Geometric Variables Research Articles

Collapsing Shear‐Free Anisotropic Embedding Star Model in f(R)$f(R)$ Gravity

AbstractThe current paper studied the dynamics of shear‐free and spherically symmetric collapsing stars by incorporating the features of anisotropic dissipative fluid in the realm of gravity. A complete radiative star model that describes the early static configuration obeying the embedding class 1 approach is generated. To acquittance the exact solutions of the geometric variables, a specific form of pressure anisotropy along with a time‐dependent Karmarkar condition is employed, leading to a spacetime solution that seems to be potentially reliable and regular throughout the collapse process. The matching conditions have been thoroughly investigated between the interior geometry and the Vaidya outgoing solution over the junction interface. The physical attributes of our solutions to the Einstein field equations under two viable and cosmologically well‐consistent models of are manifested. The presented features are in a stable equilibrium state and sustainable to model a dynamic structure of gravitational collapse without forming the black hole.

Presenting new artificial intelligence techniques for finding optimum performance of solar chimney power plant

The various applications of solar energy have progressed significantly over recent decades. In this paper, finding the optimum performance criteria of a SCPP is studied. The mathematical modelling of 1-D flow is written and the optimum performance is determined for each group of geometric and environmental variables including the angle of collector roof (β), chimney divergence (α) and ambient wind velocity (Va ). In addition, different artificial intelligence techniques including regression tree, genetic programming and a novel method named trended regression tree are applied to find optimum performance conditions at any arbitrary group of α, β and Va . Results indicate that maximum power output (Pt ) and associated mass flow rate ( m ˙ ) increase with increasing chimney divergent angle and wind velocity at a constant collector roof angle. Comparing the obtained results of artificial intelligence techniques shows that trended regression tree method predicts the optimum conditions of SCPP better than other methods. Genetic programming is used to present fitted algebraic functions on Pt and m ˙ and the ratio of turbine pressure drop to pressure potential (PR). Results demonstrate the algebraic relation of PR estimates the PR accurately at each group of variables.

Topology Optimization of Shape Memory Alloy Actuators for Prescribed Two-Way Transforming Shapes

This paper proposes a new topology optimization formulation for obtaining shape memory alloy actuators which are designed with prescribed two-way transforming shapes. The actuation behaviors of shape memory alloy structures are governed by austenite-martensite phase transformations effected by thermal-mechanical loading processes; therefore, to realize the precise geometric shape variations of shape memory alloy actuators, traditional methods involve iteration processes including heuristic structural design, numerical predictions and experimental validation. Although advanced structural optimization methods such as topology optimization have been used to design three-dimensional (3D) shape memory alloy actuators, the maximization/minimization of quantities such as structural compliance or inaccurate stroke distances has usually been selected as the optimization objective to obtain feasible solutions. To bridge the gap between precise shape-morphing requirements and efficient shape memory alloy actuator designs, this paper formulates optimization criteria with quantitatively desired geometric shapes, and investigates the automatic designs of two-way prescribed shape morphing shape memory alloy structures based on the proposed topology optimization method. The super element method and adjoint method are used to derive the analytical sensitivities of the objective functions with respect to the design variables. Numerical examples demonstrate that the proposed method can obtain 3D actuator designs that have the desired two-way transforming shapes.

The four operations on perverse motives

Let k be a field of characteristic zero with a fixed embedding \sigma:k\hookrightarrow \mathbf{C} into the field of complex numbers. Given a k -variety X , we use the triangulated category of étale motives with rational coefficients on X to construct an abelian category \mathscr{M}(X) of perverse mixed motives. We show that over \mathop{\mathrm{Spec}}(k) the category obtained is canonically equivalent to the usual category of Nori motives and that the derived categories \mathrm{D}^{\mathrm{b}}(\mathscr{M}(X)) are equipped with the four operations of Grothendieck (for morphisms of quasi-projective k -varieties) as well as nearby and vanishing cycles functors and a formalism of weights. In particular, as an application, we show that many classical constructions done with perverse sheaves, such as intersection cohomology groups or Leray spectral sequences, are motivic and therefore compatible with Hodge theory. This recovers and strengthens work by Zucker, Saito, Arapura and de Cataldo–Migliorini and provides an arithmetic proof of the pureness of intersection cohomology with coefficients in a geometric variation of Hodge structures.

