling bone anchors: A parametric finite element study

The mechanical interaction of a tilting anchor and cancellous bones of various densities was simulated using finite element modeling. The model enjoyed a sophisticated representation of the bone, as an elasto-plastic material with large deformation capability. The anchor's tilting action during implantation phase, as well as its fixation stiffness during pull-out test, were predicted by the model and a parametric study was performed to investigate the effects of the anchor's distal width and corner fillet radius, on these measures. The model predictions were validated against the results of an experimental test on ovine humerus specimens. The model could reasonably reproduce the tilting action of the anchor during the implantation phase. Comparison of the model predictions with the experimental results revealed similar trends during both the implantation and the pull-out phases, but smaller displacement magnitudes (end points: 1.4 vs. 2.1 mm and 4.6 vs. 5.2 mm, respectively). The results of the parametric study indicated substantial increase in the fixation stiffness with increasing bone density. Reducing the distal width and increasing the fillet radius improved the anchor's implantation configuration and fixation stiffness in low-density bones. For high-density bone applications, however, a larger distal width was favored for improving the fixation stiffness.

On the role of aortic valve architecture for physiological hemodynamics and valve replacement, Part II: Spectral analysis and anisotropy

Severe aortic valve stenosis can lead to heart failure and aortic valve replacement (AVR) is the primary treatment. However, increasing prevalence of aortic stenosis cases reveal limitations in current replacement options, necessitating improved prosthetic aortic valves. We investigate flow disturbances downstream of severe aortic stenosis and two bioprosthetic aortic valve (BioAV) designs using advanced energy-based analyses. Three-dimensional high-fidelity fluid–structure interaction simulations have been conducted and a dedicated and novel spectral analysis has been developed to characterise the kinetic energy (KE) carried by eddies in the wavenumber space. In addition, new field quantities, i.e. modal KE anisotropy intensity as well as normalised helicity intensity, are introduced. Spectral analysis shows kinetic energy (KE) decay variations, with the stenotic case aligning with Kolmogorov’s theory, while BioAV cases differing. We explore the impact of flow helicity on KE transfer and decay in BioAVs. Probability distributions of modal KE anisotropy unveil flow asymmetries in the stenotic and one BioAV cases. Moreover, an inverse correlation between temporally averaged modal KE anisotropy and normalised instantaneous helicity intensity is noted, with the coefficient of determination varying among the valve configurations. Leaflet dynamics analysis highlights a stronger correlation between flow and biomechanical KE anisotropy in one BioAV due to higher leaflet displacement magnitude. These findings emphasise the role of valve architecture in aortic turbulence as well as its importance for BioAV performance and energy-based design enhancement.

Disordered layers and dimerization in the crystal structure of TaOCl2

Understanding the properties of transition metal materials requires consideration of the competition between the various types of electrons that comprise the system, whether they be delocalized and metallic, localized and magnetic, or localized and bonded. Here we report the refined crystal structure determination and physical properties of the two-dimensional layered compound TaOCl2. Within each layer we find a strong in-plane dimerization of Ta atoms perpendicular to the Ta-O-Ta chains, with significant disorder in the positioning of dimers in adjacent layers, suggesting that the free electron of each Ta localizes in Ta-Ta bonds. This is supported by resistivity measurements (ρ300K = 4.4*108 Ω-cm) as well as featureless, temperature-independent magnetic susceptibility up to T = 750 K. Analysis of the phonon contribution to specific heat shows the presence of a localized Einstein mode with TE = 175 K, attributed to the localized vibrations of the Ta-Ta dimers. Density functional theory calculations show that the magnitude of the Ta displacements (0.24 Å) has a dramatic effect on the electronic structure, changing from a metal with a bandwidth of 3.2 eV to an insulator with a flat band just below EF. Our results show how direct exchange interactions between Ta atoms that are relatively far from each other can still play a central role in the behavior of 5d transition metal compounds, taking advantage of the extended 5d atomic orbitals, and produce localized dimers with a bond distance of approximately 2.84 Å.

A prediction model for residual shear strength of liquefiable soil based on lateral spreading cases

The residual shear strength of liquefiable soil plays an important role in evaluating the displacement magnitude of lateral spreading when applying the Newmark sliding block method. Currently, the empirical model is a mainstream alternative method for estimating the residual shear strength. In this study, a database of well-documented lateral spreading cases is used to establish an exponential function for residual shear strength evaluation correlated with the vertical effective stress and normalized standard penetration test blow counts for liquefied soil. A comparative analysis with two other empirical models is conducted, and the lateral spreading of the Wildlife Site during the Superstition Hills earthquake in 1987 is estimated using the Newmark sliding block method. The model exhibits good performance for soil residual shear strength estimation in cases of liquefaction-induced lateral spreading. The average estimated value of the residual shear strength may be appropriate for deterministic analyses in engineering practice.

