Natural Shape Research Articles

Bayesian structural damage identification using fraction function regularisation model based on natural frequency and mode shape curvature

ABSTRACT The existing models based on Bayesian inference and L 1 regularisation provide a feasible scheme to the uncertainty problem in structural damage identification. However, L 1 regularisation cannot accurately describe the sparsity of damage due to excessive punishment of large damage parameters, and the mode shape data used by such models are insensitive to the damage. This compromises the accuracy of damage identification. Compared with L 1 regularisation, the fraction function regularisation avoids excessive punishment for larger elements in the damage parameters, resulting in a more accurate sparse solution. The mode shape curvature is more sensitive to damage because it can be viewed as the differential form of the mode shape. Inspired by this, a fraction function regularisation model based on natural frequency and mode shape curvature data is proposed in this paper to further improve the accuracy of Bayesian damage identification. In addition, an improved cuckoo search algorithm is proposed to solve the model by introducing a ranking-based mutation strategy. The results obtained from both the numerical investigation and the experimental study consistently indicate that the proposed method can provide accurate and reliable identification results.

Performance Analysis and Operation Parameter Optimization of Shaker-Type Harvesting for Camellia Fruits

This study aims to address the challenges of achieving a high harvesting rate and low flower bud damage rate during the harvesting of camellia fruits. To this end, a dynamic model of the camellia osmantha tree and a self-developed shaker-type harvesting machine were used as research subjects. The first 24 natural frequencies and mode shapes of the camellia tree were solved using the finite element method, and the effects of vibration frequency, excitation position, and vibration duration on the harvesting rate and flower bud damage rate were quantitatively analyzed through an orthogonal experiment. The numerical analysis results indicate that the camellia tree exhibits good response characteristics at vibration frequencies of 10–15.5 Hz and 38.5 Hz. The three-factors orthogonal experiment figured out that the optimal operational parameters for shaker-type harvesting were determined to be a vibration duration of 30 s, a motor output frequency of 12.5 Hz, and a gripping position height of 50 to 60 cm above the ground. Meanwhile, under these operational parameters, the harvesting efficiency reached 96.97%, while the flower bud damage rate was only 6%.

Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations

The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim of the paper is to control the dangerous vibration of a mechanical system actuator using a pneumatic elastic coupling using different approaches such as analytical calculations, experimental measurement results, and simulation models. Based on the known mechanical properties of the laboratory system, its dynamic model in the form of a twelve-mass chain torsionally oscillating mechanical system is developed. Subsequently, the model is reduced to a two-mass system using the method of partial frequencies according to Rivin. The total load torque of the piston compressor under fault-free and fault conditions is simulated to obtain the amplitudes and phases of the harmonic components of the dynamic torque. After calculating the natural frequency and the natural shape of the oscillation, the Campbell diagram is processed to determine the critical revolutions. There is a pneumatic flexible coupling between the rotating masses, which changes the dynamic torsional stiffness. The dynamic torque curves transmitted by the coupling are compared with different dynamic torsional stiffnesses during steady-state operation and one cylinder failure. The monitored values are the position of the critical revolutions, the natural frequency, the natural shape of the oscillation, and the RMS of the dynamic load torque. The experimental model is verified by the simulation model. The accuracy of the developed simulation model with the experimental data are apparently very good (even more than 99% of the critical revolutions value obtained by calculation); however, it depends on the dynamic stiffness of the coupling. In this study, a detailed, comprehensive approach combining analytical procedures with simulation models is presented. Experimental data are verified with simulation results, which show a good agreement in the case of 700 kPa coupling pressure. The inaccuracy of some of the experiments (at 300 and 500 kPa pressures) is due to the interaction of the coupling’s apparent stiffness and the level of the damped vibration energy in the coupling, which is manifested by its different heating. Based on further experiments, a solution to these problems will be proposed by introducing this phenomenon effectively into the simulation model.

