Fundamental Natural Frequency Research Articles

Impact of point vacancy defects on vibrational behaviour of three-walled carbon nanotubes.

Through experimental observations and reports, various challenges have been identified in carbon nanotubes (CNT), including Stone Wales (SW) flaws and position flaws. Among these imperfections, point vacancies are the most prevalent in the CNT lattice. However, there is currently no established method for detecting these issues, and the influence of these flaws on the vibrational properties of three-walled carbon nanotubes (TWCNTs) remains uncertain. This research paper introduces a novel approach that utilizes vibrational analysis to detect flaws in TWCNTs. By conducting the first investigation into the impact of point vacancies on the vibrational modal frequencies of TWCNTs, our study bridges these knowledge gaps. This study examines the impact of defect quantity on various types of TWCNTs and investigates the vibrational properties of TWCNTs with point vacancies using a molecular structural mechanics technique. A total of 432 TWCNT models were simulated using molecular structural mechanics (MSM), and their modes were identified through finite element (FE) analysis. The fundamental vibration's natural frequency in TWCNTs with defects was then determined. The findings indicate that the depth of the mode shape is influenced by the TWCNTs' diameter, the extent of point vacancy defects, and the boundary condition. It was observed that as the number of vacancy defects increases from 0 to 4%, the natural frequency decreases. The study also establishes the order of TWCNTs with the highest natural vibrational frequency at 0%-point vacancy and [Formula: see text] a given attached mass, which follows the sequence of chiral, armchair, and zigzag TWCNTs.

Vibrations of porous functionally graded CNT reinforced viscoelastic beams connected via a viscoelastic layer

This work analyses the vibrational response of porous viscoelastic functionally graded (FG) carbon nanotube (CNT) reinforced double beams. The beams are simply supported, connected through a viscoelastic layer, where four functionally graded patterns of CNT in the thickness directions (uniformly distributed (UD), FG-V, FG-O, and FG-X) are considered. The porosity models considered are UD, PO-V and PO-X. After formulating the coupled equations of motion via an energy-based method, and incorporating the effects of the viscoelastic beams and viscoelastic layers, the equations are solved using an assumed series expansion technique. The equations and solution methodology are verified utilising simplified models from existing literature and also through development of a finite element method (FEM) based simplified model; very good agreement has been achieved. Effects of the stiffness and viscous coefficients of the viscoelastic layer, the structural viscosity parameter of the porous CNT reinforced double beams, the porosity coefficient, and porosity models are examined. Overall, the results indicate that the stiffness and viscous coefficients of the viscoelastic layer have increasing effects on the real and imaginary components of second series fundamental transverse natural frequency of the double beam system, respectively. An increase in the structural viscosity parameter of the porous CNT reinforced double beams leads to an increase in the imaginary components of the fundamental frequencies of both the series. Moreover, a range of different effects on the real and imaginary components of the natural frequencies were noted while varying the porosity coefficient and models. The FG-X CNT porous reinforced viscoelastic double beams with a viscoelastic layer have the highest natural frequencies of all the cases. The study demonstrates the importance of the porosity, viscoelastic layer and viscoelastic material properties on the dynamics of the system.

Influence of GNP nanoparticles on shear and dynamic behaviour of flat-joggle-flat composite joints

The focus of the current research is to examine the effects of adding graphene nanoparticles (GNP) to GFRP flat-joggle-flat (FJF) composite joints made with the co-cure manufacturing process on their mechanical and vibrational properties. The experimental results show that adding 0.25, 0.50, and 0.75 wt% GNP reinforcement to the resin greatly improved the strength properties of composite joints by 8.30%, 26.37%, and 34.73%, respectively. However, a higher percentage of GNPs (1%) reduced the strength of joints by 3.90% due to agglomeration. Field emission scanning electron microscopy (FESEM) reveals that 0.75 wt% of GNP reinforced enhanced interfacial interaction and created coarser interfaces in the bond line to postpone failure. Cutting-edge internal failure and damage progression modes are incorporated by the ultrasonic C-scan method. The modal analysis confirmed that the 0.75 wt% GNP reinforcement had the maximum fundamental natural frequency of 918.1 Hz compared to other weight percentages. The obtained experimental results and used methods are in good agreement.

