Reduction In Natural Frequencies Research Articles

Topology optimization of gradient lattice structure filling with damping material under harmonic frequency band excitation

With the rapid development of 3D printing technology, lattice structures have been widely utilized in structural designs aimed at vibration resistance due to their excellent performance. In this study, considering the moderate improvement of vibration suppression property of existing graded lattice, we introduce high-damping material into the optimization framework and further enhance the vibration resistance ability of gradient lattices. This framework extends the existing framework of stiffness and mass distribution to incorporate the distribution of stiffness, mass, and damping, which allows us to consider the damping changes with the cell configuration. Initially, the lattice cells are assigned with two different constitutive materials, one with high stiffness and the other with excellent damping properties. Different from traditional lattice units, we can obtain a series of lattice units with adjustable stiffness , mass and damping in a certain range. Via the homogenization method on the frequency domain, the complex elastic matrices about distribution of these lattice cells controlled by three parameters are obtained. In the meantime, the loss factor of these lattice cells is also obtained. A polynomial-based interpolation technique is employed to characterize the graded lattice units, which is integrated into an optimization process aimed at minimizing the lattice structures’ vibration responses. Several numerical examples are presented to illustrate this framework’s effectiveness, and experimental tests on 3D printed specimens are conducted to validate the numerical results. It’s worth noting that under the condition that the total weight of the structure remains unchanged, this weakens the overall stiffness of the structure (the reduction of first-order natural frequency), but greatly increases the damping of the structure (with a widened resonance peak) to resist the vibration of the structure. For the lattice structures induced by damping materials, the average loss factor is 0.114, which is almost doubled to the average value of those not including the damping material. When comparing the results of the mean displacement amplitude with and without damping materials, the reduction of displacement amplitude of lattice structures is above 25 %. The methodology expands the scope of optimization design for lattice structures, moving beyond stiffness maximization to include vibration mitigation by determining the appropriate distribution of stiff and damping materials, showcasing the practical applicability of the presented methods in engineering practice.

Numerical and experimental investigations in a cracked wind turbine blade using natural frequencies

In this study, the vibration behavior of a wind turbine blade under influence of the transverse crack was studied. A mathematical model based on free vibration of the blade with induced transverse crack was prepared to estimate the natural frequencies. Wind turbine blade was modeled considering double tapered beam with linearly varying width and thickness keeping constant aspect ratio. A Matlab program was constructed to obtain the frequencies from mathematical model. Modal analysis of wind turbine blade was performed simulating the induced transverse crack of different depths at various locations to estimate the natural frequencies using Fast Fourier Transform (FFT) analyzer. To verify the results obtained from mathematical model and modal analysis, finite element analysis was performed. Same methodology of FEA was implemented on another blade with different aspect ratio and blade profile to verify the obtained results. It was observed that the methods adopted are in correlation with one another depicting reduction in natural frequencies as crack approaches to the free end of blade as well as for increased depth of crack signifying reduction in stiffness of the blade.

Vibration monitoring and acoustic emission sensing during progressive load tests of corroded reinforced concrete beams

Corrosion of reinforcement in concrete civil structures poses a significant challenge to their integrity and durability. To ensure the safety and longevity of such structures, effective monitoring strategies that can accurately detect, localise and assess the progression of damage are crucial. For most existing concrete structures, this is often challenging, as damage is already present when the monitoring campaign starts. In addition, reinforced concrete structures can be subject to a combination (or a succession) of corrosion and load-induced damage. By combining multiple measurement techniques, a more accurate and reliable condition assessment of concrete civil structures can be aimed for. This paper presents a comprehensive experimental study of the combination of vibration-based monitoring (VBM) and acoustic emission (AE) sensing techniques during progressive load tests of corroded reinforced concrete beams. Five beams were subjected to a cyclic four-point bending test, three of which were previously corroded while two beams remained undamaged prior to the mechanical loading. The influence of pre-existing corrosion damage and corresponding longitudinal concrete cracking on the modal characteristics (natural frequencies and strain mode shapes) and AE outcomes is investigated during the four-point bending test. The monitoring results obtained by both techniques are shown to be influenced by the pre-existing longitudinal concrete cracking caused by the reinforcement corrosion. Lower AE activity and a lower reduction in natural frequencies is observed for corroded RC beams during load bending tests when compared to uncorroded specimens. In addition, bending cracks occurring within the corroded zones appear to have a very limited effect on the identified strain mode shapes. These observations could possibly result in an underestimation of the damage and corresponding overestimation of the load-carrying capacity, as the corrosion damage conceals the occurrence of bending cracking on the AE and VBM outcomes.