Suturing techniques

The act of suturing wounds on the skin has been done for thousands of years. Closing dead space, supporting and strengthening wounds until healing increases their tensile strength, approximating skin edges for an esthetically pleasing and functional result, and minimizing the risks of bleeding and infection remain the primary goals of suture techniques, even though suture materials and techniques have changed. A well-planned closure or flap may have its post-operative appearance jeopardized if the wrong suture technique is used or if the procedure is not performed well. On the other hand, poor surgical skills cannot entirely be made up for by careful suturing. Poor incision placement with respect to relaxed skin tension lines, excessive removal of tissue, or inadequate undermining may limit the surgeon’s options in wound closure and suture placement. Gentle handling of the tissue is also important to optimize wound healing. The choice of suture technique depends on the type and anatomic location of the wound, thickness of the skin, degree of tension, and desired cosmetic result. Proper placement of sutures enhances the precise approximation of the wound edges, which helps minimize and redistribute skin tension. Wound eversion is essential to maximize the likelihood of good epidermal approximation. Eversion is desirable to minimize the risk of scar depression secondary to tissue contraction during healing. Usually, inversion is not desirable, and it probably does not decrease the risk of hypertrophic scarring in an individual with a propensity for hypertrophic scars. To maximize the esthetic and functional outcomes, dead space must be removed, natural anatomic shapes must be restored, and stitch marks must be minimized. This page describes the methods for placing sutures for different kinds of stitches, goes over why certain suture techniques are better than others and goes over the benefits and drawbacks of each suture technique. For the best possible closure of a wound, multiple suture techniques are frequently required. After reading this article, the reader ought to comprehend the basic techniques for inserting each type of suture as well as how and why specific sutures are selected.

A comprehensive study of beam modal functions in the free vibration analysis of cylindrical shells: Critical examination on the applicability to the clamped-free boundary condition

Over the past few decades, approximate methods that can provide solutions of sufficient accuracy have received considerable attention in the free vibration analysis of cylindrical shells, where a great deal of studies adopted the beam modal functions as the trial functions for the axial mode shapes of cylindrical shells. Nevertheless, most studies were restricted to the application of single term beam modal function and failed to simulate elastic boundary conditions of cylindrical shells, while the accuracy of the corresponding methods has recently sparked significant controversy, especially for cylindrical shells under the clamped-free boundary condition. This paper presents a comparative study of three forms of beam modal functions in the free vibration analysis of cylindrical shells, one of which is proposed for the first time to simulate elastic boundary conditions of cylindrical shells. A unified model is developed using the general Rayleigh–Ritz method, incorporating the breathing modes with circumferential orders being zero, and four types of commonly used thin shell theories, namely the Donnell, Reissner, Love, and Sanders theories. From both perspectives of natural frequencies and mode shapes, numerical results are validated by comparison with those existing in the literature and those calculated from the finite element method (FEM). The results not only clarify the distinction of different forms of beam modal functions used in the Rayleigh-Ritz method, but also provide explanations for the controversy raised in recent studies. Furthermore, the unified formulations can be extended to vibration analysis of various forms of shell structures, and can also be helpful to the vibration analysis of beams and plates with elastic boundary conditions.

How natural disasters and environmental fears shape American climate attitudes across political orientation

Climate change remains a polarizing issue in the United States, with conservatives expressing greater skepticism regarding its risks. We investigate how fear shapes climate attitudes across political orientations. Utilizing data from a 2023 online survey, results support hypotheses that conservatives demonstrate lower climate concern and that fear of natural and environmental disasters increases climate concern. Interaction results show that fear of anthropogenic environmental disasters elicits greater climate concern amongst conservatives. At high levels of ecological fear, the political divisions diminish as all orientations converge on higher levels of acknowledging climate risks and causes. Practically, this relationship highlights messaging opportunities by focusing on relevant environmental threats that aid in influencing conservatives to build collective support across political divides. Theoretically, these findings challenge expectations of dominant paradigms related to threat perception and political orientation, contributing to the ongoing development of new models that more thoroughly represent the relationship between these multifaceted constructs.

A refined output-only modal identification technique for structural health monitoring of civil infrastructures