Thick- and thin-skinned contractional styles and the tectonic evolution of the northern Sangre de Cristo Mountains, Colorado, USA

AbstractThe Sangre de Cristo Mountains of southern Colorado and northern New Mexico, USA, contain an unusual combination of thick- and thin-skinned contractional structures involving both basement and cover rocks in the Laramide Rocky Mountain foreland. These structures are truncated by down-faulted extensional basins to the east and west. Together with synorogenic sediments, these structures preserve a record of the rise of the Ancestral Rocky Mountains, the Laramide orogeny, and Rio Grande rifting. Laramide structures within the mountains provide clues to processes that link the three events and to necessary conditions for thin-skinned and thick-skinned contractional structures to form together in continental interiors.To examine the full variety of structural styles, a portion of the northern Sangre de Cristo fold- and-thrust belt in Colorado was described and interpreted using geologic maps and structural cross-sections. Stratigraphic relations of the Ancestral Rocky Mountain highlands and basin fill were reconstructed from existing maps. These relations allow identification of faults inherited from the Ancestral Rocky Mountains, differentiation of thrust sheets, and in some cases, estimation of the magnitude of displacement. To examine relations between Laramide thrusts and Rio Grande rifting, kinematic data were collected from a thrust fault adjacent to rift faults.Three thrust fault styles were recognized: thin-skinned basement, thin-skinned cover rocks, and thick-skinned basement. Thin-skinned thrusts arising from a hinterland beneath the present San Luis Valley carried sheets of Proterozoic basement rocks northeast over a Laramide foreland. These basement thrusts are interpreted to be faults of the Ancestral Rocky Mountains that reactivated during the Laramide orogeny. The Laramide foreland consists of thin-skinned thrusts and folds in sedimentary cover rocks as young as 49 Ma. Both thin-skinned thrusts in basement and cover rocks are bounded by thick-skinned basement thrusts that moved intermittently throughout the Laramide orogeny.We infer that thin-skinned thrusts form in continental interiors where deformation is focused in weak strata of thick basin fill and in fluid-reaction weakened preexisting faults in basement rocks. Both conditions are met in the Sangre de Cristo Mountains. Basement thrusts adjacent to the San Luis Valley contain evidence of plastic contractional microstructures overprinted by extensional microstructures that may record the transition from Laramide contraction to Rio Grande extension of the crust.

Automating the determination of low-temperature fracture resistance curves of normal and rubberized asphalt concrete in single-edge notched beam tests using convolutional neural networks

As materials undergo large-scale yielding or exhibit large sizes of fracture process zone in the crack tip region, multi-parameter fracture concepts should be employed to describe the complex crack-tip stress-strain fields. Fracture resistance curves (R-curves) are an established tool in characterizing the entire fracture process of such materials. However, for complex materials such as bituminous mixtures, the development of these curves is subject to experimental and computational intricacies. In this research, a framework is developed to automate the construction of R-curves for normal and rubberized asphalt concrete (AC) mixtures. AC mixtures are produced using PG58–22 and PG58–28 binders. Limestone and siliceous aggregates are used, and three binder contents are considered for the mixtures. Single-edge notched beam (SE(B)) fracture testing is conducted on AC beams with two different notch patterns. A convolutional neural network (CNN) model is developed and trained over 1260 test images with varying temperatures, notch geometries, and setups. The CNN model was used to detect the growing crack on the beam surface and each crack-detected image was sent to an image processing framework to measure the crack length. Crack extension increments were calculated and synchronized with test time and magnitude of load, load-line displacement, and cumulative fracture energy, and the R-curve could be constructed. A training accuracy of 0.91 was obtained for the model and a loss of below 0.10 as a result of a hyperparameter tuning indicating reliable classifications by the CNN architecture. The R-curves showed desirable agreement for control mixtures at temperatures of 0 °C and −15 °C. As the mixtures are rubberized, the R-curves showed favorable agreement in the crack blunting phase, transition zone, as well as the unstable propagation phase at −20 °C. Cohesive energy magnitudes were compared for the two methods with a Pearson coefficient of 0.81 while fracture rate and fracture energy magnitudes showed favorably close magnitudes with coefficients of 0.89 and 0.98 respectively.

