Reduction In Natural Frequencies Research Articles

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.

Investigation of fluid viscosity and density on vibration of nano beam submerged in fluid considering nonlocal elasticity theory

Predicting the dynamical behavior of nanostructures in contact with fluid is of paramount importance owing to their vast range of applications in civil engineering, aerospace, etc. Therefore, the free vibration of a nonlocal Euler-Bernoulli beam in contact with fluid is studied in this research. Using the Navier-Stokes relation, the interaction forces between the fluid and nanobeam are obtained. The equation of motion is solved using the Galerkin method of weighted residuals, and the natural frequency values in different fluids are presented, considering the viscosity effect. Further, the fluid-solid interaction model on a macroscopic scale is compared with the finite element analysis results. By considering the fluid parameters to be zero, the results of the nonlocal beam have been validated with past research. According to the obtained results, when studying the vibration of nanobeams, while density has a remarkable impact on the reduction of nanobeam natural frequencies, the fluid viscosity can be neglected. The fluid has the greatest impact on lower modes, whereas the nonlocal parameter exerts the biggest influence on higher modes. Moreover, in all vibration modes, with the increase of the nonlocal parameter, the effect of the fluid on the reduction of the natural frequencies increases, and in the nanoscale, it has a more significant role in changing the vibrational behavior of the system compared to the classical condition.

FREQUENCY OF NON-LINEAR DYNAMIC RESPONSE OF A POROUS FUNCTIONALLY GRADED CYLINDRICAL PANELS

In this article, a nonlinear dynamical investigation of porose functionally graded cylindrical panels using a proposed analytical model is carried out. The material's properties are considered to be porosity-dependent and graded in the thickness direction, corresponding to a power-law distribution. The classical shell theory, with the geometrical shape of nonlinear in von Karman–Donnell, is employed to get the Lagrange motion equations. By applying the Galerkin procedure, the system of nonlinear dynamic vibration equations is found. The natural frequencies and dynamic amplitude vibrations are obtained by using the fourth-order Runge–Kutta approach. In numerical analyses, the effects of porosity factor, power-law index, porous FGM thickness, frequency–amplitude relation, and excitation force on the dynamic response of thin functionally graded porous cylindrical panels are investigated. Through the obtained results, it is discovered that the porosity coefficients have important effects on the natural frequencies and amplitude of the nonlinear dynamic response of the FG structures. It leads to a reduction in natural frequencies by 5.74 % at 10% pores.

Examination of the reduction in natural frequency of laterally loaded piles due to strain-dependence of soil shear modulus

Society's transition to low-carbon energy sources has resulted in significant expansion in offshore wind technology. Most offshore wind turbines (OWTs) are founded on large-diameter steel tubular piles driven into the seabed, termed monopiles. OWTs are subjected to large numbers of dynamic and cyclic environmental loads during their lifetime. To avoid fatigue or resonance issues, accurate characterisation of soil-structure interaction under operating and extreme conditions is paramount. There is a need to further improve understanding of the dynamic lateral response of piles after large lateral load cycling (storm events). This paper presents the results of lateral load field tests on piles with two different slenderness ratios, where the natural frequency was measured after a series of applied lateral load-unload events. 1D numerical models of the piles were developed and several operating parameters were varied to identify the parameters of importance in the nonlinear soil-pile interaction. Approaches to estimate the operating soil shear modulus both in-situ and post load-unload were trialled, and five subgrade reaction models were used to couple soil and pile properties, to ascertain the performance at predicting the measured frequencies from the experiments. Results suggest that predicted frequencies are highly sensitive to choice of model and degradation method used.