The increasing installation of structural health monitoring systems has raised the need for efficient and rapid data interpretation algorithms. Operational modal analysis is currently one of the most used techniques for extracting modal properties, and some attempts have been made to automate this procedure. However, automated techniques often require manual calibration of hyperparameters and show inconsistencies across different case studies. This paper proposes a refined version of the automated frequency domain decomposition (AFDD) using the modal assurance criterion (MAC) to obtain natural frequencies and mode shapes. Sensitivity analyses were conducted on the ambient vibration response of the Yonghe cable-stayed bridge in China, accounting for influential factors including noise levels, acceleration record length, sensor layouts. A novel approach is then introduced to interpret the results of the sensitivity analyses. The approach consists in plotting the result of each analysis in a stabilization diagram and then using a Gaussian mixture model that clusters the poles into core and outliers. This allows to identify regions where the MAC thresholds are optimal. By comparing the results of all the sensitivity analyses it was possible to define a single optimal MAC threshold, avoiding the need for fixing a value based on the user’s experience. Three substantially different case studies were analyzed to extensively test the methodology: the Yonghe cable-stayed bridge, the PolyU footbridge in Hong Kong, and Moletta Tower in the Circus Maximus archeological site in Italy. The analysis compared the proposed AFDD algorithm to the traditional frequency domain decomposition and covariance-driven stochastic subspace identification. Specifically, the efficiency in identifying close frequencies, weakly excited modes, spurious peaks, and complex modes was evaluated for each method, which highlighted the robustness of the proposed optimized AFDD. The analysis showcases peculiar characteristics and drawbacks of each method when trying to identify complex vibrational modes of the specific case studies. It was found that the proposed AFDD procedure performs better than traditional methods despite it may misidentify complex modes due to the constraints of a narrower modal domain and similar geometries.

Vibration Analysis of the Bow Bridge With and Without the Soil Foundation

Abstract. Earthquakes can impart the phenomenon of resonance, where the frequencies of seismic waves align with a bridge's natural frequency, causing amplification of vibrations that can lead to structural failures. Aiming to accurately predict potential vulnerabilities posed to the bridge when subjected to earthquakes, this research presents a vibration analysis of the Bow Bridge. Two models, which simulate the Bow Bridge with and without soil foundation, are conducted to investigate the bridges natural frequencies and mode shapes under soilless and soiled conditions. The research result shows that the average vibration frequency in a soiled environment is much lower than that in a non-soil environment, intuitively proving the mitigation of soil environment to bridges vibration frequencies. Based on the agreeable data output, this research demonstrates the feasibility of modeling in the prediction of practical construction.

Modeling Nonspherical Hailstones

Abstract Hail research and forecasting models necessarily involve explicit or implicit—and uncertain—physical assumptions regarding hailstones’ shape, tumbling behavior, fall speed, and thermal energy transfer. Whereas most models assume spherical hailstones, we relax this assumption by using hailstone shape data from field observations to establish empirical size–shape relationships with reasonable degrees of randomness considering hailstones’ natural shape variability, capturing the observed distribution of triaxial ellipsoidal shapes. We also incorporate explicit, random tumbling of individual hailstones during their growth to simulate their free-falling behavior and the resultant changes in cross-sectional area (which affects growth by hydrometeor collection). These physical attributes are incorporated in calculating hailstones’ fall speeds, using either empirical relationships or analytical relationships based on each hailstone’s Best and Reynolds numbers. Options for drag coefficient modification are added to emulate hailstones’ rough surfaces (lobes), which then modifies their thermal energy and vapor exchange with the environment. We investigate how applying these physical assumptions about nonspherical hail to the Penn State hail growth trajectory model, coupled with Cloud Model 1 supercell simulations, impacts hail production and examine the reasons behind the resulting variability in hail statistics. The choice of hailstone size–mass relation and fall speed scheme have the strongest influence on hail sizes. Using nonspherical, tumbling hailstones reduces the number of large hailstones produced. Applying shape-specific thermal energy transfer coefficients subtly increases sizes; the effects of lobes vary depending on the fall speed scheme used. These physical assumptions, although adding complexity to modeling, can be parameterized efficiently and potentially used in microphysics schemes. Significance Statement In numerical modeling of hailstorms, we usually consider hailstones to be spherical to simplify calculations, but in nature, hailstones generally are not spheres and can be rather lumpy and have spikes. The purpose of this study is to examine how the model result would change when nonspherical hailstone shape is implemented. We examine the relationship between hailstone shape and physical processes during hail growth in effort to explain why these changes occur and offer insights on how nonspherical hailstone shape may be parameterized in bulk microphysics schemes.

Comparison Study on the Fatigue Damage of a Container Ship Applying Hydroelastic Fatigue Analysis Procedures of LR and BV Classification Societies

