Natural Frequencies Of Vibration Research Articles

Numerička analiza titrajnog odziva dalekovoda velikog raspona prijenosnih vodova izazvanog vjetrom

Based on the engineering background related to ±800 kV ultra-high voltage (UHV) transmission lines spanning the Yellow River, finite element models were developed for single-tower and transmission tower-line systems, with their wind-induced responses under wind loads were simulated and analysed. In addition, the coupling effect in a large-span transmission tower line system was investigated. The results showed that the natural vibration frequency of the tower-line system was slightly lower than that of a single tower and that the torsional natural frequency was the most significantly reduced. The transmission tower-line system has a maximum displacement of 1.92 times that of a single tower when the wind angle is 0°. The maximum axial force and stress in the tower-line system are 1.6 times and 1.37 times higher than those in a single tower. The interaction between the tower and wires significantly affects the wind-induced response of the tower body. Hence, considering the dynamic coupling effect of the tower-line transmission system is important when designing a tower.

System identification for structural condition assessment: Application to critical neoclassical monuments in Nepal

This paper presents structural condition assessment of some critical neoclassical monuments in Nepal using nonparametric and parametric system identification techniques. Neoclassical buildings in Nepal house critical administrative units. Structural condition assessment of such buildings is therefore important for the safety of their occupants and interrupted function during and after major earthquakes. The historical and cultural values of such monuments necessitate regular structural assessment for maintenance, repair, and preservation. Dynamic characteristics such as natural vibration frequencies of structures provide valuable insights on their structural condition. While numerical models are commonly used to estimate eigen frequencies of structures, they are associated with large uncertainties in massive monuments with complex structural and geometrical configurations. Noninvasive dynamic identification techniques provide an alternative means in such structures. Ambient vibration records from six neoclassical monuments in the Kathmandu Valley, Nepal are used in this study to estimate vibration frequencies of the structures in different states. The structures were damaged during the 2015 Gorkha earthquake, and subsequently retrofitted. Changes in vibration frequencies before and after retrofitting provide useful insights on structural improvement through retrofitting. Input-output and output-only system identification techniques are tested to simplify the structural condition assessment approach. We conclude that the state space system identification can stably quantify dynamic properties so stiffness variation can be confidently extracted, which is the key application for noninvasive structural system identification. Also, using minimum number of sensors, we captured damage aggravation deploying the modal assurance criterion. The outcomes indicate that structural condition assessment of complex structures is possible using a limited number of sensors for circumstances such as damage aggravation to temporal variation (evolution/reduction) of dynamic characteristics.

Anisotropic elasticity measurements of the retina using optical coherence elastography

Anisotropic elasticity measurements of the retina are essential for retinal disease diagnosis and function assessment. Optical coherence elastography (OCE) is a high-resolution imaging technique for mapping the elasticity distribution of tissues. However, previous OCE measurements quantified the tissue elasticity in a single direction, resulting in a biased estimation of the elastic properties. In this study, we propose an OCE method with acoustic radiation force (ARF) excitation to map the retinal anisotropic elasticity in the depth and lateral directions. The axial elasticity was analyzed using the natural frequency of free vibration, and the lateral elasticity was quantified using the elastic wave velocity. After evaluating the feasibility of the OCE method on the phantoms, the anisotropic elasticity of ex vivo porcine retinas was mapped. The results show that the OCE method with ARF excitation can assess the elasticity in orthogonal directions and provide a comprehensive understanding of the elasticity of the anisotropic tissues.

