Reduction In Natural Frequencies Research Articles

Tension-tension fatigue life estimation of CFRP composites by modal testing

This study investigates the tension- tension fatigue behavior of carbon/epoxy laminates under constant amplitude loading. Workpieces were prepared as per with fiber orientation of 45˚ were tested at different stress levels, for R = 0.1 with a frequency 5 Hz. The overall stiffness reduction was evaluated in terms of natural frequency by using modal testing. The modal testing was applied at specific intervals by interrupting the fatigue testing. It is shown that modal testing a Nondestructive testing (NDT) method can be applied to the fatigue life stimation of CFRP laminates. Curve fitting technique was used for developing an empirical model for prediction of fatigue life of CFRP components. The experimental results found good agreement with the model results. From the experimental results it was concluded that the modal testing is useful as a NDT for estimation of fatigue life, natural frequency reduction model is capable of representing the overall stiffness reduction due to fatigue. Change in damping ratio (ζ) is more significant than change in natural frequency due to fatigue.

Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation

The present study covenants with the static and free vibration behavior of nanocomposite sandwich plates reinforced by carbon nanotubes resting on Pasternak elastic foundation. Uniformly distributed (UD-CNT) and functionally graded (FG-CNT) distributions of aligned carbon nanotube are considered for two types of sandwich plates such as, the face sheet reinforced and homogeneous core and the homogeneous face sheet and reinforced core. Based on the first shear deformation theory (FSDT), the Hamilton\'s principle is employed to derive the mathematical models. The obtained solutions are numerically validated by comparison with some available cases in the literature. The elastic foundation model is assumed as one parameter Winkler - Pasternak foundation. A parametric study is conducted to study the effects of aspect ratios, foundation parameters, carbon nanotube volume fraction, types of reinforcement, core-to-face sheet thickness ratio and types of loads acting on the bending and free vibration analyses. It is explicitly shown that the (FG-CNT) face sheet reinforced sandwich plate has a high resistance against deflections compared to other types of reinforcement. It is also revealed that the reduction in the dimensionless natural frequency is most pronounced in core reinforced sandwich plate.

Health assessment based on dynamic characteristics of reinforced concrete beam using realtime wireless structural health monitoring sensor

ABSTRACT The uses of dynamic estimations on existing structures are numerous: evaluation of their seismic vulnerability, structure’s abilities in post-quake circumstances or after changes in the region, and so on. At present, this sort of estimation enables auxiliary conclusion on a global scale, while the identification and the assessment of local damage (each element of the structure) needs to be investigated. Additionally, we begin to co-exist and interact with smart interconnected devices known as the Internet of Things (IoT). The IoT brought new opportunities for our society. Yet, most of the existing Structural Health Monitoring (SHM) systems are not connected to the IoT. Hence, this article studies the integration of complete real-time SHM platform with the Iot system, which can provide structural health of a structure and the performance of this sensor was check on a reinforced concrete (RC) beam. The RC beam was loaded in the central part in several stages corresponding to different damage states. Displacements were measured simultaneously using displacement sensors. After each load/unload cycle, dynamic measurements were taken using accelerometers. The perceptions from investigation were displayed, with the presence of damage and the reduction in natural frequencies that occurred in conjunction with reduction in stiffness.

Sealant Delamination Detection of Structural Sealant Glazing Systems Based on Driving-Point Accelerance

The structural sealant glazing system is widely used in glass curtain wall worldwide. However, due to the aging of the sealants, cracking may form along the sides of the glass. If the panel of curtain wall arises, delamination may occur and induce failure or loss of the system. In order to detect the delamination of the sealant, in this paper, a new vibration-based damage identification method is proposed by using the difference between the predamage and postdamage driving-point accelerance (DA). This detection method would require only one acceleration sensor on a glass panel and a rubber hammer, which operates very conveniently. When the rubber hammer taps the glass panel near the acceleration sensor, the glass curtain wall panel would generate acceleration response which can be measured by the acceleration sensor. The measured acceleration responses will be used to calculate the DA and lead to a new delamination index, called relative accumulative difference of DA, which will give indications on the potential delamination of the sealant. In addition, the influence of the acceleration sensor installation position was analysed by the finite element method, and the optimal sensor location was determined to be at the intersection of the long-side quarter and the short-side quarter. Nine cases on various delamination severities were identified by the new method, as well as the natural frequency reduction and modal assurance criterion. The laboratory experiments showed that the relative accumulative difference of DA is extremely sensitive to sealant delamination. Even if delamination severity was only 6.39%, the relative accumulative difference of DA would be larger than 18%. As the delamination of the sealant progresses, the relative accumulative difference of DA increases, resulting in an effective detection method for sealant delamination of the structural sealant glazing system. The fundamental frequency reduction is suitable to identify relatively large delamination, and the modal assurance criterion of higher modes is also sensitive to sealant delamination.