<i>Container ships, which have hatch openings, are subject to low natural frequencies and exhibit elastic behavior due to wave loads, a phenomenon referred to as the hydroelastic effect. Classification societies have established hydroelastic fatigue analysis procedures to address the increased fatigue damage caused by this effect. This study compares the fatigue damage increase ratios at the hatch coaming top corners according to the procedures provided by Lloyd's Register (LR) and Bureau Veritas (BV). The weight distribution was adjusted using mass and interpolation elements, and normal mode analysis was conducted to obtain the natural frequencies and mode shapes of the ship, which were then used in frequency-domain hydroelastic motion analysis. The fatigue analysis was performed based on LR and BV procedures, using mode response amplitude operators (RAOs) and hydrodynamic coefficients derived from the hydroelastic motion analysis. Despite the differing methodologies between LR and BV, similar stress RAOs were obtained, with the midship showing a higher fatigue damage increase ratio than the forward and aft ends. For the LR procedure, more modes are needed for greater accuracy at the aft end, and for the BV procedure, further investigation is required to address the unreasonable response of the dynamic stress RAO in the low-frequency region, which is distant from the resonance frequency.</i>

Free vibration of flexible two links manipulator with variable cross-sectional areas

This paper demonstrated the free vibration of a planar two-link flexible manipulator with harmonic drivers and non-uniformity in the cross-section of links. A dynamic model has been developed that incorporates flexibilities in both link and joint experiencing harmonic vibration, with joint flexibility modeled as torsional spring-inertia components combination. Two links were modeled based on Von Karman’s nonlinear strain relations and theory of the Euler-Bernoulli beam. The nonlinear governing equations were derived using the extended Hamilton’s principle for planar two-link flexible manipulators with variable cross-sections for each link. The coefficients of the obtained partial differential equations were as a function of spatial coordinates and were reduced to the ordinary differential equations for a family of cross-section geometries with exponentially varying widths of rectangular sections of each link. The frequency equation was obtained and analytical solutions of the vibration were achieved for different exponential shapes of each link (widening and narrowing beam for each link). Natural frequencies and mode shapes were presented for varying cross-section areas of the links. The effects of the end masses, payload, beam mass density, flexural rigidity ratio, and joint frequency were investigated on the mode shapes and natural frequencies when the power of the exponential function of the cross-sectional areas of two links was varied. The numerical results were verified with experimental results.

Experimental and Theoretical Studies on the Vibration Serviceability of Composite HCS Floors with RC Topping

Composite hollow–core slab floor with reinforced concrete topping (i.e. CHFT) is relatively new, which can be applied to various long-span structures. However, these systems are typically lightweight and exhibit low damping, posing potential serviceability concerns related to human vibrations. This paper presents a comprehensive vibration test on a 9[Formula: see text]m-long CHFT system. Natural frequencies, damping ratios, and mode shapes of the floor system were obtained through modal tests. The peak acceleration, root–mean–square acceleration, maximum transient vibration value, and perception factor of the floor under heel-drop excitation were obtained through the perceived vibration test and were checked against the available design codes and standards. Sensitivity studies using the finite element method were made to investigate the vibration performance of the CHFT system. Analytical formulas for the fundamental frequency and peak acceleration were derived, which are therefore suggested for practical use. Additionally, an approach for evaluating the vibration serviceability of CHFTs is described.

Flexible Piezoelectric Nanocolumnar Composite Films as Flat-Panel Loudspeakers: Application and Modeling.

Highly anisotropic piezoelectric composites promise to progress electroacoustic devices as a class by combining the advantages of both piezoceramics and polymers. Fundamentally, piezoelectric loudspeakers employ the converse piezoelectric effect to convert electrical to mechanical energy. Quasi-1-3 piezoceramic/polymer composites enable flat-panel loudspeakers that are tunable in elastic modulus, with opportunities for mechanical flexibility, optical transparency, and large-area coverage. Their processing route enables relatively flexible design parameters, such as the particle loading, polymer-matrix modulus, film thickness, film size, and electrode-material stiffness. Alternative processing routes of electric field (E-field) aligned-piezoelectric composites are demonstrated, including using the relaxor ferroelectric lead magnesium niobate-lead titanate (PMN-PT) to enhance the acoustic performance and photocurable resins to accelerate the materials processing. Material properties critical for dielectrophoresis are characterized, and loudspeakers were fabricated based on the optimal processing conditions. Subsequently, electroacoustic characterization explores the effect of loudspeaker size, substrate stiffness, the microphone distance, the piezoceramic material, and the matrix modulus. Finally, finite-element (FE) modeling of the electromechanical behavior validates the natural frequencies and modes shapes of the loudspeakers via the analytical solution and frequency response to electrical and mechanical excitation. Good correspondence between the predicted electroacoustic performance and experimentally validated model is observed.