Free Vibration Analysis of a Tunable Micro-Fabrication Device Comprising Asymmetric L-Shaped Membranes.

Membrane sensors have been widely used in various fields owing to their multifunctionality and cost-effectiveness. However, few studies have investigated frequency-tunable membrane sensors, which could enable versatility in the face of different device requirements while retaining high sensitivity, fast response times, and high accuracy. In this study, we propose a device comprising an asymmetric L-shaped membrane with tunable operating frequencies for microfabrication and mass sensing applications. The resonant frequency could be controlled by adjusting the membrane geometry. To fully understand the vibration characteristics of the asymmetric L-shaped membrane, the free vibrations of the membrane are first solved by a semi-analytical treatment combining domain decomposition and variable separation methods. The finite-element solutions confirmed the validity of the derived semi-analytical solutions. Parametric analysis results revealed that the fundamental natural frequency decreases monotonically with the increase in length or width of the membrane segment. Numerical examples revealed that the proposed model can be employed to identify suitable materials for membrane sensors with specific frequency requirements under a given set of L-shaped membrane geometries. The model can also achieve frequency matching by changing the length or width of membrane segments given a specified membrane material. Finally, performance sensitivity analyses for mass sensing were carried out, and the results showed that the performance sensitivity was up to 0.7 kHz/pg for polymer materials under certain conditions.

3D numerical analysis of the structural behaviour of a carbon fibre reinforced polymer drive shaft

Due to their high strength and favourable mechanical behaviour, metals are used in a variety of applications within the automotive industry, including drive shafts. However, the use of metallic drive shafts in the automotive sector presents some disadvantages such as high inertial masses. This work investigates the mechanical benefits of using Carbon Fibre Reinforced Polymers (CFRP) for manufacturing drive shafts. A Formula Student car was used as a model for the present work design for the drive shaft. Drive shafts made of Steel AISI 4340, Aluminium, and CFRP are investigated when subjected to mechanical excitations. Simulation includes the use of Comsol Multiphysics software. The CFRP drive shaft was modelled using the layered material feature. Various stacking sequences are tested. Results show that [90°/0°/-45°/+45°] sequence presents the best mechanical behaviour. Analytical and numerical calculations for the natural frequencies are performed and compared. CFRP drive shaft is observed to give the highest fundamental natural frequency when compared to the metallic counterparts. Fatigue analysis are also studied and revealed that the drive shafts can sustain the applied load for its expected fatigue life, with the CFRP drive shaft having the highest fatigue usage factor. Critical buckling analysis showed that the drive shaft made of steel has the highest critical buckling torque. However, drive shafts made of carbon fibre reinforced polymer was found to be 40.7% lighter than the aluminium tube and 79.6% lighter than the steel tube.

Evaluating Stochastic Fundamental Natural Frequencies of Porous Functionally Graded Material Plate with Even Porosity Effect: A Multi-Machine Learning Approach

Evaluating Stochastic Fundamental Natural Frequencies of Porous Functionally Graded Material Plate with Even Porosity Effect: A Multi-Machine Learning Approach

Object Identification With Minimal Precomputed Library Using Physical Aspect of Singularity Expansion Method

In this letter, we propose a method for estimating the circumferential length of metal objects without any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information regarding object shape and dimension. Object type can also be determined using this method with a reduced precomputed library consisting of the quality factor of fundamental natural resonance frequency and the ratio of second-order to first-order damped resonance frequency for each object type. The proposed method is applied to identify different canonical objects. Natural resonance frequencies, extracted using the matrix pencil method of singularity expansion from the scattered field from different metal objects, have been validated with physical reasoning. Simple methods for predicting the resonance frequency of triangular plates and discs have been proposed.