Control of deposits on pipeline systems by the method of free oscillations

RELEVANCE. There are a large number of heat exchangers in operation enterprises that operate under various temperature conditions. Steam, hot water, heated products of oil refining and other industries, which may contain oxides of iron, aluminum, calcium sulfate silicates, etc., are used as a heating agent. The efficiency of the heat exchange equipment depends on the condition of the heating surfaces. Contamination of these surfaces with various deposits dramatically reduces the heat transfer coefficient, which leads to a significant increase in heat consumption. The nature of the deposits depends on the properties of the heating agent and the heated medium.THE PURPOSE. The purpose is to assess the possibility of controlling deposits on the surfaces of heat exchange equipment by the free oscillation method. The presence of deposits changes the mass of structures and, consequently, the natural frequencies of vibrations, the analysis of which can determine not only the presence and thickness of deposits, as well as their appearance.METHODS. The paper shows the results of experimental studies conducted using a hardware and software package and calculations of natural vibrations of the surfaces of heat exchange equipment in the ANSYS software package to identify their dependence on the thickness and density of deposits. A plate, a pipe, and a pressurized pipe were modeled as heat transfer surfaces.RESULTS. The results obtained experimentally and computationally coincided, and it was concluded that the free oscillation method makes it possible to determine not only the presence of deposits on heat exchange surfaces, but their thickness and appearance.CONCLUSION. The free oscillation method can detect deposits in a timely manner and monitor their condition, which in turn will, reduce overall operating costs, increase energy efficiency and extend service life.

Modal analysis of Lamb waves of steel pipeline with calcium deposits

The relevance of the work lies in the study of the effect of calcium deposits of various thicknesses on the inner walls of the pipeline on the parameters of its own vibrations.OBJECTIVE: To construct a mathematical model of a steel pipeline without deposits and with calcium deposits of various thicknesses on its inner walls. To perform a modal analysis of the natural vibrations of the steel pipeline. Theoretically confirm the dependence of the change in the oscillation frequency of the pipeline when exposed to sediments.METHODS. The paper highlights a method for analyzing the natural frequencies of the pipeline using the acoustic method of non-destructive testing, since it can be implemented with one-way access and does not violate the integrity of the object of control. In solving this problem, the method of mathematical analysis in the software package of finite element analysis was used. results. The article describes the relevance of the topic, discusses the main methods of non-destructive testing, and defines Lamb waves. A mathematical model of a steel pipeline section with out internal deposits and with calcium deposits of 5 different thicknesses has been constructed.CONCLUSION. Calculations have shown that the natural vibration frequencies of the pipeline without deposits and with calcium deposits change in the direction of increasing values, the frequency increase occurs in waves. The highest frequency values are obtained when modeling calcium deposits with a thickness of 10 mm on the walls of the pipeline.

Oscillation mechanism and predictive model of explosion load for natural gas in confined tube

Gas explosion in confined space often leads to significant pressure oscillation. It is widely recognized that structural damage can be severe when the oscillation frequency of the load resonates with the natural vibration frequency of the structure. To reveal the oscillation mechanism of gas explosion load, the experiment of gas explosion was conducted in a large-scale confined tube with the length of 30 m, and the explosion process was numerically analyzed using FLACS. The results show that the essential cause of oscillation effect is the reflection of the pressure wave. In addition, due to the difference in the propagation path of the pressure wave, the load oscillation frequency at the middle position of the tunnel is twice that at the end position. The average sound velocity can be used to calculate the oscillation frequency of overpressure accurately, and the error is less than 15%. The instability of the flame surface and the increase of flame turbulence caused by the interaction between the pressure wave and the flame surface are the main contributors to the increase in overpressure and amplitude. The overpressure peaks calculated by the existing flame instability model and turbulence disturbance model are 31.7% and 34.7% lower than the numerical results, respectively. The turbulence factor model established in this work can describe the turbulence enhancement effect caused by flame instability and oscillatory load, and the difference between the theoretical and numerical results is only 4.6%. In the theoretical derivation of the overpressure model, an improved model of dynamic turbulence factor is established, which can describe the enhancement effect of turbulence factor caused by flame instability and self-turbulence. Based on the one-dimensional propagation theory of pressure wave, the oscillatory effect of the load is derived to calculate the frequency and amplitude of pressure oscillation. The average error of amplitude and frequency is less than 20%.