Investigation of Modal and Damage Parameters of Isotropic Cantilever Beam under Double-Sided Crack

In this study, the modal and damage parameters of isotropic mild steel cantilever beam under double-sided crack are studied. Static, modal and harmonic analyses for un-cracked and cracked cantilever beams have been carried out using finite element analysis software ANSYS. The natural frequencies and mode shapes for both un-cracked and cracked cantilever beams for the first five modes of bending vibration have been extracted using block Lanczos method through modal analysis. Harmonic analysis for both un-cracked and cracked cantilever beams has been performed, and deformation response in Y-direction in the range of 0–80 Hz has been plotted to determine the reduction in natural frequencies for the cracked beams by noticing the shifts in the natural frequencies. The results show that the amount of shifts in the natural frequencies of the cracked beam depends on pattern of mode shape and its deviation with respect to that of un-cracked beam. Rotational stiffness and flexibility at crack location have been analytically calculated, and the results show that by increasing the crack depth rotational stiffness decreases and flexibility increases. Zero frequency deflections for un-cracked and cracked beams have been determined through static analysis using ANSYS, and stiffness ratios for cracked beams were calculated. As the crack depth increases and the crack position from fixed end decreases, then the stiffness ratio for the cracked beam decreases. The evaluation of modal and damage parameters of cracked cantilever beams is crucially important to monitor the condition of the beams to eliminate the sudden failure.

Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches

The main objective of this research paper is to consider vibration analysis of vacancy defected graphene sheet as a nonisotropic structure via molecular dynamic and continuum approaches. The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defected graphene sheets. Molecular dynamic simulations have been performed to estimate the mechanical properties of graphene as a nonisotropic structure with single- and double- vacancy defects using open source well-known software i.e., large-scale atomic/molecular massively parallel simulator (LAMMPS). The interactions between the carbon atoms are modelled using Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of single-layered graphene sheets deflection field and the governing equations are derived using nonlocal elasticity theory. The dependence of small-scale effects, chirality and different defect types on vibrational characteristic of graphene sheets is investigated in this comprehensive research work. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The interesting results indicate that increasing the number of missing atoms can lead to decrease the natural frequencies of graphene sheets. It is seen that the degree of the detrimental effects differ with defect type. The Young\'s and shear modulus of the graphene with SV defects are much smaller than graphene with DV defects. It is also observed that Single Vacancy (SV) clusters cause more reduction in the natural frequencies of SLGS than Double Vacancy (DV) clusters. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems.

Degradation of Dynamic Parameters of Reinforced Concrete Buildings during an Earthquake

The article presents the results of a numerical study of the effect of local damage to load-bearing structures on the dynamic characteristics during an earthquake. The studies were carried out in the LS-DYNA software package, which implemented the nonlinear concrete model, Continuous Surface Cap Model (CSCM). The computational model of the building uses solid finite elements for concrete and bar elements for reinforcing bars. As the object of modelling, a 1-storey building with a frame structural layout was chosen. Studies have shown that during an earthquake with an intensity of 7 points, specified by the corresponding accelerogram, there is no change in natural frequencies, that is, the damage resulting from this earthquake is insignificant. During an earthquake with an intensity of 8 points, a significant (up to 55 %) reduction in natural frequencies occurs. This suggests that the structure is damaged, and the overall stiffness of the building is reduced. Analysis of the results shows that the most intense decrease in natural frequencies occurs in the active phase of an earthquake. After the end of the active phase, the frequencies stabilize and stop falling. The LS-DYNA software package enables to perform studies of the effect of local damage of the load-bearing structures on the dynamic characteristics during an earthquake with the direct reinforcement of concrete with reinforcing bars and can be used in the calculations and the design of buildings and structures.

Modal Analysis on Impeller Rotor of the Axial Flow Pump based on Fluid-structure Interaction

It is important to study the vibration characteristics of the impeller rotor of an axial flow pump for avoiding resonance and ensuring the safe and stable operation of the pump. Based on the fluid-structure coupling method and considering the compressibility of fluid, the coupling equation of fluid and solid is solved by inserting APDL command flow into ANSYS Workbench platform. The natural frequencies of the runner of horizontal axial flow pump in water and the reduction coefficients of each order of frequencies are obtained, and the distribution of each order of modes is analyzed. Additional mass theory is used to analyze the reasons for the reduction of natural frequencies. The results show that the natural frequency of the impeller of an axial flow pump decreases due to the water medium. The increase of the vibration quality of the whole system caused by the water body vibration is the fundamental reason for the reduction of the natural frequency of the impeller. The damp dissipation of the water body will lead to the decrease of the amplitude of the impeller in water.