Modal Identification of 38 Supertall Buildings and Establishment of Predictive Models

Information on natural frequencies and damping ratios is essential for structural dynamic analysis. To develop predictive models of modal parameters applicable for modern high-rise buildings with increasing heights, an advanced interferometric radar system was employed to measure the displacement responses of 38 supertall buildings with heights ranging from 200 to 600 m under ambient excitations. Then, a combined approach of the stochastic subspace method and an uncertainty bound estimation method are adopted for modal identification, and its accuracy is validated by a numerical simulation study. By applying the modal identification method to the field measurements, modal parameters of the 38 supertall buildings are identified. Based on these results, predictive models for fundamental natural frequency and damping ratio of supertall buildings are accordingly proposed, which are more applicable for the wind-resistant serviceability assessment or design of high-rise buildings with heights over 200 m than existing empirical models.

Design Optimization of a Hybrid Vibration Control System for Buildings

Control of high-rise structures under seismic excitations was investigated using a passive hybrid control system consisting of a base-isolation (BI) subsystem and a passive tuned liquid column damper (TLCD) system. Both of the systems were optimized considering using the other system in the same structure. An optimization method was developed, and a computer code was written based on dynamic analysis of the structure and metaheuristic optimization methods. Within the scope of the study, a general solution was found by using many earthquake records during the optimization process. Moreover, one of the most suitable and successful metaheuristic algorithms was used in this study. In addition, numerical simulations were performed on a benchmark high-rise building structure to investigate the effectiveness of the optimized hybrid control system in controlling the seismic response of the building. The performance of the base-isolated TLCD-controlled structure was examined when the TLCD was placed on the base floor by using a set of 44 recorded ground motions as base excitations. Based on the results obtained from this study, the use of a base-isolation subsystem decoupling the superstructure from the ground motions by lowering the structure’s fundamental natural frequency reduces the structural responses of the building in most cases. The responses of the base-isolation subsystem were not too large since the parameters of the BI subsystem were optimized specifically for the investigated structure. Nevertheless, displacements of BI might exceed the maximum limit to undesirable values in some cases. The TLCD system appears to be quite effective in protecting the base-isolation subsystem by reducing its displacements to the maximum allowable limit or below when attached to it. Moreover, the proposed passive hybrid control system can effectively reduce the structural responses under seismic excitations.

Coupling performance of two tandem and side-by-side inverted piezoelectric flags in an oscillating flow

The flow-induced vibration characteristics and energy extraction performance of two flexible inverted piezoelectric flags arranged in tandem and side-by-side configurations in an oscillating flow are studied. An immersed boundary-lattice Boltzmann method is employed for Reynolds number of 100, mass ratio of 2.9 and non-dimensional bending stiffness of 0.26 which correspond to the maximum flapping amplitude for a single inverted flag in a uniform flow. 2D simulations are conducted by varying the ratio R of the frequency of the oscillating flow to the fundamental natural frequency of the flag and the horizontal velocity amplitude (Au) of the flow. Three coupling regimes at Au=0.5 are identified for both tandem and side-by-side flags: chaotic oscillations regime I (0.1≤R≤1), large periodic and symmetric oscillation regime IIa1.1≤R≤1.5andIIb(2.1≤R≤3.0), and small periodic and asymmetric oscillation regime III(1.6≤R≤2). The maximum mean electrical power coefficient C¯P occurs in regime IIa at R=1.5 with, α (piezo-mechanical coupling parameter) = 0.5, and β (piezo-electric tuning parameter) = 1.5. C¯P is 0.1 for a tandem upstream flag, 0.068 for the tandem downstream flag and 0.1 for both side-by-side flags, and is respectively 120%, 300% and 213%, higher than that of the corresponding flag in the uniform flow. This improvement is attributed to the higher flapping angular amplitude (180°), the higher ratio of the flapping frequency of the flags to the oscillating frequency of the flow (virtually constant at 0.5), and constructive vortex interaction in regime IIa.