Seismic assessment of the in‐plane/out‐of‐plane interaction of masonry infills in a two‐storey RC building subjected to bi‐directional shaking table tests

AbstractThis paper presents a series of shaking table tests conducted on a 60%‐scaled two‐storey infilled reinforced concrete building. The main parameters include the presence of openings in the masonry infills and the effect of bi‐directional dynamic shaking to the latter. The building was subjected to four different levels of shaking intensity, ranging up to the Maximum Considered Earthquake (MCE), equivalent to 150% of the design earthquake. The study focuses on and evaluates the damage caused by combined in‐ and out‐of‐plane shaking. Under the design level earthquake, the second‐storey infill walls with openings were severely damaged, with near‐collapse of a masonry pier. For the fully infilled direction without openings instead, diagonal cracking as well as out‐of‐plane inclination of the infill wall in the second storey were observed. Due to the interaction between the two loading directions and the direct adverse effect of the in‐plane damage on the out‐of‐plane resistance of the infills, the out‐of‐plane collapse of 3/4 of the second storey masonry infill occurred during the MCE. The reported damage observations on the masonry‐infills with or without openings provide further insights on the vulnerability of non‐seismically designed reinforced concrete buildings. Additionally, the seismic performance of the structure is assessed using further structural response quantities recorded during testing, including floor accelerations, inter‐storey drifts, base shear forces and reductions in natural frequency. Future testing will focus on investigating the effectiveness of retrofitting measures in improving the connection between the infill and frame, reducing in‐plane damage, and preventing out‐of‐plane failure of the infills.

Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

Effect of depth ratio on Faraday instability in a binary liquid system

The response of two incompressible and immiscible liquids of comparable densities at different depth ratios in a rectangular container subject to parametric sinusoidal forcing, similar to Faraday waves, has been considered in the present study. The effect of various depth ratios on the instability threshold and the flow field are investigated for (0, 2) and (0, 4) modes. Numerical simulation has been performed using OpenFOAM to solve Navier-Stokes equations. A source term is added in the interFoam module of OpenFOAM to take the effect of the oscillating container without using any dynamic mesh function. The threshold amplitude and wavenumbers are validated following the linear Floquet analysis of Kumar and Tuckerman (1994 J. Fluid Mech. 279 49–68). The Floquet analysis showed a substantial shift in natural frequency (reduction) and an increase in threshold amplitude when the interface is in close proximity to the wall. The response amplitude follows a square law with the forcing amplitude for all the depth ratios considered in the present study. The wave amplitude response above the threshold curve is found to be an exponential function of liquid depths and forcing parameters.

CRACK EFFECT ON THE NATURAL FREQUENCY OF COMPOSITE BEAM: FINITE ELEMENT ANALYSIS WITH EXPERIMENTAL STUDY

Cracks in structural elements can significantly affect their dynamic behaviour and lead to detrimental consequences. This study investigates the influence of cracks on the natural frequency of a laminated beam under free vibration, employing a combination of finite element method (FEM) analysis and experimental work. The numerical computation is done using ABAQUS simulation software by developing a comprehensive FEM model that accurately represents the laminated beam's mechanical behaviour, considering material anisotropy, geometry and crack propagation. The finite element model is validated through experimental tests conducted on both intact and cracked laminated beam specimens. The experimental setup utilizes Fast Fourier Transform (FFT) analyzer high-precision measurement tool to obtain accurate natural frequency values. The parametric study is conducted to analyze the impact of crack location, size, and orientation on the laminated beam's natural frequency. The FEM simulations reveal that the presence of cracks leads to a reduction in natural frequency, indicating a decrease in structural stiffness. The extent of frequency reduction is found to be influenced by crack characteristics and their proximity to critical locations within the beam. The experimental investigations corroborate the FEM findings, highlighting the consistency between numerical predictions and actual measurements.