Generalizability of transformer-based deep learning for multidimensional turbulent flow data

Deep learning has been going through rapid advancement and becoming useful in scientific computation, with many opportunities to be applied to various fields, including but not limited to fluid flows and fluid–structure interactions. High-resolution numerical simulations are computationally expensive, while experiments are equally demanding and encompass instrumentation constraints for obtaining flow, acoustics and structural data, particularly at high flow speeds. This paper presents a Transformer-based deep learning method for turbulent flow time series data. Turbulent signals across spatiotemporal and geometrical variations are investigated. The pressure signals are coarsely-grained, and the Transformer creates a fine-grained pressure signal. The training includes data across spatial locations of compliant panels with static deformations arising from the aeroelastic effects of shock-boundary layer interaction. Different training approaches using the Transformer were investigated. Evaluations were carried out using the predicted pressure signal and their power spectra. The Transformer's predicted signals show promising performance. The proposed method is not limited to pressure fluctuations and can be extended to other turbulent or turbulent-like signals.

Design Optimisation of Metastructure Configuration for Lithium-Ion Battery Protection Using Machine Learning Methodology

The market for electric vehicles (EVs) has been growing in popularity, and by 2027, it is predicted that the market valuation will reach $869 billion. To support the growth of EVs in public road safety, advances in battery safety research for EV application should achieve low-cost, lightweight, and high safety protection. In this research, the development of a lightweight, crashworthy battery protection system using an excellent energy absorption capability is carried out. The lightweight structure was developed by using metastructure constructions with an arrangement of repeated lattice cellular structures. Three metastructure configurations (bi-stable, star-shaped, double-U) with their geometrical variables (thickness, inner spacing, cell stack) and material types (stainless steel, aluminium, and carbon steel) were evaluated until the maximum Specific Energy Absorptions (SEA) value was attained. The Finite Element Method (FEM) is utilised to simulate the mechanics of impact and calculate the optimum SEA of the various designs using machine learning methodology. Latin Hypercube Sampling (LHS) was used to derive the design variation by dividing the variables into 100 samples. The machine learning optimisation method utilises the Artificial Neural Networks (ANN) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to forecast the design that produces maximum SEA. The optimum control variables are star-shaped cells consisting of one vertical unit cell using aluminium material with a cross-section thickness of 2.9 mm. The optimum design increased the SEA by 5577% compared to the baseline design. The accuracy of the machine learning prediction is also verified using numerical simulation with a 2.83% error. Four different sandwich structure configurations are then constructed using the optimal geometry for prismatic battery protection subjected to ground impact loading conditions. An optimum configuration of 6×4×1 core cells arrangement results in a maximum displacement of 7.33 mm for the prismatic battery in the ground impact simulation, which is still less than the deformation threshold for prismatic battery safety of 10.423 mm. It is shown that the lightweight metastructure is very efficient for prismatic battery protection subjected to ground impact loading conditions.

On the scalability of helium-filled soap bubbles for volumetric PIV

The scalability of experiments using PIV relies upon several parameters, namely illumination power, camera sensor and primarily the tracers light scattering capability. Given their larger cross section, helium-filled soap bubbles (HFSB) allow measurements in air flows over a significantly large domain compared to traditional oil or fog droplets. Controlling their diameter translates into scalability of the experiment. This work presents a technique to extend the control of HFSB diameter by geometrical variations of the generator. The latter expands the more limited range allowed by varying the relative helium-air mass flow rates. A theoretical model predicts the bubble size and production rate, which is verified experimentally by high-speed shadow visualization. The overall range of HFSB produced in a stable (bubbling) regime varies from 0.16 to 2.7 mm. Imaging by light scattering of such tracers is also investigated, in view of controversies in the literature on whether diffraction or geometrical imaging dominate the imaging regime. The light scattered by scaled HFSB tracers is imaged with a high-speed camera orthogonal to the illumination. Both the total energy collected on the sensor for a single tracer, as well as its peak intensity, are found to preserve scaling with the square of the diameter at object magnification of 10–1 or below, typical of PIV experiments. For large-scale volumetric applications, it is shown that varying the bubble diameter allows increasing both the measurement domain as well as the working distance of the imagers at 10 m and beyond. A scaling rule is proposed for the latter.Graphical abstract

Accelerated simulation methodologies for computational vascular flow modelling.