A modal analysis based optimal mounting support locations of a printed circuit board

Purpose This paper aims to improve the life of the printed circuit boards (PCB) used in computers based on modal analysis by increasing the natural frequency of the PCB assembly. Design/methodology/approach In this work, through experiments and numerical simulations, an attempt has been made to increase the fundamental natural frequency of the PCB assembly as high as practically achievable so as to minimize the impacts of dynamic loads acting on it. An optimization tool in the finite element software (ANSYS) was used to search the specified design space for the optimal support location of the six fastening screws. Findings It is observed that by changing the support locations based on the optimization results the fundamental natural frequency can be raised up to 51.1% and the same is validated experimentally. Research limitations/implications Manufacturers of PCBs used in computers fix the support locations based on symmetric feature of the board not on the dynamic behavior of the assembly. This work might lead manufacturers to redesign the location of other surface mount components. Practical implications This work provides guidelines for PCB manufacturers to finalize their support locating points which will improve the dynamic characteristics of the PCB assembly during its functioning. Originality/value This study provides a novel method to improve the life of PCB based on support locations optimization which includes majority of the surface mount components that contributes to the total mass the PCB assembly.

Snap-through energy harvester with buckled mechanism and hierarchical auxetic structures for ultra-low-frequency rotational excitations

In this Letter, a snap-through energy harvester is proposed to break through the energy output bottleneck of ultra-low-frequency (&amp;lt;1 Hz) rotational energy harvesting. On one hand, a buckled mechanism provides large-amplitude snap-through motion that enhances the output power. On the other hand, the hierarchical auxetic structures enable the simultaneous operation of d31 and d32 modes of piezoelectric buzzers and boosts the energy harvested. Moreover, both the buckled mechanism and auxetic structures can reduce the fundamental natural frequency of the total system. A finite element model is established to predict the harvester performances, which are validated via experiments. Experimental results show that the integration of the buckled mechanism and auxetic structures can improve the output power by 3224.75% at 0.5 Hz. Specifically, the proposed harvester can achieve an output power of 146.2 μW and a normalized power density of 1.392 μW/mm3 Hz2 at 0.5 Hz, which are superior to other state-of-the-art rotational piezoelectric energy harvesters. Therefore, the proposed harvester can provide sufficient energy for low-power sensors at ultra-low rotational frequencies and has a great application potential in the structural health monitoring of wind turbine blades.

Vibration of a Flexible Follower in a Cam Mechanism with Time-Dependent Boundary Effect

A vibration analysis of a flexible follower in an oscillating follower cam system undergoing a rise-dwell-fall-dwell (RDFD) motion is performed. Owing to the time-dependent boundary effect caused by considering simultaneously the axial and the lateral displacements of the follower, two geometric constraints are formulated and added to Hamilton’s principle to establish the vibration equation of the motion of the follower. The coupled axial and lateral vibration of the flexible follower has been studied for the first time. The fast Fourier transform (FFT) spectrum generated from the time history is used for parametric studies. The numerical results of the present study show some new findings. The major spectral peaks for the lateral follower response locate at the low frequencies of 1 Ω, 3 Ω, 5 Ω, and 7 Ω and the high frequency near the fundamental natural frequency where Ω is the cam speed. The largest peak locates mostly at the frequency of 3 Ω. For the ascending and descending motions of the follower RDFD motion, three types of cam profiles are designed. Important new results are found: although the three cam profiles nearly overlap, the vibration results of the follower are quite different. By using a modified sinusoidal acceleration motion, the magnitude of the main lateral peak at low frequencies is minimized. The lateral peak amplitude near the fundamental natural frequency of the follower is the smallest when the cycloid displacement motion is adopted.

Structural design optimization of a high-speed rotor system for mechanical vibration mitigation

This work proposes a design optimization approach for a high-speed rotor system, commonly used in a wide range of industrial applications, in order to address the issue with the flexural flexibility of a rotor system which can cause significant vibration and noise problems due to shaft whirl. For this purpose, the numerical modeling of a flexible rotor system was used to carry out the optimization process considering the effects of the mass and transverse natural frequency to the optimized design. Torque and geometrical sizing were also incorporated as the constraints in the optimization. The rotor system was modeled as a multi-disc Jeffcott rotor system that allows a rapid design optimization process. A case study on a high-speed rotor was carried out to demonstrate the effectiveness of the developed optimization approach, yielding the reduction of the rotor mass by at least 45.6%, while the fundamental transverse natural frequency has been increased by 2.91% as the result.