Determination of the Modal Parameters of the Historical Elevated Water Tank Using Experimental and Numerical Methods

Determining the modal parameters of historical buildings is crucial for understanding their dynamic behavior, which is essential for their preservation and safety for future generations. Experimental and numerical studies are commonly used to characterize modal properties such as natural frequencies and mode shapes. Experimental studies typically employ the operational modal analysis method, while numerical studies employ the finite element method. Vibration measurements of the structure under various environmental conditions, including wind and traffic, were used to determine the modal parameters. However, discrepancies often arise between modal parameters obtained from experimental research and those assessed by finite element models, primarily due to unknown factors like boundary conditions and material properties. The purpose of this study was to measure the vibrations of a historic elevated water tank a 150-year history under ambient conditions to determine its modal characteristics. Comparing the modal parameters obtained from numerical and experimental investigations revealed that the water tank's finite element model requires updating to align with the findings of the experimental modal study. Using the updated finite element model in future evaluations or assessments of the structure can lead to a better understanding of the behavior of the structure.

Vibro-acoustic characterization of Functionally Graded Multiwalled Carbon Nanotube composite cylindrical panels: An experimental approach

This study experimentally investigates the vibro-acoustic properties of Functionally Graded Multiwalled Carbon Nanotubes (FG-V MWCNT) Glass Fiber Reinforced Polymer composite cylindrical panels, a topic often explored through numerical methods. A novel process methodology is introduced to realize FG-V MWCNT composites, and the results are compared with those of uniformly distributed and conventional composites. Using an in-house developed experimental setup, the natural frequencies, mode shapes, acceleration, and Sound Pressure Levels (SPL) are measured. The FG-V MWCNT composites demonstrate a notable enhancement in fundamental frequency (21.13%) and a reduction in SPL in the lower frequency range compared to conventional composites. The proposed material composition and process methodology show potential for creating lightweight, structurally efficient large airframe components.

Initial monitoring of a six-story lightweight timber frame building under different environmental conditions

AbstractThis study presents a comprehensive investigation of the dynamic behavior of a six-story lightweight timber frame building through periodic and continuous ambient vibration tests. Seasonal changes in temperature and relative humidity can influence the dynamic response of timber buildings, by affecting stiffness, strength, and connection properties due to changes in moisture content. Systematic tests were performed from October 2022 until May 2024 to identify natural frequencies, damping ratios, and mode shapes of the building using five battery-driven data acquisition units equipped with 15 uni-axial accelerometers. Two different only-output frequency and time domain Operational Modal Analysis (OMA) methods were used to evaluate the dynamic properties of the building. Additionally, the building has been continuously monitored with temperature and humidity sensors since its construction. Results obtained from the periodic measurements highlighted the need for a permanent system to capture the transient changes in the modal parameters. A complementary permanent system to record the accelerations at the roof level was installed in May 2024. The modal parameters from in situ measurements were compared with those obtained from the Finite Element (FE) model of the structure. The FE model, calibrated through a multi-stage approach, incorporating non-structural elements, and varying imposed loads, showed good agreement with experimental data. Comparative analysis of the results obtained under different temperature and humidity conditions showed the effect of the environmental conditions on the building dynamics properties, for both periodic and permanent measurements. This study highlights the importance of continuous monitoring and detailed FE modeling in understanding the dynamic properties and long-term structural behavior under varying conditions. This information can be used to ensure that the building meets safety and performance requirements and to identify potential issues that may need to be addressed during the design and maintenance phases.

Modal and harmonic analysis of femur bone using different boundary conditions by Finite Element Analysis.

The longest and largest bone in the human body is the femur. Pelvic bone sustains the weight of the body to which the femur bone is connected. Many researches have been carried out to identify the behaviour of the femur bone. The study aimed to explore the natural frequencies and mode shapes of vibrating devices to gain insights into the dynamic behavior of the femur bone during various physical activities. Examining the impact of patient-specific bone shape and density on bone natural frequencies is crucial. The primary goals of femur bone analysis involve employing computer simulations for fracture detection and employing Finite Element (FE) models to determine natural frequencies and vibration modes. To obtain the natural frequency of the femur bone, different boundary conditions such as free-fixed and fixed-fixed are applied. Avoiding the coincidence of the natural frequency with external excitation frequencies is crucial to prevent femur bone fractures. Also, for different magnitude of loads, femur bone is involved in harmonic analysis is to identify the amplitude and stress against acceleration.