Analytical Solution for Free Vibration of Annular Mindlin Plate with a Circumferential Open Crack

Mindlin plate theory is employed to obtain the free vibration response of an annular moderately thick plate with a circumferential open crack with fixed-free boundary conditions. To model the crack, a set of continuously distributed rotational springs are employed at the crack location. The corresponding spring stiffness value is a function of the crack depth and is given as a closed-form function. To obtain the vibration behaviour, the eigenvalue problem is solved to obtain the natural frequencies and mode shapes. The current method is verified by comparing the results with those obtained from finite element analysis. Through a parametric study, the effects of the crack depth and its radial location on the natural frequencies and mode shapes are investigated. The results show that for a constant crack depth, the reduction in natural frequency is a strong function of the radial location of the crack.

Experimental study on models of cylindrical steel tanks under mining tremors and moderate earthquakes

The aim of the study is to show the results of complex shaking table experimental investigation focused on the response of two models of cylindrical steel tanks under mining tremors and moderate earthquakes, including the aspects of diagnosis of structural damage. Firstly, the impact and the sweep-sine tests have been carried out, so as to determine the dynamic properties of models filled with different levels of liquid. Then, the models have been subjected to seismic and paraseismic excitations. Finally, one fully filled structure has been tested after introducing two different types of damages, so as to verify the method of damage diagnosis. The results of the impact and the sweep-sine tests show that filling the models with liquid leads to substantial reduction in natural frequencies, due to gradually increasing overall mass. Moreover, the results of sweep-sine tests clearly indicate that the increase in the liquid level results in significant increase in the damping structural ratio, which is the effect of damping properties of liquid due to its sloshing. The results of seismic and paraseismic tests indicate that filling the tank with liquid leads initially to considerable reduction in values of acceleration (damping effect of liquid sloshing); however, beyond a certain level of water filling, this regularity is inverted and acceleration values increase (effect of increasing total mass of the structure). Moreover, comparison of the responses under mining tremors and moderate earthquakes indicate that the power amplification factor of the mining tremors may be larger than the seismic power amplification factor. Finally, the results of damage diagnosis of fully filled steel tank model indicate that the forms of the Fourier spectra, together with the frequency and power spectral density values, can be directly related to the specific type of structural damage. They show a decrease in the natural frequencies for the model with unscrewed support bolts (global type of damage), while cutting the welds (local type of damage) has resulted in significant increase in values of the power spectral density for higher vibration modes.

Spring amplification and dynamic friction modelling of a 2DOF/2SDOF system in an electromagnetic vibration energy harvester – Experiment, simulation, and analytical analysis

Abstract A cantilever beam-based vibration energy harvester is generally preferred due to its simplicity and effectiveness as compared to a spring mass system. This paper analyses the use of a spring to amplify the performance of a conventional single degree of freedom (SDOF) cantilever beam-based vibration energy harvester. A spring was introduced to modify the conventional SDOF design into a two single degree of freedom (2SDOF) system and a two degree of freedom (2DOF) system. The motion of the spring was restricted in the vertical motion using a slider and a linear guide rail fixed to the vibrating base, hence introducing a dynamic friction into the system. Both designs were analysed under three different cases to observe the effect of natural frequency reduction on the frequency bandwidth and power harvested by each design. The vibration-friction interaction in the designs was modelled based on the concept of relative motion. Two different friction theories were applied and verified with simulation and experiment. It was shown that the stick condition would not occur in a SDOF system with a dynamic friction interaction. It was also found that it is possible to tune the friction force of a dynamic friction surface to induce a favourable output at the isolation frequencies of a 2DOF system. Analysis shows that the 2DOF design displayed a larger power density than the conventional SDOF design below a certain natural frequency value, being 78.1% higher at 9.5 Hz. The power densities of the 2SDOF design were almost similar to the SDOF design. However, the 2SDOF design displayed a significant drop in power when under the condition of matched natural frequencies. Nevertheless, the frequency bandwidth of the 2SDOF design can be improved by tuning its two resonant peaks closer to each other.