Effect of material anisotropy on the first-order vibration of piezoelectric oscillators in circular plate configurations

Valveless piezoelectric pumps are widely used in microfluidic actuation because of their simple structure, ease of integration, absence of electromagnetic interference, minimal valve wear, and absence of frequency–response lag issues. These pumps primarily rely on chamber volume changes, causing most piezoelectric oscillators to operate in the first-order vibration mode. However, recent studies on valveless piezoelectric pumps have observed that many pumps exhibit two flow peaks at similar operating frequencies; the underlying mechanism behind this anomaly remains underexplored. In this study, we investigated the impact of substrate metal on the first-order vibrations of piezoelectric oscillators. By conducting tensile tests on rolled pure copper sheets, we measured Poisson's ratio and the elastic modulus in both the parallel and perpendicular rolling directions. Subsequently, we derived the natural frequencies on the plane. Experimental verification of the theoretical predictions was achieved through amplitude experiments conducted on piezoelectric oscillators in air. The dual-peak flow phenomenon was demonstrated to be solely related to the substrate metal of the piezoelectric oscillator. This is attributed to the presence of two first-order vibration natural frequencies on the plane of the substrate metal, resulting in the generation of two amplitude peaks and consequently the appearance of two flow peaks.

Efficient Forced Response Minimization Using a Full-Viscosity Discrete Adjoint Harmonic Balance Method

A forced response induced by inlet distortion and blade row interactions can lead to high-cycle fatigue failure, especially when the unsteady excitation frequency is close to the natural vibration frequency of a blade. This paper presents the study of forced response sensitivity analysis and minimization using a full-viscosity unsteady discrete adjoint method. The goal is to improve the aeroelastic performances of turbomachinery blades and simultaneously constrain/improve aerodynamic performances. The decoupled modal reduction method is used to compute the forced response, which is considered the objective function in adjoint-based design optimization. To analyze aeroforcing and aerodamping flow and adjoint fields efficiently, the harmonic balance method and its adjoint counterpart developed by an automatic differentiation tool are applied. Two cases—the NASA Rotor 67 with inlet distortion and a three-row configuration with multiple fundamental frequencies in the second row—are used to demonstrate the effectiveness of the aerodynamic and aeroelastic coupled design optimization system developed in this work. For the latter case, the Fourier-transform-based method that first decomposes and then matches the time and space modes at two sides of an interface is used for interface coupling. The almost-periodic Fourier transform method is used to determine the time instances for cases with multiple fundamental frequencies.

Methodology and Monitoring of the Strengthening and Upgrading of a Four-Story Building with an Open Ground Floor in a Seismic Region

Many buildings around the world fail to meet current earthquake resistance requirements and have significant potential to be a risk to human life and property. Therefore, a seismic upgrade of such buildings is quite necessary. Over the past decades, hundreds of buildings have been strengthened and upgraded to improve their seismic resistance, and thousands more are planned for years to come. In Israel, this was followed by National Outline Plan No. 38, which provides a basis for retrofitting and adding new areas to existing buildings. It should be noted that adding new floors to existing buildings increases seismic forces. Moreover, structure material properties change over a building’s lifetime, which should be also considered for strengthening. The proposed research investigates and validates the existing practice for strengthening and upgrading buildings in seismic regions and suggests ways of improving their efficiency. Experiments and numerical analysis were performed on a real existing residential building that requires strengthening and upgrading. A corresponding methodology was proposed for monitoring the strengthening and upgrading processes, including selecting measurement devices and their real use. Using sensors with the highest sensitivity enabled measurements of micro-vibrations and investigations of the recorded signal to obtain the building’s natural vibration frequencies. Experimental measurements allowed us to distinguish different frequencies of the building at all strengthening and upgrading stages. The measured dynamic parameters of the building allowed a more accurate calculation of seismic forces for all of these stages and consequently made the design more effective. Therefore, we recommended monitoring buildings in each stage of seismic strengthening and upgrading.

Evaluating the Piezoelectric Energy Harvesting Potential of 3D-Printed Graphene Prepared Using Direct Ink Writing and Fused Deposition Modelling.