Effect of charge-discharge with higher capacitance performance of Ni-substituted CoFe2O4 magnetic nanoparticles for energy storage

In this work, we synthesized NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) magnetic nanoparticles (MNPs) by using ultrasonication-assisted reverse chemical co-precipitation method. The X-ray diffraction (XRD) patterns confirm the single-phase with mixed spinel structure of the NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs with the crystallite size range between 12 nm - 17 nm. The molecular dynamics and oleic acid coated Ni-substituted CoFe2O4 magnetic nanoparticles were confirmed by FTIR measurements. The surface composition of NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs (Ni, Co, Fe and O) and their oxidation states were estimated using X-ray photoelectron spectroscopy. The NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs are spherical in shape and polycrystalline in nature, confirmed by FESEM and HRTEM measurements. The Ni-substituted CoFe2O4 MNPs with higher zeta potential (ζ) from −24 mV to -41 mV with an increase in Ni concentration, signifies the stable colloidal stability due to the electrostatic repulsion between MNPs. The DC magnetization (M-vs-H) measurements reveal the ferrimagnetic behavior of NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs, which suppress the saturation magnetization (MS) from 48.6 emu/g to 5.3 emu/g with the enhanced coercivity (HC) from 335 Oe to 1700 Oe with the substitution of Ni2+ ions is in corroboration with electron paramagnetic resonance (EPR) measurements. The enhanced EPR resonance field (Hres = 2335 Oe - 3261 Oe) with the substitution of Ni2+ ions is attributed to the generation of oxygen vacancies and defects, which are predominant in Ni0.8Co0.2Fe2O4, resulting in significantly enhanced electrochemical performance. Therefore, the three-electrode system was utilized to investigate the electrochemical properties of NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs. The Ni-substituted CoFe2O4 MNPs have demonstrated significantly enhanced capacity retention of 77 % even after 5000 cycles in 1 M H2SO4 electrolyte solution. NixCo1-xFe2O4 (0 ≤ x ≤ 0.8) MNPs exhibit an excellent specific capacity (Cs) of 794.5 F/g at a current density of 1 A/g, signifies the rate of redox reaction at surface electrolyte interface (SEI) is greatly influenced by the surface to volume ratio. Thus, with the enhancement of Ni2+ ions, redox reaction kinetics might become more efficient resulting in the enhanced charge storage capacity.

Experimental and numerical analysis of the vibrational behaviour of metallic structures filled with damping materials

This work focuses on characterizing and modeling the vibrational behavior of hollow metallic structures filled with damping material. Vibration tests are first carried on a hollow structure, then two filling materials are considered: a cast viscoelastic material and a granular material composed of epoxy and polyurethane beads. Modal parameters (natural frequencies, modal damping and mode shapes) are extracted from the Frequency Response Functions with experimental modal analysis tools. Damping ratios greater than 5~\% are measured. Given the difference in the nature of the filling materials, dissipation mechanisms are different. The effectiveness of a damping material depends on the type of structural modes (bending, torsion or wall mode) to be damped, and dissipation in filling materials cannot be modelled by a constant loss factor or viscous damping. Consequently, a finite element modeling of the structure filled with viscoelastic material is proposed. Numerical modal parameters of the structure are correlated with experimental measurements. By extension, a bead mix material law, based on a fractional Zener model, is proposed, whose parameters are obtained by inverse identification.

Study on the self-vibration characteristics of non-circular arches with cracks based on the transfer matrix method

As the span of reinforced concrete arch bridges continues to increase, so does the difficulty of construction. The structure is at risk of cracking. Most of the bridges under construction are non-circular arches, and there are few studies on such arches. The current study tried to investigate the self-vibration characteristics of non-circular arches with existing cracks. A computational approach proposed in the original non-circular arch is substituted with multiple infinitesimal arch segments having different radii of curvature, enabling the determination of natural frequencies and mode shapes of the non-circular arches with cracks. Furthermore, a finite element model (FEM) of the reinforced concrete structure with existing cracks is developed to assess the effects of various factors, including axial location, crack depth, and positions within the same cross-section. The results demonstrate the feasibility of the computational method using multiple infinitesimal arc segments with varied radii of curvature, yielding a maximum error of only 1.58 %, which satisfies engineering application standards. An increase in crack depth leads to a reduction in the natural frequencies of specific modes of the structure, while the effect on others is insignificant. For cracks situated at the top or bottom plates within the same cross-section, the impact differs based on the local deformation being convex or concave. If the deformation is convex, the top plate cracks exhibit a higher rate of change in natural frequencies compared to the bottom plate cracks; conversely, with concave deformation, the bottom plate cracks have a greater influence than the top plate cracks.