A Study on Dynamic Behaviour of Thermally Distributed Exponentially Graded Rotor System with Induced Porosities

The present work deals with the dynamic analysis of exponential law-based functionally graded (FG) rotor-bearing systems. The effect of thermal gradation and porosity on dynamic characteristics of FG rotor shafts has been studied first time, using exponential law with a novel two-nodded FG rotor element based on Timoshenko beam theory (TBT). Porous material properties are assorted using exponential law and thermal gradation across the cross section of the FG shaft using exponential temperature distribution (ETD). The effects of temperature and porosity on natural frequencies and whirl frequencies are studied. It has been observed that there is a significant reduction in natural frequencies and whirl frequencies with an increase in volume fraction of porosity and temperature. Attempts have been made to obtain suitable reasons for the behaviours based on the material properties. Furthermore, the steady-state and transient vibration responses have been simulated using the Houbolt time marching technique for the ceramic-based FG rotor shaft system. The result shows the maximum amplitude of the steady-state and transient vibration responses is increased, and the critical speed of the FG rotor system shifts towards the left with the increase in volume fraction of porosity and temperature.

A practical two-parameter model of pile–soil gapping for prediction of monopile offshore wind turbine dynamics

Monopile mounted offshore wind turbines (OWTs) are expected to experience a very large number of cyclic loads throughout their operational lifetime, and the existing p–y method of foundation modelling does not fully account for the effects of dynamic cyclic loading, such as pile–soil gapping. In this paper a dynamic model based on the beam on non-linear Winkler foundation scheme with a novel algorithm capable of capturing the effects of pile–soil gapping is presented. It can account for gap cave-in, and the resulting gap size can react dynamically to changing loading amplitudes, using only two calibration parameters. Static and dynamic cyclic loaded model validations are presented, and give very good agreement with experimental results, performing better than existing p–y curves for dynamic loading. The model is also applied to an OWT case study and predictions of natural frequency reduction due to soil erosion agree well with measured results. It is shown that the inclusion of gapping may result in a significant decrease to the natural frequency prediction of OWTs relative to the value predicted without gapping. As such, not to consider gapping could lead to unconservative predictions, and any additional soil degradation throughout the serviceable lifetime could therefore result in unwanted resonance. The method provided in this paper provides a simple and accurate model to predict this behaviour which is crucial to ascertain during the design phase.

Dynamic characteristics of RC structures in short and long duration real fires

The change in the dynamic behaviour of reinforced concrete (RC) structures after the fire events is still an unsolved issue for research communities and regulatory authorities. To fill the gap, this paper presents the experimental results of the shift in dynamic characteristics of a single scaled-down two-storey RC structure after exposure to short and long-duration real fires. The structure having normal strength concrete was constructed and well-instrumented with temperature sensors to obtain a large database of temperature profiles in the compartment and various element sections. Short Duration Fire Test (SDFT) of 20 min with a maximum temperature of 852 °C and Long Duration Fire Test (LDFT) of 100 min with a maximum temperature of 813 °C were created using wooden logs to represent a realistic office fire. The structure was further tested for dynamic characteristics such as natural frequencies and mode shapes by gently hitting it with a mass source that generated an impulse leading to free vibration in the structure. The natural frequency reduction of 14.71% and 49.5% were observed after the structure was exposed to short and long duration fires respectively. The mode shapes after the fires also showed variation indicating damages in the structure due to fires. The study will be useful in understanding the dynamic behaviour of structures in short and long-duration real fires as well as it will serve as a database for numerical modelling of RC structures.

Identifikacija učinka prirodne frekvencije na veličinu oštećenja na sendvič materijalu pomoću analize slobodnih vibracija

One of the most innovative developments in the field of advanced materials is sandwich materials. Sandwich material applications need standard requirements to be applied to marine structures, especially on ship construction. Sandwich material research is conducted on a laboratory scale to obtain the appropriate material composition in its development. In the process of developing this material, the material can be damaged. Most damage occurs in the core material, which results in difficulties in the identification process. This study compares damage identification methods based on free vibration analysis on the side sandwich plate of the ship’s hull. Damage-based identification is carried out to determine the response of vibration to the damage that occurs. Moreover, the method in this research uses a numerical approach and experimental vibration measurement. Numerical modelling is used to determine the appropriate boundary conditions and is shifted in experimental measurement. Damage modelling assumes that the material experiences core failure with a numerous variation model. Quantification of damage on the core correlates with natural frequency reduction due to a decrease in the stiffness of the sandwich material. Hence, the difference in the deviation value is used to determine the accuracy of damage identification.