This research aims to use energy harvested from conductive materials to power microelectronic components. The proposed method involves using vibration-based energy harvesting to increase the natural vibration frequency, reduce the need for battery replacement, and minimise chemical waste. Piezoelectric transduction, known for its high-power density and ease of application, has garnered significant attention. Additionally, graphene, a non-piezoelectric material, exhibits good piezoelectric properties. The research explores a novel method of printing graphene material using 3D printing, specifically Direct Ink Writing (DIW) and fused deposition modelling (FDM). Both simulation and experimental techniques were used to analyse energy harvesting. The experimental technique involved using the cantilever beam-based vibration energy harvesting method. The results showed that the DIW-derived 3D-printed prototype achieved a peak power output of 12.2 µW, surpassing the 6.4 µW output of the FDM-derived 3D-printed prototype. Furthermore, the simulation using COMSOL Multiphysics yielded a harvested output of 0.69 µV.

Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters

In this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics.

On flexural vibrations of orthotropic strips of variable thickness taken into account of transverse effects with elasticaly built in edges in the presence of axial force

Abstract The problem of bending vibrations of orthotropic strips of variable thickness is considered, taking into account transverse effects elastically built in edges in the presence of axial force. The problem was solved using the numerical collocation method. A numerical analysis of the problem was carried out. The problem of Euler stability of orthotropic plate-strips of variable thickness under plane strain conditions is considered, taking into account transverse shear and rotational inertia. The resulting equations make it possible to determine both the frequencies of natural vibrations and the critical values of the axial force at which the plate-strip loses stability. The problems are solved using a modified collocation method under various boundary conditions at the ends and values of geometric and physical parameters characterizing a plate-strip of variable thickness.

Vibration of multilayer cantilever beams towards piezoelectric power harvesters

This paper investigates the vibration characteristics of a commonly employed mechanical structure, the cantilever beam, concerning its potential for direct electricity harvesting from piezoelectric crystals. Piezoelectric materials are renowned for their ability to generate electric charges when subjected to mechanical stress. To ensure continuous current generation, these materials require sustained excitation by external forces, typically achieved through vibration. However, piezoelectric crystals lack sufficient elasticity, necessitating attachment to a structurally conducive and easily vibratable framework. The cantilever beam, renowned for its simplicity and widespread use, serves as an ideal platform for this purpose. Layers of piezoelectric material (PZT5H) are affixed to brass-based cantilever beams to create various multilayer configurations. External forces are then applied at the free end of the beam to induce vibration. Given that the harvested power from PZT5H crystals correlates with the mechanical stress they experience, achieving optimal deformation is paramount. This is accomplished by leveraging the resonance effect of vibration, wherein the vibration modes and natural frequencies of the multilayer PZT5H beams must be thoroughly characterized. To this end, numerical methods and Finite Element Analysis via Abaqus software are employed. The vibrations of the brass base layer, as well as single-sided and double-sided PZT5H beams, are analyzed across four distinct mode shapes and corresponding natural frequencies. The study culminates in a comprehensive examination of the relationship between natural frequencies and dimensional parameters of the beams. Ultimately, this research offers valuable insights into the vibration behavior of cantilever beams, laying the groundwork for the development of efficient power harvesting devices utilizing mechanical vibration sources or tailored to specific applications.

Electromechanical responses of a piezoelectric semiconducting nanoplate with the Steigmann-Ogden surface

Abstract Piezoelectric semiconductors (PSCs) find widespread applications in smart electronic devices due to their unique combination of piezoelectric and semiconductive properties. With the increasing demand for smaller and more efficient electronic devices, the performance of their components needs to be carefully optimized, especially when they are scaled down to nanoscale sizes. Pioneering studies have demonstrated that the surface elastic properties play a significant role in determining the mechanical performance of nanoscale materials and structures. Therefore, it is important to comprehensively investigate the effects of surface elasticity, including surface residual stress, surface membrane stiffness and surface bending stiffness, on the electromechanical responses of a PSC nanoplate. Additionally, it is also crucial to examine the influence of flexoelectricity at the nanoscale. Our results demonstrate that surface elastic properties predominantly impact mechanical performance, while the flexoelectric effect plays a more prominent role in electric field and redistribution of charge carriers. In particular, the significance of surface bending rigidity, which was often overlooked in previous literature, becomes pronounced when the thickness of a PSC nanoplateisless than 10 nm. Furthermore, the dependence of natural vibration frequency on surface elastic moduli, flexoelectricity and size is also systematically explored. The redistributions of electric potential and charge carriers across the cross-section are also evidently affected. Our findings provide valuable insights for improving the performance of electronic devices that utilize nanoscale PSCs.