Effect of Different Step-Lap Joints on the Natural Frequencies of Different Adhesively Bonded Metallic Materials: A Numerical Study

Due to their many applications' benefits, adhesively bonded joints are widely utilized in nearly every industry, including space, marine, automotive, and aeronautics. Since unpredicted loadings may cause resonance in the structures, an accurate prediction of the bonded joints' dynamic characteristics is crucial. Therefore, in this study, modal analysis was performed on the two-, three-, four- and double-step adhesively bonded lap joints of Aluminum (Al), Copper (Cu), and Mild steel (Ms) materials with Epoxy Araldite adhesive. Ansys commercial program was utilized to analyze it numerically. The results showed that modeling the bonding region of single lap joints as two-, three-, and four-step adhesively bonded lap joints has no significant effect on the natural frequencies. This modeling has a minor incremental effect on the natural frequencies. However, Double-step lap joints were found to cause a considerable reduction in natural frequencies compared to not only single lap joints but also two-, three-, and four-step adhesively bonded lap joints. Double-step bonding caused a decrease of 8.82%, 8.57%, and 8.73% for Al-Al, Cu-Cu, and Ms-Ms. In general, in all models, the best increase or decrease in terms of natural frequencies was found to be Cu-Cu adhesively lap joints.

Deep learning enhanced metamodel design based on reduced mode shapes for delamination identification in composite structures

Structures requiring robust maintenance and accessibility pose challenges for structural integrity monitoring. This monitoring, crucial in various engineering applications, enables corrective actions to ensure machinery and equipment safety. Laminated composite materials, prevalent in aeronautical structures, often exhibit imperceptible delaminations or cracks, demanding the use of artificial intelligence for damage characterization. This study employs a numerical-experimental methodology, integrating artificial neural networks, to identify delaminations. Delamination, a structural damage form, was intentionally induced in epoxy-fiberglass composite structures. Modal tests captured characteristics in damaged and undamaged structures, revealing artificial intelligence effectiveness in pinpointing damage location and size. Damage significantly altered beam mode shapes, generating complex modes. Induced delaminations led to a measurable 15% reduction in natural frequencies, and damping ratios increased by approximately 10% in damaged structures. Artificial neural networks achieved an impressive 92% accuracy in predicting delamination location and size. Quantitative analysis of mode shape alterations validated the proposed methodology’s efficacy. This study provides valuable quantitative insights into damage detection in laminated composite structures, highlighting AI's potential for enhanced structural health monitoring. The numerical–experimental approach, supported by quantitative results, emphasizes the importance of advanced techniques for precise and efficient damage characterization in critical engineering applications.

Vibration Characteristics of FML Cylindrical Shell Bonded by Thin Piezoelectric Actuator and Sensor Layer with and Without Fluid–Structure Interaction Resting on Pasternak Elastic Foundation

The present study investigates the vibration analysis of cylindrical shells composed of fiber metal laminate (FML) with embedded piezoelectric layers, undergoing fluid-structure interaction (FSI) and resting on a Pasternak elastic foundation based on the principles of three-dimensional elasticity theory. Using the state space approach, the equations of motion were derived under simply supported boundary conditions. The natural frequencies of the FML cylindrical shell, accounting for the presence of a moving fluid, were computed by solving the eigenfrequency equations. The study examined the influence of various parameters, including boundary conditions, length-to-radius ratio, fluid type, fluid velocity, circumferential wave number, and radius-to-thickness ratio, on glass-reinforced aluminum laminate (GLARE), aramid-reinforced aluminum laminate (ARALL), and carbon-reinforced aluminum laminate (CARALL). A constant composite/metal volume ratio was assumed. The results obtained were validated by comparing with natural frequency values from the existing literature, confirming the agreement and convergence with previous studies. The results confirm that the highest natural frequency values are assigned to the CARALL, ARALL and GRALE structures in descending order. Furthermore, an increase in fluid flow velocity through the cylindrical shell correlates with a reduction in natural frequency.