A novel vector field analysis for quantitative structure changes after macular epiretinal membrane surgery.

The aim of this study was to introduce novel vector field analysis for the quantitative measurement of retinal displacement after epiretinal membrane (ERM) removal. We developed a novel framework to measure retinal displacement from retinal fundus images as follows: (1) rigid registration of preoperative retinal fundus images in reference to postoperative retinal fundus images, (2) extraction of retinal vessel segmentation masks from these retinal fundus images, (3) non-rigid registration of preoperative vessel masks in reference to postoperative vessel masks, and (4) calculation of the transformation matrix required for non-rigid registration for each pixel. These pixel-wise vector field results were summarized according to predefined 24 sectors after standardization. We applied this framework to 20 patients who underwent ERM removal to obtain their retinal displacement vector fields between retinal fundus images taken preoperatively and at postoperative 1, 4, 10, and 22months. The mean direction of displacement vectors was in the nasal direction. The mean standardized magnitudes of retinal displacement between preoperative and postoperative 1month, postoperative 1 and 4, 4 and 10, and 10 and 22months were 38.6, 14.9, 7.6, and 5.4, respectively. In conclusion, the proposed method provides a computerized, reproducible, and scalable way to analyze structural changes in the retina with a powerful visualization tool. Retinal structural changes were mostly concentrated in the early postoperative period and tended to move nasally.

Analytical approach to piezoelectric model synthesis with the use of Cauer's method for system design.

Piezoceramic materials have unique property which enables direct and bilateral conversion between mechanical and electrical energy. This ability facilitates significant miniaturisation of technology and opens many opportunities in design of new actuators and energy harvesters. Mathematical modelling of piezoelectric modules is notoriously hard due to complex constitutive equations defining mechanical and electrical energy conversion. The article presents research on a new synthesis method based on the Cauer's method. Mechanical damping is introduced with the use of Rayleigh's approximation. A discrete electromechanical model is formed based on the Mason's piezoelectric model. The proposed approach allows modelling of piezoelectric systems based on a set of characteristic frequencies. The method allows a more general approach to the problem of modelling new systems, as opposed to application-oriented methods seen in literature. A non-standard model analysis method using edge graphs and structural numbers is also verified as a potential alternative for matrix-based method. The authors compare their precision and computation requirements. The structural method of mechanical model analysis gave identical results as the reference matrix method. However, the non-classical algorithm took much longer to calculate and was using more memory. The electromechanical model analysis has shown an error of 5% in comparison to resonance frequencies taken from a reference plate specification. The calculated magnitude of displacement was well above the capability of a 3.5mm thick piezoelectric plate. The synthesis method presented in this paper allows synthesizing piezoelectric cascade models based on limited information in form of characteristic frequencies. Currently this method allows a coarse approximation of the real piezoelectric parameters with limited number of inputs. The additional method of analysis based on structural numbers offers a promising alternative to matrix calculations but requires a more thorough investigation of the computational power required to determine whether it can compete with existing algorithms.

Моніторинг сезонних вертикальних зміщень греблі Дніпровської ГЕС

The relationship Methods. A program developed for this purpose processed a time series of GNSS measurements, which allows for determining vertical seasonal displacements and their dependence on seasonal changes in ambient air temperature. Results. A review of scientific works on the temperature field impact on the deformation of hydraulic structures is presented. Based on the studies performed, it was found that in the absence of sharp drops in the water level in the upper reservoir, seasonal changes in ambient temperature have a significant impact on the vertical displacements of dams (in the example of the Dnipro HPP). The magnitude of extreme displacements and the epochs of their manifestation will depend on the dam design and technical parameters. Based on the processed data, a linear relationship was established between the average ambient temperature and the vertical displacements of GNSS control points located at the Dnipro HPP dam, which makes it possible to predict the value of vertical displacements of control points based on the measured temperature value. Accordingly, monitoring these displacements and their changes over time is one of the criteria for assessing the overall condition of the dam. We noticed that during the study period, the extremely positive average rate of the vertical displacements of the control points was in the first half of 2018, +1.03 mm per month, and the extremely negative average rate of 0.83 mm/month was in the second half of 2019. It explained the correlation between the vertical displacement rate of the control point and the depth of the reservoir near it. Scientific novelty and practical significance. The regularities of the relationship between temperature changes and GNSS point displacements revealed in the study can be useful for further research on the processing and analysis of monitoring data for hydraulic structures.