Analysis of Torsional Vibrations of Rotary Winding Machines

This work is chosen to analyze the rotary winding machines because these machines are existed in our country and this analysis is practical from the side of input values and getting the results. Good rotary winding machine design practice demands the analysis of the system to insure that the reaction due to operation of the machine will not cause damaging vibrations. The widest phenomenon in vibration forms in mechanical transmission is the torsional vibration. The aim of this work is the analysis of the torsional vibrations of these rotary winding machines and to minimize that vibrations and to alleviate recurring costly maintenance problems. &#x0D; To minimize system dynamic torques it is necessary to spread the torsional natural frequencies. This is best achieved by lowering the fundamental torsional natural frequency. In main rotary winding machine drives this is most readily accomplished by lowering the torsional stiffness at the lead spindle location or, by making the lead spindle torsional flexibility greater by increasing the shaft separation or, if necessary, by using a torsionally flexible spacer. Torsional stiffness is inversely proportional to shaft length. For the solution of the problem one must first of all estimate the physical system parameters taking into consideration the real set of components of a rotary winding machine and then to transform them into a mathematical model. In this work there was also the method of calculation model presented. &#x0D; The equations of motion of the whole vibrating system are defined and the study include solution of torsional vibration of this machine by using Jacobi method as method of solution because it is easy to program and accurate. A computer program (Math Lab) has been used in order to Facilitate the solution because it is contain already comments specialized to solve the vibration problems. Finally, finding the final results gave a good vision to forecast the failure of the machine that could caused either by errors in design or operating conditions. &#x0D;

Behavior of Cross-Laminated Timber Panels Made from Fibre-Managed Eucalyptus nitens under Short-Term Serviceability Loads

In this study, the preliminary serviceability performance of cross-laminated timber (CLT) panels constructed from fibre-managed Eucalyptus nitens (E. nitens) was investigated via bending and vibration tests. Linear four-point bending tests were performed to determine the stiffness and deflection of all CLT panels under serviceability loads. The dynamic response of CLT panels was tested using a basketball and an accelerometer. The fundamental natural frequencies of all tested panels were above the minimum frequency limit (8 Hz) when extrapolated to spans of up to 4.4 m. The configurations of E. nitens CLT panels were based on different modulus of elasticity (MOE) values for each board. Using higher MOE timber boards as the top and bottom layers can significantly increase the serviceability performance of both bending and vibration tests. The same experiments were carried out on two CLT panels made of strength class C24 Spruce-Pine-Fir to compare the serviceability performance of E. nitens CLT. The results demonstrated that E. nitens is a reliable resource for CLT manufacturing, and exhibits better serviceability performance compared to Spruce CLT. This provides more sustainable options for a species traditionally destined for pulp.

Evaluating dynamic behaviour of a concrete dam using modal analysis

Modal Analysis is the most fundamental aspect of the dynamic study of structures. It is used to determine the vibrational characteristics of linear elastic structures. It suggests the natural frequencies and mode shapes, which are essential to understand the dynamic behaviour of that structure. In this study, Shahpurkandi Dam, a concrete gravity dam of height 55.5 m is considered in order to investigate its dynamic properties using the finite element package ‘ANSYS’. Furthermore, structure-acoustic interaction is explicitly modelled, and a case of the full reservoir is taken into account to analyze the modal response of the dam. The first 6 mode shapes are extracted, and the total displacement is recorded through the numerical simulation of the direct solver including the block Lanczos method. This study shows the maximum deformation is recorded for the first fundamental natural frequency, which is 0.0039 mm at the crest of the dam. Henceforth, it is essential to monitor the mode shape and natural frequency of initial modes. The comparison of natural frequency is also demonstrated for full reservoir and empty reservoir cases.