Investigation of vibration of carbon nanotube and quality factor with confined and submerged fluid under hammer impact Test: A molecular dynamics study

Because of their unique dynamic properties and high-quality factors, one and two-dimensional (1D and 2D) materials have been increasingly in favorin recent years for the construction of a new generation of nano sensors. While numerous research has explored these qualities in vacuum, there is a need to analyze the influence of van der Waals interaction on their vibrational properties when they are exposed to fluids such as water which is significant as it plays a vital role in defining the stability of CNT-based nano-fluidic systems. Using molecular dynamics approach, the behavior of a single walled carbon nanotube (SWCNT) affected by water environment inside or around the structure is investigated. Moreover, the influence of nanotube dimensions and water density are examined using the newly presented method called hammer impact test in nanoscale, which is a conventional modal analysis method in macroscale. The findings show thatthe presented hammer impact test can predict the frequencies and quality factor with high precision and at a far reduced computational cost. The results show that the presence of fluid reduces the natural frequency of the nanotube, and that the natural frequency of the nanotube drops as fluid density increases. In addition, increasing the diameter of fluid carrier nanotubes leads to a rise in the natural frequency of the nanotubes in varied chiralities. At a constant density of water, comparing the results of interior fluid CNT with those of submerged CNT, the results show a meaningful reduction in natural frequency, quality factor, and vibration amplitudes, which makes the interior fluid CNT an ideal case for future investigation on CNT-based nano-fluidic systems. Our resultsreveal a novel aspect offluid-CNTinteraction and examines its impact to design high performance nano sensors.

Comparative Study on Numerical Calculation of Modal Characteristics of Pump-Turbine Shaft System

Because a pump-turbine mainly undertakes the role of energy conversion and pumped storage in the field of hydropower engineering, the complex transition process and frequent conversion between different working conditions lead to the increase in the stress and strain of core components such as the unit shaft system, and even cause resonance phenomena. Based on ANSYS finite element numerical calculation software, this paper adopts the acoustic fluid–structure coupling method to study the influence of the shaft of the pump-turbine on the dynamic characteristics of the runner. At the same time, the paper analyses the influence of different contact modes between the runner and the shaft on the modal characteristics of the shaft system. The numerical simulation results have shown that the runner is affected by the added mass of the water. The natural frequency reduction rate of each order of wet modal is ranged from 19% to 64%. The main shaft has a greater influence on the simplification of the shaft system calculation method. The type of contact surface between the main shaft and the runner has a smaller influence on the modal characteristics and the natural frequency of the shaft system. The research in this paper contributes an evaluation of the dynamic characteristics of the runner of a hydraulic turbine unit, which is of great significance for the optimization of the analysis algorithm of the runner structure for large pumped storage units.

Structural seismic response prediction based on convolutional neural networks

The seismic response of buildings is crucial for structural performance analysis. For structures with complete design data, the seismic response can be predicted using finite element analysis. However, for structures lacking necessary information, building finite element models and predicting their seismic response can be challenging. Compared to finite element analysis, convolutional neural networks (CNNs) can establish a neural network mapping relationship between the structure and the seismic response to predict the structural response without design data. In this paper, a structural response prediction model based on CNNs is established, aiming to analyze the effect of natural frequency reduction on the structural response after the Tohoku earthquake. The successful prediction of the structural acceleration and displacement response provides a new analytical method for predicting the seismic response of buildings lacking design data.