Numerical Investigation Into the Influence on Hydrofoil Vibrations of Water Tunnel Test Section Acoustic Modes

High-speed water tunnels are typically used to investigate the single-phase and two-phase flows around hydrofoils for hydraulic machinery applications but their dynamic behavior is not usually evaluated. The modal analysis of an NACA0009 hydrofoil inside the test section was calculated with a coupled acoustic fluid–structure model, which shows a good agreement with the experimental results. This numerical model has been used to study the influence on the hydrofoil modes of vibration of the acoustic properties of the surrounding fluid and of the tunnel test section dimensions. It has been found that the natural frequencies of the acoustic domain are inversely proportional to the test section dimensions. Moreover, these acoustic frequencies decrease linearly with the reduction of the speed of sound in the fluid medium. However, the hydrofoil frequencies are not affected by the change of the speed of sound except when they match an acoustic frequency. If both mode shapes are similar, a strong coupling occurs and the hydrofoil vibration follows the linear reduction of natural frequency induced by the acoustic mode. If both mode shapes are dissimilar, a new mode appears whose frequency decreases linearly with speed of sound while keeping the acoustic mode of vibration. This new fluid–structure mode of vibration appears in between two hydrofoil structure modes and its evolution with sound speed reduction has been called “mode transition.” Overall, these findings reinforce the idea that fluid–structure interaction effects must be taken into account when studying the induced vibrations on hydrofoils inside water tunnels.

Reduction of Pipeline Natural Frequencies by Negative Stiffness Vibration Isolators

The paper is devoted to the problem of reduction of vibration level of pipelines, caused by resonance with the disturbing frequency of pumping units. The causes of large vibrations of main pump units piping and its influence to the level of the pump unit oscillations are analyzed. The source of increased vibration exposure in the “pump - pipe” system is often not only the pump unit, but pump piping also. Piping of the pumping unit in case of its operating parameters changing can be entered to resonance. It is offered to use disk springs with negative stiffness area for vibration isolation. Pipeline in this case acts as a “stabilizer” for a vibration isolator with negative stiffness. Analytical calculations and experiment have been made to prove the effectiveness of proposed solution.

Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface

In the current investigation, the small and large amplitude free vibration characteristics of long cylindrical panels made of FGMs is investigated using the higher order shear deformation shell theory and Donnell kinematic assumptions. The interaction of the panel with a nonlinear hardening/softening foundation in also included into the formulation. The properties of the panel are assumed to be graded across the thickness of the panel and assumed to be temperature dependent. Using the neutral surface concept, the three coupled motion equations of the shell are established and solved for the case of long panels which are immovable simply supported on straight edges. The solution method is based on the two step perturbation technique which results in a closed form expression for the frequencies of the panel as a function of the mid-point deflection. Numerical studies are first validated for the case of long FGM plates. Afterwards novel numerical results are given to show the effect of geometrical parameters, power law index, foundation stiffnesses and temperature elevation. As shown, temperature elevation results in the reduction in natural frequencies and enhancement of the frequency ratio of the panel. Also temperature dependency reduces the natural frequencies and frequency ratios of the panel.

Small strain effect on the mechanical vibration behavior of cross-linked functionalized carbon nanotubes with polyethylene: A molecular-dynamics study

Based on the classical molecular-dynamics (MD) simulations, the vibrational behavior of cross-linked functionalized carbon nanotubes (CNTs) with polyethylene (PE) chains is studied under the applied mechanical tensile and compressive strains. So, different distribution patterns, namely mapped and wrapped distribution patterns are chosen. According to the results, it is seen that natural frequency of cross-linked functionalized CNTs reduces in which this reduction increases by increasing the weight percentage of attached chain. Under tensile strain, it is observed that the frequency of functionalized CNTs increases. Moreover, it is observed that the frequency shifts rise by increasing the applied tensile strain. By contrast, the compressive strain results in higher reductions in natural frequency of functionalized CNTs which considerably rises by increasing the applied strain. Moreover, it is shown that as the weight percentage of cross-linked functionalized CNTs increases, the sensitivity of the frequency shift to the applied tensile and compressive strains decreases and increases, respectively.

Enhancement of low cycle vibration induced fatigue life of composite beam having central hole using CNT reinforcement: An experimental study