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.

Design and compressive behaviors of the gradient re-entrant origami honeycomb metamaterials

In recent years, origami honeycomb metamaterials have garnered extensive attention from researchers. Re-entrant origami honeycomb metamaterials exhibit excellent mechanical performances by virtue of lightweight, high-energy-absorbing characteristics and diverse configurations. In this study, the gradient re-entrant origami honeycomb metamaterials are designed by changing significant geometric parameters. To investigate the effects of geometric parameters variations on compressive behaviors, the theoretical analysis model of the re-entrant origami honeycomb is built to predict the compression stress under low-velocity and high-velocity impact. Subsequently, the energy absorption of the uniform re-entrant origami honeycomb (UROH), the gradient-thickness re-entrant origami honeycombs (GTROHs) and the gradient-angle re-entrant origami honeycomb (GAROHs)are investigated under different compression velocities. The impact resistances of UROH, GTROHs and GAROHs are discussed systematically. By adjusting the gradient distribution of thickness, the deformation modes and Poisson’s ratio curves of the structure could be altered. Furthermore, under the high-velocity impact, the specific energy absorption (SEA) of the unidirectionally negative GTROH is increased by 36% than that of UROH at the strain of 0.29. The SEA of the unidirectionally positive GTROH is higher by 14.4% than that of UROH at the strain of 0.8. In addition, the unidirectionally positive GTROH exhibits better impact resistance performance than UROH by comparing the peak stress and SEA value under different compression velocities. This study is expected to provide the new route for designing advanced origami-inspired honeycomb structures and improving buffer protection devices.

Trans-reflective tunable color filter using electro-optic material

This research presents designing a tunable trans-reflective color filter utilizing Barium Titanate (BTO) and optimizing its performance by applying an artificial intelligence (AI) based inverse design model. The AI-based color filter design process is efficient and minimizes design challenges. The AI model comprising two sub-blocks is trained using a dataset that correlates geometrical parameters, refractive index, and input voltage variations with desired color outputs to precisely control the color filter's performance. The first is the parametric optimization block (POB), which employs two deep neural networks (DNNs) in the forward and inverse directions to achieve the optimized geometry of the proposed meta-atoms. Once the optimal parameters are completed, the next block, i.e., voltage tuning block (VTB), is employed to map specific colors onto the refractive index and the applied voltage of the BTO layer. In this way, by changing the voltage of the BTO layer, we can leverage BTO's tunable optical properties, which allow for a broad range of vibrant and customizable colors. The optimized color filter demonstrates enhanced tunability and efficiency, opening up new possibilities for applications in displays and imaging devices.

Deep gold prospectivity modeling in the Jiaojia gold belt, Jiaodong Peninsula, eastern China using machine learning of geometric and geodynamic variables

Gold mineralization in the Jiaojia gold belt was formed in a structurally-dominant hydrothermal mineral system showing a close spatial association with the Jiaojia detachment fault. This study delves into the Jiaojia gold belt from the perspective of coupled spatial association and ore-forming processes by employing spatial analysis of three-dimensional (3D) models, 3D ore-forming numerical modeling, and 3D prospectivity modeling using machine learning techniques (random forest (RF) and multilayer perceptron (MLP)). The overarching goal is to gain insight into the structural-hydrothermal gold system and pinpoint potential areas of deep-seated gold deposits for future exploration endeavors. The spatial analysis of ore-controlling faults uncovers a close correlation between gold enrichment and specific fault geometrical attributes, including a dip angle ranging from 20° to 40°, minimal variations in dip angle (less than 5°), and convex topographical features. These attributes likely stem from the influence of fault morphology on the flow and pooling of fluids. In conjunction with this, 3D ore-forming numerical modeling of structural deformation and fluid flow reveals that gold mineralization is intertwined with moderate volumetric strain and shear strain of rock and fluid divergence. This interaction seems particularly pronounced in areas characterized by channel-like or gentle features. Consequently, it is plausible that gold distribution in the Jiaojia region is the outcome of a comprehensive coupling process involving strain localization, rock deformation, fluid flow, heat transfer and/or interaction. The deep gold prospectivity models of RF and MLP for the Jiaojia district jointly using the predictive variables of fault geometry features and ore-forming simulation data (volume strain, shear strain, temperature variation, and fluid flux) exhibit higher AUC (area under the curve) values compared to models employing individual predictor variable datasets. This improvement underscores their enhanced predictive capability. The prospectivity results thus were used for identifying gold potential within the Jiaojia region, where five promising gold targets at depth were ultimately determined.