Vibration and damping of carbon fiber reinforced polymer orthogonal lattice truss sandwich panels manufactured by a new manufacturing process

A new method of fabricating carbon fiber reinforced polymer (CFRP) orthogonal lattice truss sandwich panels is proposed. Inner trusses are inserted into outer trusses. Three structures are prepared using different adhesives: epoxy resin, ethylene–vinyl acetate copolymer (EVA), and nitrile butadiene rubber (NBR). The mode shapes, natural frequencies, and loss factors of the structures are tested and predicted using the finite element modal strain energy method with a solid model and two shell models, respectively. The shell stiffness matrixes are calculated using representative volume element (RVE) method and analytical method. The results show that these three theories can accurately predict the sandwich panels with epoxy or EVA adhesive, while the sandwich panel with rubber layer cannot be accurately predicted. The strain energy composition, shell stiffness matrices, influence of node offset and influence of adhesive layer thicknesses are studied. The EVA adhesive improves the loss factors of the structure within an acceptable reduction of natural frequency.

Free vibration behaviour and some mechanical properties of micro particle reinforced epoxy composites

Abstract The epoxy composite specimens of certain sizes were produced by adding graphite, silicon carbide and boron carbide microparticles separately at the rates of 5, 10 and 15 wt% to the epoxy resin. Free vibrations of these composite samples were investigated experimentally in a simple supported vibration test setup. Frequency spectrums were obtained by modal analysis method in this experimental setup. The damping ratios were calculated using the half power bandwidth method. The mechanical properties of these composite specimens were also determined by applying the tensile test. By controlling the obtained vibration values theoretically, the effects of microparticle contributions to these specimens at certain rates on natural frequency and damping properties were investigated in detail. The maximum reduction in natural frequency was observed at 5 wt% of each reinforcement. Only the first natural frequency of the 15 wt% boron carbide reinforced epoxy composite was slightly increased. The damping ratio was increased at 10 wt% graphite added and 5 wt% boron carbide added epoxy composites compared to pure epoxy, but decreased in other composite specimens.

Vibration Fatigue Testing Procedure of High Strength MARS 600 Steel Fillet Welds Using Stainless Steel Consumable Electrode

Implementation of high strength steels in welded structural designs in the automotive, defence and construction industries is constantly increasing. Prolonged usage of such structures requires deep understanding of welded joint fatigue as well as a reliable and feasible life estimation methods development. Conventional fatigue testing methods often require costly, expensive in maintenance, high loading capacity equipment. They are also commonly restricted to specific specimen geometry and are time consuming due to the limit of a single specimen per test setup. This work presents high cycle fatigue (HCF) testing of high strength MARS 600 welded steel using a quick, simple and efficient resonance fatigue testing (RFT) method. The specimen is a simple cantilever fillet welded to a base plate using austenitic stainless steel 307L consumable electrode. Electrodynamic shaker is used for harmonic base excitation at a constant operating frequency. Several specimens welded to the common base are tested simultaneously, allowing completion of a high number of cycles and statistics in a relatively short time period. A hybrid, practical research approach combining experimental, finite element analysis (FEA), numerical and analytical calculations is presented. Fracture mechanics approach for fatigue life assessment is implemented. Crack growth calculation is based on the Paris - Erdogan law. Reduction in structural integrity due to crack propagation causes a reduction in natural frequency and transmissibility. The change in gain is evaluated via the open crack FEA model and integrated into the crack propagation algorithm. Resonance search, track and dwell module (RSTD) for maintaining constant gain throughout the test is not required. Fatigue life Wohler (SN) curve is constructed. Standard weld fatigue data is often provided for direct loading (tensile stress) and for different stress ratio (R) values. Corrections for mean stress and loading application are required. Current fully reversed (R = -1), indirect loading (bending stress) test results may be readily applied for random vibration fatigue analyses post processing. As expected, actual fatigue life results are higher compared to standard design curves, implying correctness of the manufacturing welding process of examined specimens. The presented procedure is of interest for research as well as for industrial welding processes testing, optimization and qualification.