Global weak solutions to a time-periodic body-liquid interaction problem

We prove existence of time-periodic weak solutions to the coupled liquid-structure problem constituted by an incompressible Navier–Stokes fluid interacting with a rigid body of finite size, subject to an undamped linear restoring force. The fluid flow is generated by a uniform, time-periodic velocity field {\boldsymbol V} far from the body. We emphasize that our result is global, in the sense that no restriction is imposed on the magnitude of {\boldsymbol V} and, rather remarkably, the frequency of {\boldsymbol V} is entirely arbitrary. Thus, in particular, it can coincide with any multiple of a natural frequency of vibration of the body so that, with this model, resonance cannot occur. Although based on the classical “invading domains” technique, our approach requires several new ideas. Indeed, due to the lack of sufficient dissipation, it appears quite unfeasible to show the existence of a fixed point of the Poincaré map at the finite-dimensional level along the Galerkin approximant. Therefore, unlike the usual strategy, such a result must be proven directly in a class of weak solutions, and therefore in the infinite-dimensional framework.

Scaling Laws for Deployable Mesh Reflector Antennas

This paper begins with the formulation of a general, rapid design method for deployable mesh reflector antennas based on the AstroMesh architecture. This method is then used to obtain estimates of the total mass, stowed envelope size, and fundamental natural frequency of vibration for antennas with a range of aperture diameters and focal lengths, assuming an operational radio frequency of 10 GHz. A study of the scaling trends of this reflector design shows that the distribution of prestress in the inner tension structure has a major impact on the mass of the outer perimeter truss. Based on this result, a prestress optimization problem to design reflectors of minimum mass is formulated, and analytical scaling laws are obtained for the mass, stowed envelope, and natural frequency of optimally prestressed reflectors with aperture diameters up to 200 m. It is then shown that aperture diameters of 70–100 m are at the limit of launchers that are currently available or under development. A semianalytical homogenization model that accurately estimates the fundamental natural frequencies for batten-supported and free-free boundary conditions is also presented.

Design and Control of the Natural Frequency of Brake Discs in the Aspect of the Gray Cast Iron Production Process.

The results of research on the influence of the chemical composition of cast iron and its potential changes in the production cycle on the elastic properties and the correctness of numerical simulations of the natural frequency of ventilated brake discs are presented. The tests were carried out for three grades of gray cast iron with flake graphite with a eutectic saturation coefficient ranging from 0.88 to 1.01. A quantitative metallographic assessment of the pearlitic cast iron matrix and graphite precipitates was carried out, and the hardness and compressive/tensile strength of individual cast iron grades were determined, taking into account the limit contents of the alloying elements. Next, ultrasonic tests were performed, and the elastic properties of cast iron were determined. Based on the obtained data, a numerical modal analysis of brake discs was performed, the results of which were compared with the actual values of an FRF frequency analysis. The error of the computer simulations was estimated at approx. 1%, and it was found that the accuracy of the calculations of the first natural frequency did not depend on the dimensions (size) of the discs and the chemical composition of the cast iron from which they were cast. The functional relationships between the chemical composition of cast iron, its strength and elasticity and the first natural frequency of the disc vibrations were determined, and a database of the material parameters of the produced cast iron grades was developed. An implementation example showed the validation of the brake disc design with natural frequency prediction and demonstrated a high convergence of the experimental results with the simulated values. Using I-MR control cards, both the effectiveness of designing and predicting the natural vibrations of brake discs based on the implemented material database as well as the stability of the gray cast iron production and disc casting processes were confirmed.