Optimization of Customized Industrial Pneumatic Nozzle to Reduce Noise Emissions

This study proposes a customized industrial nozzle for generating impulsive air jets. It is installed on an automatic machine in which wine caps are stacked and shot consecutively into a rotating cylinder by an air jet. This process is very noisy; hence, this study aimed to investigate possible geometric variations of the nozzle that can reduce the emitted noise. First, the nozzle was tested in a laboratory to measure the air consumptions at different supply pressures. Subsequently, 3D models of the nozzle and its variations were created and used for computational fluid dynamics simulations. Different boundary conditions were set, first to validate the model and compare it with the experimental test results, and then to simulate the real working conditions and determine the geometry that is less noisy while maintaining the velocity peak. Among the various possibilities, shortening the final ducts of the nozzle appears to be the most promising solution. These modified nozzles could be easily added to current machines to provide immediate benefits, and this study represents a promising start for action on other machines in which this type of device is present.

Long-Term Evaluation of the Shape of the Reconstructed Diaphragm in Patients with Left-Sided Congenital Diaphragmatic Hernia Using Serial Chest Radiographs and Correlation to Further Complications.

Background: Defining risk factors for long-term comorbidities in patients after neonatal repair of congenital diaphragmatic hernia (CDH) is an important cornerstone of the implementation of targeted longitudinal follow-up programs. Methods: This study systematically assessed serial chest radiographs of 89 patients with left-sided CDH throughout a mean follow-up of 8.2 years. These geometrical variables for the left and right side were recorded: diaphragmatic angle (LDA, RDA), diaphragmatic diameter (LDD, RDD), diaphragmatic height (LDH, RDH), diaphragmatic curvature index (LDCI, RDCI), lower lung diameter (LLLD, RLLD) and thoracic area (LTA, RTA). Results: It was demonstrated that the shape of the diaphragm in patients with large defects systematically differs from that of patients with small defects. Characteristically, patients with large defects present with a smaller LDCI (5.1 vs. 8.4, p < 0.001) at 6 months of age, which increases over time (11.4 vs. 7.0 at the age of 15.5 years, p = 0.727), representing a flattening of the patch and the attached rudimentary diaphragm as the child grows. Conclusions: Multiple variables during early follow-up were significantly associated with comorbidities such as recurrence, scoliotic curves of the spine and a reduced thoracic area. Some geometrical variables may serve as surrogate parameters for disease severity, which is associated with long-term comorbidities.

Synthesis, Characterization, in silico DFT, Molecular docking, ADMET Profiling Studies and Toxicity Predictions of Ag(I) Complex Derived from 4‐Aminoacetophenone