On the Adaptability and Effect of High Damping Rubber Bearings in the Seismic Resistance of Large Aqueducts

Being the critical hydraulic structure in the construction of national water diversion projects, the large-scale aqueduct is one of the indispensable buildings in the rational allocation of water resources. Moreover, its safe operation during an earthquake is related to the success of the national water network’s construction. In this paper, HDRBs (high damping rubber bearings) have been used as the seismic isolation device for the large aqueduct, considering the FSI (fluid solid interaction) between the water and the walls of the aqueduct, and the mechanical model of HDRBs has been constructed by the bilinear model. The dynamic responses of the large aqueduct under different ground motion excitations, including different peak ground accelerations (PGAs) and operating conditions, have been calculated using the precise integration method. At the same time, the influence of RB (rubber bearings) and HDRBs, two kinds of bearings, on the seismic response of the large aqueduct is compared and analyzed. The maximum reduction in natural frequency with HRDB is about 72%, compared with the use of RB under different working conditions. When there is substitution of HDRB for RB, the stresses in the concrete at the corresponding positions decrease from 1.87 MPa to about 0.71 MPa. The analysis shows that HDRBs are equipped with well seismic isolation and energy dissipation performance, which can effectively reduce the seismic responses and improve the seismic performance of the large aqueduct. In addition, it shows that HDRBs have well adaptability to different operating conditions, ground motion excitation, and PGA, which can be extended to the constructions of aqueduct projects with high seismic intensity and complex geological conditions.

Static and dynamic control of smart damaged variable stiffness laminated composite plate with piezoelectric layers

The aim of the present study is to investigate the static and dynamic responses of damaged curved fiber laminated plates embedded with piezoelectric sensor/actuator. The damage characterized by anisotropic damage formulation is incorporated into the FE model to represent the damaged part of the structure. It is observed that continuous change of fiber orientation in lamina makes VSCL plates less affected by this type of damage and the reduction in natural frequencies can be minimized by adjustment of fiber orientation. Further, an active feedback control approach is adopted to damp out the vibration of the smart damaged VSCL plates.

Research on cumulative effect and diagnosis method of transformer short-circuit impulse

After transformers suffer from short-circuit impact, their mechanical performance decreases significantly. This article establishes a two-wire vibration model to represent the coupling between forces and mechanics and analyzes the transient vibration signals of a 400 V transformer during 22 short-circuits impact. To illustrate the cumulative effect of short-circuits, the vibration entropy, and energy ratio of the main vibration frequency and half frequency are adopted. The results show that transient vibration signals of transformer in short-circuits contain half frequency components, such as 25 Hz and 75, etc., and with the increase of the number of short-circuits, plastic deformation exists in insulation material, which leads to the loss of winding clamping pressure, the reduction of natural frequency, and the upsurge of parametric resonance. With the increase of short circuits, the vibration entropy and half-frequency energy ratio increase, and the main frequency energy ratio decreases. After winding completely lose the axial stability, the vibration entropy and half frequency ratio decrease, and the main frequency ratio increases. The conclusion is of great significance to the analysis of the cumulative effect of short circuits on power transformers.

Study on Staged Damage Behaviors of Rock-like Materials with Different Brittleness Degrees Based on Multiple Parameters

Understanding the brittle fracture behavior of rock is crucial for engineering and Earth science. In this paper, based on acoustic emission (AE) and laser Doppler vibration (LDV) monitoring technology, the staged damage behaviors of rock-like materials with different brittleness degrees under uniaxial compression are studied via multiple parameters. The results show that the brittleness degree determines the fracture mode. As the specimen's brittleness degree increases, the tensile failure increases and shear failure decreases. AE activity is enhanced at the crack damage point. With an increasing specimen brittleness degree, different instability precursor information is shown during the unstable crack growth stage: the AE b value changes from the fluctuating to continuously decreasing state, and the natural frequency changes from the stable fluctuation to upward fluctuation state. The AE b value near the stress drop is the smallest, and it decreases with an increasing brittleness degree. The natural frequency reduction indicates the rock-like fracture. The natural frequency is a symbolic index that reflects staged damage characteristics and predicts the amount of energy released by brittle failure. These findings provide guidelines for rock stability monitoring and provide support for better responses to stability evaluations of rock slopes, rock collapses, and tunnel surrounding rock in engineering.