Mathematical modelling and dynamic analysis of composite hollow shaft

A numerous sector like aerospace, marine and automobile industries are extensively adopted the composite shaft due to its magnificent engineering properties. It possessing an excellent strength to weight ratio, higher the fundamental natural frequency and damping property over to conventional shaft. Present study deals with dynamic behaviour of composite shaft through improved simplified homogenized beam theory. Various influencing parameters like rotary inertia. Internal damping, and stacking sequence of composite material on composite shaft’s dynamic property has been studied. The finite element formulation has been accomplished to get the solution of the governing equations. The fundamental frequency of hollow carbon-epoxy composite shaft has been computed and verified with the published literature results. The present model has been extended for the analysis of hollow shaft with disc mounted on it. The effect of disc position and stacking order on critical speed and natural frequency of shaft rotor system has also been studied. It has been noticed that, critical speed and natural frequency is extensively affected by location of the disk and the staking order. When the disk is at center position has least natural frequency and critical speed. Natural frequency increases with shifting the disk towards the bearing end. The first natural frequency with the staking sequences 0°, 45°, and 90° gives 58.1 Hz while 75° gives 17.13 Hz. Authors of this study believe that the present dynamic model will be useful to practicing engineers for dynamic analysis of composite shaft with confidence.

Dynamical Stability Analysis of Rotating Composite Cutter Bar with Nanocarbon Materials

This paper studies the free vibration response of a spinning and variable cross-section composite cutter bar homogeneously enhanced with carbon nanomaterials. Based on the Rules of Mixture (ROM) and the Halpin–Tsai Model (HTM), we establish a motion model of the spinning and variable cross-section composite cutter bar by containing carbon nanomaterials, which combines the Euler–Bernoulli beam theory and Hamilton principle. In addition, the dynamic governing equations are solved by using the Galerkin method so as to obtain the characteristic equation. The curves of decay rate-rotating speed and natural frequency-rotating speed are obtained especially by numerical analysis, and the corresponding critical speed and instability threshold of the composite cutter bar are also calculated. By selecting different parameters such as length-to-diameter (or length-to-width-to-thickness) ratios and volume contents of carbon nanomaterials, cutter bar taper ratios, ply orientations, and stacking sequences, the relation between instability threshold and loss factor is obtained with respect to the composite cutter bar. The results obtained found that the cutter bar’s stiffness is increased by adding carbon nanomaterials into the carbon fiber-reinforced polymer composites. Its natural frequency and critical speed are increased, but the cutter bar’s damping decreases with the increasing content of carbon nanomaterials. The results of critical speed and fundamental natural frequency of composite cutter bar for high-speed machining are greatly meaningful.

Nonlinear Seismic Analysis of RC Elevated Liquid Storage Tanks

Liquid storage tanks are strategically important due to their essential requirement of service in the post-earthquake situation. Numerical modeling of the liquid storage tank needs special attention and cannot be done in the same manner as that of the conventional buildings. In the present paper, a numerical simulation of the RC elevated liquid storage tank is presented. The staging of the tank is modeled as a multi-degree freedom system, and the container with contained liquid is modeled as a two-mass system. Free vibration analysis of the tank is carried out, and mode shapes are extracted. Further, to study the seismic response of the tank, nonlinear time history analysis is carried out. The tank is subjected to time histories of real earthquake ground motions. The varying level of the liquid in the container is another characteristic feature of tanks. The filled condition of the tank is taken into account by considering the aspect ratio (S), defined as the ratio of height of the liquid to the radius of the container. The response of the tanks with two different aspect ratios viz. 0.5 (broad) and 2.0 (slender) is studied. The linear modal analysis also carried out to understand the significance of nonlinear analysis, particularly in liquid storage tanks. Displacement, velocity, and acceleration response at the bracing levels, as well as at container levels, are obtained. Additionally, the base shear response is also obtained. The effect of aspect ratio on the free vibration analysis and the seismic response of the tanks are presented. Liquid storage tanks are special structures that have typically low fundamental natural frequencies. The nonlinear time history response of the tank showed that the higher displacement and velocity response occurs at the convective level. It is found that the linear modal analysis significantly underestimates the response of the liquid storage tank.