AbstractThe reaction of the synthesized (E)‐1‐(4‐((2,4‐dihydroxy‐6‐methylphenyl)diazenyl)phenyl)ethan‐1‐one, (DMPDE) ligand with Ag(I) ion at room temperature resulted in the formation of the complex; [Ag(DMPDE)(H2O)2]. 1H NMR, 13C NMR, FTIR, UV‐Vis, mass spectra, elemental analyses, thermal analysis (TGA/DTA), and molar conductance measurements were done to elucidate the structure of synthetic compounds. The results revealed an interesting geometrical variation; tetrahedral for Ag(I) complex. FT‐IR spectra demonstrated that the ligand (DMPDE) under investigation behaves as a bidentate ligand (N,O) through the nitrogen atom of the azo group which is the farthest of the acetophenone moiety and oxygen phenolic for benzene moiety and forms a stable five‐membered chelating ring. The electronic structure, molecular electrostatic potential (MEP) and quantum chemical calculations of the newly synthesized compounds are investigated theoretically at the DFT/B3LYP level of theory. Additionally, the ligand (DMPDE) and Ag(I) complex were screened against the growth of pathogenic bacteria [Actinomycosis (G+), E. Escherichia Coli (G−)] and fungi (Penicillium spp.) compared with the reference antibiotics, Chloramphenicol and Nystatin. Furthermore, 1,1‐diphenyl‐2‐picrylhydrazyl (DPPH) was used to evaluate the antioxidant activities of the ligand and its complex, which showed they both possess significant antioxidant properties in comparison with L‐ascorbic acid (Vit. C) as standard. Based on docking studies, (DMPDE) and Ag(I) complex demonstrated a greater affinity for (PDB ID: 3T88), which corresponds to Escherichia coli protein (−6.7818 kcal/mol) and (−6.7928 kcal/mol), respectively. Interestingly, the most active Ag(I) complex inside the active site of cervical cancer receptor (PDB ID: 4XR8) demonstrated a higher binding energy (−6.2631 kcal/mol) than free ligand (−5.8561 kcal/mol). In silico, ADMET displayed that compounds obey the Lipinski rule and the “Veber's rule. Consequently, is likely to exhibit oral bioavailability with good LD50 and a safety profile that includes non‐cytotoxicity, non‐immunotoxicity, and non‐skin sensitization. Finally, the compounds synthesized showed significant anticancer activity in human cervical cancer cell lines HeLa and SiHa compared with positive controls (cisplatin) and normal human hepatic cells (WRL‐68). In the present study, all tested cancer cell lines showed promising activity against Ag(I) complex, whose IC50 value ranged from (61.02 to 71.09) μg/mL.

Numerical evaluation of acoustic emission (AE) sensors by lead-zirconate-titanate (PZT) geometric design

The effect of geometric variation of lead zirconate titanate (PZT) layers on the impedance performance of cylindrical acoustic emission (AE) sensors is investigated through numerical simulations. The finite element numerical models are developed with the use of the simulation program ANSYS and verified by comparing the impedance–frequency responses of the numerical simulations with those of the experiments. The effect of the dimensional changes of the individual PZT disk and ring on the impedance performance is investigated. We devise a total of 13 sensor designs consisting of a disk and either a ring or two rings with varying dimensions, and their impedance-based performances are quantitatively evaluated by counting the number of impedance resonant frequencies nr and average impedance at the resonant frequencies Zr,avg. As a result, it is discovered that the performance of the AE sensors is dominantly influenced by the total area of piezoelectric material At and the area ratio of the disk to ring Rdr. These two geometric indicators might be useful to enhance the performance of the AE sensors in various applications.

A dimensionality reduction method for uncertainty study of geometric variations of turbomachinery blades

Studies on performance impact due to the high-dimensional geometric uncertainties face the “curse of dimensionality” problem, making the cost of uncertainty quantification (UQ) unaffordable. To reduce the number of uncertainties, a sensitivity-based deep dimensionality reduction (SBDDR) method is introduced, verified and applied to the UQ studies of a low-pressure turbine cascade considering geometric variations. The basis modes of geometric variations are extracted from more than one thousand casting turbine blades using principal component analysis (PCA) and ordered by eigenvalues. However, the selection of primary basis mode by PCA neglects the performance impact of geometric variations. In the study, total-order sensitivities of performance parameters to the basis modes are calculated by Sobol analysis, in which fast performance prediction methods are employed. The total-order sensitivities are given in detail, by which the basis modes previously obtained by PCA are reordered. Furthermore, considering different numbers of basis modes ordered by PCA and SBDDR, the statistical means and standard deviations of performance changes are calculated and compared with those obtained by the direct Monte Carlo simulation (MCS). The results show that the SBDDR-based statistics are closer to the MCS ones, especially in the cases considering a limited number of basis modes.

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Abstract. Wind turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend–twist coupling. To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bondline. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We reaffirm that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties, providing updated guidelines for designers in industry.

Effects of Chalcogen Atoms on Excited-State Double-Proton Transfer Behavior for 3,6-bis(4,5-Dihydroxyoxazo-2-yl)benzene-1,2-diol Derivatives: A Computational Investigation.