A methodological framework to relate the earthquake-induced frequency reduction to structural damage in masonry buildings

The diffusion of seismic structural health monitoring systems, evaluating the dynamic response of engineering structures to earthquakes, is growing significantly among strategic buildings. The increasing availability of valuable vibration data is being backed by continuously evolving techniques for analysing and assessing structural health and damage. Within this framework, the paper proposes a novel model-driven vibration-based methodology to support the assessment of the damage level in masonry buildings hit by earthquakes. The leading idea is to exploit, in the pre-event phase, synthetic equivalent-frame modelling and nonlinear dynamic analyses to systematically relate the gradual reduction of natural frequencies to increasing levels of structural damage. The resulting behavioural chart (seismic chart) of the building, constructed by employing computational tools and robustly defined on a statistical base, may provide the theoretical expectation to ascertain a certain level of seismic damage, based on the decrease in vibration frequency experimentally identified in the post-event phase. The methodology is firstly formalized, integrating common identification techniques with a novel damage grade estimation procedure, and finally exemplified for a monitored strategic masonry building damaged by the 2016–2017 Central Italy earthquake sequence. The outcomes of this application confirm the operational validity of the methodology, which can be intended as effective support for the decision-making process regarding structural usability and safety in the post-earthquake scenario.

Numerical Studies on Mode I Delamination and its Effect on the Vibrational Characteristics in Fibre Metal Laminates

Fibre metal laminates (FMLs) afford the notable advances over ongoing composite materials for aerospace and automotive applications due to their low weight and outstanding mechanical properties. Nevertheless, FMLs are prone to damages during manufacturing and loading conditions. Double cantilever beam (DCB) and vibration test are the commonly used tools to assess fracture energy values and the level of damage influence on the material properties respectively. Therefore, this paper aims at correlating the numerical validation of mode I delamination with already published experimental data by Y.Pan et.al and study the influence of delamination under free vibration analysis of Magnesium (Mg AZ31) alloy based fibre metal laminates. For the presented model, the numerical values showed good acceptance with the experimental values of DCB test. It was also further observed that there is significant reduction in natural frequency due to delamination in the fibre metal laminates.

Vibration and damping analysis of smart sandwich nanotubes using surface-visco-piezo-elasticity theory for various boundary conditions

Present research includes damping as well as vibration evaluations of advanced sandwich nanotube. This nanostructure comprised of carbon nanotube (CNT) contains internal and external layers composed of ZnO provided as sensor and actuator. The structure is subjected to 2D magnetic and electric field as well. In order to presume this sandwich structure much more realistic, Kelvin model will be utilized and it is surrounded by visco-Pasternak foundation. Further, non-local piezoelasticity theory is employed regarding small scale influence. Gurtin-Murdoch model is noticed to account surface stresses. Besides zigzag shear-deformation theory for modeling the structure mathematically, Hamilton principle is applied to achieve motion equations. Generalized differential quadrature method (GDQM) is employed as numerical method for calculating sandwich structure's natural frequency and damping. So as to show accuracy of methods and validate, the obtained results are compared by another simplified cases. Finally, the influences of diverse traits and variables covering surface stresses, small scale parameter, magnetic and electric fields, surrounding medium and their effects on natural frequency will be studied. Citing the results, rise of nonlocal parameter results in reduction of natural frequency and regarding stress of surfaces leads to increase in natural frequency.

A semi-analytical nonlocal elasticity model for static stability and vibration behaviour of agglomerated CNTs reinforced nano cylindrical panel under non-uniform edge loads

A semi analytical nonlocal elasticity model to analyze the effect of non-uniform edge loads on static stability and free vibration characteristics of agglomerated carbon nanotubes (CNTs) reinforced nano cylindrical panels are presented. Effective material properties of the agglomerated CNT reinforced composite are obtained using a two-parameter micro-mechanics model while Eringen’s non-local theory is used to account the size effect. Sinusoidal shear deformation theory is adopted to analyze the buckling and vibration parameters using Galerkin’s approach. The accuracy of the proposed model is presented first by comparing the results in the literature. Then a comprehensive study is carried out to analyze the influence of various degrees of agglomeration (complete, partial), nature of edge load, and non-local effects on the buckling and free vibration response of CNT reinforced nano cylindrical panel. The results revealed that non-local size effect leads to a reduction in stiffness and thus reduces buckling and dynamic characteristics. Moreover, it is observed that critical buckling load varies with type of in plane load and reduction in natural frequency is different for different in plane loading conditions.