In the present study, experimental investigations have been carried out to study the effect of low cycle vibration fatigue on the dynamic characteristics of hybrid composite beams with central hole reinforced with carbon nanotubes (CNT) and compare the performance of composite beams without central hole. Neat glass fiber reinforced polymer (GFRP) and CNT hybridized GFRP composite beams (CNT-GFRP) were fabricated using vacuum-assisted hand lay-up technique. Quasi-isotropic composite beams with ply orientation of [45°/−45°/0°/90°]S were fabricated. Initially, experimental modal analysis was carried out to identify the natural frequencies of GFRP and CNT-GFRP composite beam without and with central hole under clamped-free end conditions. Then, the composite beams were exposed to vibration induced fatigue through an electrodynamic shaker at various cycles of operation nearer to their fundamental natural frequencies. The experimental modal analysis was performed on the test specimens at every stages of vibration induced fatigue cycle and the natural frequencies and damping ratios were identified. Owing to the cyclic fatigue induced on the composite beams, a reduction in stiffness of the composite beams with increase in cyclic fatigue was observed through the reduction in natural frequencies of composite beams without and with CNT reinforcement. The results also showed that the presence of CNT not only imparted a higher stiffness to the composite beams but also enhanced its resistance to the deteriorating stiffness and provided an improvement in overall life of the structure. Further, the results provide a guideline for the designer on enhancement of low cycle fatigue life of structures using CNT reinforcement.

Investigation of Natural Frequency Reduction Mechanism of a Historic Masonry Building in Patan following the 2015 Gorkha Earthquake in Nepal

Investigation of Natural Frequency Reduction Mechanism of a Historic Masonry Building in Patan following the 2015 Gorkha Earthquake in Nepal

Impact of Constraint Conditions and Cutouts on Natural Frequency of Glass Fiber Reinforced Plastic Composite

Majority of the activities of a human being is associated with vibrations of one or other form. Application of vibrations can be found from a simple example like listening to music to challenging ones like design of complex machines and structures. Design of any system will not be rugged if it does not consider vibrations and its effects. The energy dissipated per cycle can be understood as damping. Presence of damping in a structure is represented by damping factor or damping ratio. Fibre reinforced plastic composites are a class of materials made from matrix and reinforcement. Matrix can be a resin system and reinforcement is usually fabric made of glass, carbon or aramid. The vibrating mechanical system causes resonance resulting in failure of machine components. By knowing the natural frequency and changing it from the range of operating machine member, resonance phenomenon could be avoided. This work focuses on finding the damping ratio and natural frequency of s glass fibre reinforced polymer composites through harmonic & modal analysis both by experimental method and FEM analysis for bare plate, plate with rectangular cutouts and plate with circular hole. The reduction in natural frequency and increase in damping corresponds to a change in stiffness and damping of the system. These changes are attributed to freeness of the system and introduction of cutouts in the laminate.

Crack detection of cantilever beam by natural frequency tracking using experimental and finite element analysis

The investigation of a crack in a cantilever beam is very imperative in various mechanical applications such as turbo machinery impeller blades, propeller shafts and airplane wings. As a result, a full study is performed in this paper to investigate the crack consequences on a cantilever beam; this is carried out by monitoring the natural frequency of the beam, taking into consideration the probe mass used in data collection. The investigation is divided into two phases; the first phase is experimentally performed by measuring the natural frequency of a specimen with different thicknesses and widths while changing specimen material to illustrate the specimen dimensional and material effect on natural frequency reduction. This is carried out on different specimen configuration by changing crack location and depth. The second phase is to validate the acquired results from the first phase. This is achieved by using finite element analysis (FEA) techniques, this is performed by modeling the experimental phase conditions into ANSYS 16.2, one time considering the probe mass and other time without putting probe mass into consideration. Finally, the FEA results are compared with experimental phase results.

A model-based data-interpretation framework for post-earthquake building assessment with scarce measurement data

Recent earthquake events throughout the world have once again exposed the vulnerability of buildings with respect to earthquakes. It is unlikely and unsustainable to design and - especially in regions with low-to-moderate seismic hazard – to retrofit all buildings to remain within elastic displacement ranges during earthquakes with high return periods. Therefore, post-earthquake assessment plays a fundamental role in the resilience of cities, given the potential to reduce time between an earthquake event and the clearance for (renewed) occupancy of a building. In this paper, a framework for model-based data interpretation of measurements of earthquake-damaged structures is presented. The framework allows engineers to combine ambient-vibration measurements and visual inspection to reduce parametric uncertainty of a high-fidelity model using the error-domain model-falsification methodology. For building types that have limited stiffness contributions from non-structural elements (i.e. shear-wall buildings) and for which non-ductile failure modes (such as out-of-plane failure) can be excluded, reduction in natural frequency and damage grades derived from visual inspection provide global measurement sources for structural identification. The application of the proposed methodology to a shear-resisting building tested on a shake table illustrates that vulnerability-curve predictions provide accurate damage estimates for subsequent earthquakes with probabilities between 50% and 100% for five measured scenarios. In complete absence of baseline information regarding the initial building state and the earthquake signal, parametric uncertainty is reduced by up to 76%. This study thus demonstrates usefulness for certain building types to enhance post-seismic vulnerability predictions.