The impact of the chalcogen atomic electronegativity (O, S, and Se atoms) of new organic molecules on excited-state dynamical reactions is self-evident. Inspired by this kind of distinguished photochemical characteristic, in this work, we performed a computational investigation of chalcogen-substituted 3,6-bis(4,5-dihydroxyoxazo-2-yl)benzene-1,2-diol (BDYBD) derivatives (i.e., BDYBD-O, BDYBD-S, and BDYBD-Se). In this paper, we pay close attention to characteristic BDYBD derivatives that contain intramolecular double hydrogen bonds (O1-H2···N3 and O4-H5···N6). The main goal of this study was to explore how changes in atomic electronegativity affect the way hydrogen bonds interact and how excited molecules affect transfer protons. We go into further detail in the main text of the paper. By fixing our attention to geometrical variations and infrared (IR) vibrational spectra between the S0 and S1 states, exploring hydrogen bonding behaviors using the core-valence bifurcation (CVB) index, and simulating hydrogen bonding energy (EHB) via the atom in molecule (AIM) method, we clarified the photo-induced strengthened dual hydrogen bonding interactions that facilitate the excited-state dual-proton transfer (ESDPT) behavior of BDYBD derivatives. The reorganization of charge stemming from photoexcitation further verifies the tendencies of ESDPT reactions. We relied on constructing potential energy surfaces (PESs) by adopting a restrictive optimization approach, and herein, we finally clarify the gradual ESDPT mechanism of BDYBD derivatives. Particularly, we confirm that the variation in chalcogen atomic electronegativity has a regulatory effect on the ESDPT behavior of BDYBD derivatives; that is, the lower the atomic electronegativity, the more favorable it is for the gradual ESDPT reaction.

Prediction of fatigue life of geometrically deviated steam turbine blades under thermo-mechanical conditions

This study explores the intricate factors affecting the fatigue life of steam turbine blades, encompassing steam flow-induced bending, centrifugal loading, vibration response, structural mistuning, and temperature-dependent influences. By focusing on the significance of mistuned steam turbine blades with varying blade geometries due to manufacturing tolerances, this research has paramount relevance for the power generation industries. By employing finite element analysis (FEA) software, a simplified, mistuned, scaled-down steam turbine bladed disk model was developed, considering temperature-dependent material properties. Initial FEA provided insights into the vibration characteristics and steady-state stress responses, with numerical stress distributions evaluated, which were subsequently exported to Fe-Safe software for fatigue life calculations based on centrifugal and harmonic sinusoidal pressure loadings. By investigating the vibration characteristics and response to geometric blade variations, this study affirmed the reliability of the developed FEA model, with findings highlighting the pronounced sensitivity of fatigue life to blade length, width, and thickness variations, in this order. However, in order to validate the developed numerical models, analytical life cycle assessments were calculated, which exhibited a discrepancy of under 3.37%, reinforcing the applicability of the developed numerical methodology to real-world scenarios involving mistuned steam turbine blades experiencing manufacturing deviations in blade geometry.

Analysis of free in-plane vibrations of a rectangular plate with various boundary conditions canonical form using the modified Riley-Ritz method

This paper investigates the free in-plane vibrations of rectangular sheets under various boundary conditions using an improved Riley-Ritz method. A novel approach involving graph theory and canonical forms is introduced, marking a first in the study of symmetric structures. The research presents an advanced version of Riley’s theory for accurately computing the natural frequencies of structures, showing significant improvements in efficiency and precision over traditional methods like Monte Carlo simulations. Key findings include the ability of the upgraded Riley theory and graphs to conduct comprehensive structural reliability and sensitivity analyses, particularly in evaluating changes in failure risk and aiding in precise design. Numerical analysis demonstrates the method’s rapid convergence and accuracy, proving its effectiveness in structural analysis. The study also explores the impact of geometric parameter variations on the free vibrations of rectangular sheets, offering crucial insights for various engineering applications. These findings have broad implications in mechanical, marine, aerospace, and civil engineering, particularly in the design and analysis of structural components such as fuselages, airplanes, missiles, and tank bottoms.