A numerical evaluation on nonlinear dynamic response of sandwich plates with partially rectangular skin/core debonding

Abstract As one of the most dangerous defects in the sandwich panel, debonding could significantly degrade load carrying capacity and affect dynamic behaviour. The present work dealt with debonding detection of the rectangular clamped hybrid sandwich plate by using ABAQUS software. The influence of various damage ratios on the linear and nonlinear dynamic responses has been studied. The finite element model was initially validated by comparing the modal response with the experimental test. Rectangular debonding was detected by comparing dynamic responses of free and forced vibrations between intact and debonded models. A wide range of driving frequency excitation corresponding to transient and harmonic concentrated loads was implemented to highlight nonlinear behaviour in the intermittent contact in the debonded models. The results showed that debonding existence contributed to the natural frequency reduction and modes shape change. The numerical results revealed that debonding affected both the steady-state and impulse responses of the debonded models. Using the obtained responses, it was detected that the contact in the debonded region altered the dynamic global response of the debonded models. The finding provided the potential debonding diagnostic in ship structure using vibration-based structural health monitoring.

Investigation on the damping of rectangular water tank with bottom-mounted vertical baffles: Hydrodynamic interaction and frequency reduction effect

Internal obstructions are commonly employed in Tuned Liquid Damper (TLD) tanks to produce sufficient inherent damping for improving its vibration control performance. However, the hydrodynamic interaction between obstacles has a significant effect on damping ratio of liquid sloshing when the obstacles are becoming close to each other. At the same time, the natural sloshing frequency of the water tank decreases because of the added mass produced by these obstacles. By adopting potential flow and linear wave theory, a linearized analysis model is proposed in this paper to estimate the damping ratio of rectangular water tank with bottom-mounted vertical baffles. The formula of its damping ratio is then further modified to take into account the effect of hydrodynamic interaction between vertical baffles on the fluid velocity and the added mass coefficient. In this study, reduction in the natural frequency of liquid sloshing due to vertical baffles is also investigated in detail. Shaking table tests were conducted on scaled models of the rectangular tank with bottom-mounted vertical baffles to validate the accuracy of the proposed analytical model in this study. Parametric studies are performed to study the effect of the distance between vertical baffles, different water depth ratios, various sinusoidal excitation amplitudes, and the different number of bottom-mounted vertical baffles on the damping ratio. The analyzed results showed that good agreement between the proposed analytical solutions and the experimental results was found. The study also showed that the proposed methodology can effectively estimate the damping ratio by considering the hydrodynamic interaction and natural frequency reduction effect due to the installed bottom mounted vertical baffles.

Study the correlation of natural frequency and damage index of 2D steel EBF-vertical shear link

Study of damage index of Eccentrically Braced Frame-Vertical Shear Link (V-EBF) was performed. The study was part of the research of damage index of several types of seismic resistance of steel structure. Three different stories of the V-EBF were taken from the preceding experimental study conducted by other researchers. Monotonic and semi-cyclic pushover analysis was carried out by using OpenSees software to get the parameters needed to determine the damage index which was calculated according to Park Ang’s theory. The index is measured as a sum of deformation per-cycle and the energy absorption. The study found that the natural frequency of the structure decrease with the increasing of structural damage. The reduction of natural frequency from the initial condition to the third damage is 70.79%, 71.68%, and 62.13% of the one, two and three stories of The V-EBF structure, respectively. The study observed the critical limit where the damage index begins to increase drastically, followed by a decrease of the natural frequency. It occurred when the ratio of natural frequency to the initial frequency was in the range of 43% to 59%.

Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

Exact Dynamic Characteristic Analysis of Steel-Concrete Composite Continuous Beams

The free vibration characteristics of steel-concrete composite continuous beams (SCCCBs) are analyzed based on the Euler–Bernoulli beam theory. A modified dynamic direct stiffness method has been developed, which can be used to analyze the SCCCBs with some lumped masses and elastic boundary conditions. The results obtained by the proposed method are exact due to the elimination of approximated displacement and force fields in derivation. The proposed method is verified by comparing its results with those obtained by ANSYS software and laboratory tests. Then, the influencing factors on the reduction of natural frequency are analyzed and discussed in detail using the proposed method. The results show that stronger interfacial interaction results in higher values of natural frequency as well as larger steel subbeam and thinner concrete slab. The smaller the natural frequency of the SCCCBs is, the more significant effect the interfacial interaction on the natural frequency is. The reduction of natural frequency is not affected by the different numbers of spans but the equal single-span length and various ratios of the side span to the main span but equal total length, but it is influenced by the extra single-span length and different ratios of the side span to the main span but equal main span length. And it is only affected by bending stiffness. Furthermore, the reasonable ratio of the side span to the main span is 0.9∼1.0.

Identification of damage in a ship hull sandwich plate by natural frequency

The damage of the sandwich plate occurs in the core material identification used for modal analysis on the ship hull using finite element analysis. This analysis detects the effect of damage. Five varied models using different damage percentage size is developed to ensure whether the hull is appropriate. This paper investigates the influence of the increasing damage percentage on the sandwich plate using the based natural frequencies as a parameter to determine the location of the damage. Five cases are being simulated for the damage. The location of the damage modelling used utilizing FEA software to adapt to the problems. Moreover, the sensitivity influence of percentage damage size, boundary condition, and application of spring element on the natural frequency behaviour of damage identification is also executing. The damage is detected by comparing the natural frequency reduction of the intact and damaged plate using free vibration analysis. The mode shape of the sandwich plate displayed to observe the location of damaged. The results show that the damage in the sandwich plate decrease the natural frequency and influence the mode shape, and evaluating both reveals the location of the damage.

Fatigue life prediction of cfrp composites in plane bending by modal analysis

This is investigation of the fatigue behaviour of carbon fiber reinforced polymer laminates under various angles of deflections of cantilever beam in bidirectional (R=-1) plane bending. The Unidirectional 45˚ carbon fiber oriented CFRP composite were tested at different cantilever bending angles at frequency of 8 Hz. The non- destructive modal testing is conducted to evaluate reduction in structural stiffness in fully reversed plane bending in terms of natural frequency. The modal test at specific intervals is conducted by interrupting the fatigue test. The curve fitting technique for prediction of fatigue life over experimental analysis is used to formulate behaviour of CFRP in plane bending fatigue. It is shown that A Non-destructive Testing method (Modal Test) can be applied for the fatigue life estimation of CFRP laminates. The natural frequency reduction model is able to represent the overall reduction in stiffness due to fully reversed plane bending fatigue.

Numerical investigation on behaviour of cylindrical steel tanks during mining tremors and moderate earthquakes

Cylindrical steel tanks are important components of industrial facilities. Their safety becomes a crucial issue since any failure may cause catastrophic consequences. The aim of the paper is to show the results of comprehensive FEM numerical investigation focused on the response of cylindrical steel tanks under mining tremors and moderate earthquakes. The effects of different levels of liquid filling, the influence of non-uniform seismic excitation as well as the aspects of diagnosis of structural damage have been investigated. The results of the modal analysis indicate that the level of liquid filling is really essential in the structural analysis leading to considerable changes in the shapes of vibration modes with a substantial reduction in the natural frequencies when the level of liquid increases. The results of seismic and paraseismic analysis indicate that the filling the tank with liquid leads to the substantial increase in the structural response under ground motions. It has also been observed that the peak structural response values under mining tremors and moderate earthquakes can be comparable to each other. Moreover, the consideration of spatial effects related to seismic wave propagation leads to a considerable decrease in the structural response under non-uniform seismic excitation. Finally, the analysis of damage diagnosis in steel tanks shows that different types of damage may induce changes in the free vibration modes and values of natural frequencies.