Natural Frequency Transmissibility for Detection of Cracks in Horizontal Axis Wind Turbine Blades.

Defects on horizontal axis wind turbine blades are difficult to identify and monitor with conventional forms of non-destructive examination due to the blade's large size and limited accessibility during continuous operation. This article examines both strain and acceleration transmissibility as methods of continuous damage detection on wind turbine blades. A scaled 117 cm offshore wind turbine blade was first designed, 3D printed, and modelled numerically in ANSYS. Transverse cracks were deliberately introduced to the blade at 10 cm intervals along its leading edge. Subsequent changes in the transmissibility, relative to an undamaged baseline model, were measured using different variable combinations at the blade's first three natural frequencies. Experimental results indicated that strain transmissibility was able to locate a 1.0 cm defect at a range of 70-110 cm from the blade hub using the amplitudes of the first natural frequency of vibration. The numerical model was able to simulate the strain experimental results and was determined to be valid for future defect characterization. Acceleration transmissibility was unable to experimentally identify defects sized at 1.0 cm and below but was able to identify 1.0 cm sized defects numerically. It was concluded that transmissibility is viable for continuous damage detection on blades but that further research into other defect types and locations is required prior to conducting full-scale testing.

ANISOTROPY AND MECHANICAL CHARACTERISTICS OF ULTRA-HIGH PERFORMANCE CONCRETE AND ITS INTERPENETRATING PHASE COMPOSITE WITH TRIPLY PERIODIC MINIMAL SURFACE ARCHITECTURES

Abstract This work numerically explores the anisotropy, impact phase wave propagation, buckling resistance, and natural vibration of ultra-high performance concrete (UHPC) and UHPC-steel interpenetrating phase composite (IPC) with triply periodic minimal surfaces (TPMSs), including sheet and solid Gyroid, Primitive, Diamond, and I-WP. The experiment is conducted verifying the accuracy of the numerical model in terms of Young's modulus of polylactic acid (PLA)-based TPMS lattices and PLA-cement IPCs with TPMS cores, with the highest percent difference of 15% found for IPCs and 17% found for lattice. The results indicate that UHPC material with sheet Gyroid exhibits the least extreme anisotropy in response to the varying orientation among other lattices regardless of the change of solid density, making it the ideal candidate for construction materials. Interestingly, compared to UHPC-based TPMS lattice, IPCs possess a much smaller anisotropy and exhibit almost isotropy regardless the variation of solid density and TPMS topology, offering a free selection of TPMS type to fabricate IPCs without much care of anisotropy. The phase wave and buckling resistance of UHPC- and IPC-based beams with TPMSs nonlinearly decrease with a drop of TPMS solid density, but it is the almost linear pattern for the case of natural vibration frequency. UHPC material and IPC with sheet Gyroid lattice are found to possess the lowest phase wave velocity and exhibit the least anisotropy of wave propagation, showing it as an ideal candidate for UHPC material to suppress the destructive energy induced by the external impact.

Improving the identification of dynamic parameters of bridges by UAV: approach for SHM

The structural integrity of bridges is susceptible to deterioration caused by traffic loads, environmental conditions, and weather phenomena. To maintain the safety and stability of bridges, regular inspections of their elements are required. Recent advances in the field of unmanned aerial vehicles (UAVs) provide a viable option for accurate and autonomous inspections of bridge structures without disrupting normal operations. This study focuses on the determination of the dynamic structural parameters of a suspension bridge. The methodology focuses on determining the natural vibration frequency of the bridge cables using UAV imagery. This paper contains a detailed theoretical presentation of the algorithm used, accompanied by a careful analysis of simulation results and empirical data from laboratory experiments and real case studies. In addition to the image processing-based approach for estimating the vibration frequency, the sensors on board the drone are also scrutinized and their effectiveness in detecting structural vibrations after the drone lands on the bridge surface is evaluated.