Cantilever Boundary Conditions Research Articles

Nonlinear transient response of rotating graphene platelets reinforced metal foams blades with initial geometric imperfection

In this paper, a new mechanical model including initial geometric imperfection is developed to investigate the nonlinear transient response of graphene platelets reinforced metal foams (GPLRMF) blades subjected to blast load. Combined with higher-order shear deformation plate theory (HSDT) and von-Karman geometric nonlinearity, the nonlinear motion equations are established, in which the Coriolis force, centrifugal force as well as initial geometric imperfection are simulated. Considering cantilever boundary condition, the partial differential equations are transformed into a series of ordinary differential equations by Galerkin discretization. Using the four order Runge-Kutta algorithm, the nonlinear transient response is numerically researched, and the time histories and phase trajectories are obtained. In addition, the effectiveness of the current research is validated by comparing the results with the existing valuable literatures. The influences of rotating speed, presetting angle, initial geometric imperfection, material property, damping coefficient, and blast load parameter on the dynamic deflection and instantaneous speed are presented. Numerical results reveal that the nonlinear transient dynamics of the composite blades under blast load are significantly influenced by initial geometric imperfection.

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

Vibration characteristics of pre-twisted rotating Ti-SiC composite airfoil blade

In this paper, a pre-twisted blade model is established based on the FSDT (first-order shear deformation theory), where the Ti-SiC fiber reinforced composite and NACA 4-digit airfoil are innovatively proposed. Rayleigh-Ritz method is utilized to deduce the pre-twisted blade natural frequencies and mode shapes where the exponential polynomials satisfying the cantilever boundary conditions are taken as admissible functions. Comparing with the existing literature, the precision of the model and the method is verified. The material properties of Ti-SiC fiber reinforced composites are calculated by the M-T (Mori-Tanaka) method and FE (Finite Element) method to guarantee the reliability of the calculation method. In addition, the parameters affecting blade vibration, such as rotating speed and aspect ratio, are studied in detail. The research findings indicate that the addition of SiC fibers enhances the properties of the composite blade, and then improves the frequency of the rotating blade. Additionally, the pre-twisted angle, rotating speed, aspect ratio and blade shape significantly affect the natural frequency of Ti-SiC composite airfoil blade. The well-established model accurately predicts the dynamic behaviors of the rotating blade, which has certain guiding value for the optimization of blade material and geometric size.

Flutter investigation and deep learning prediction of FG composite wing reinforced with carbon nanotube

Abstract The flutter of a composite wing reinforced with functionally graded carbon nanotubes (CNTs) has been investigated. A rectangular plate models a supersonic wing with cantilever boundary conditions. To determine displacement fields of a moderately thick plate, shear deformation theory is used. Using the Hamilton principle, a first-order piston theory was used to simulate supersonic airflow. This study examines four types of CNT thickness. Also, four different CNT distribution patterns are investigated. In a two-layer asymmetric composite, the effects of patch mass, mass distribution, fiber orientation angle, and distribution of CNTs were examined. Moreover, the results are compared and verified with other studies. A greater mass ratio led to a smaller flutter boundary, while a longer added mass increased the flutter boundary. A variation in the distribution pattern in CNT fiber orientation results in a distinct behavior of the flutter boundary for asymmetric composites with increasing orientation angles. The artificial neural network is utilized to predict the damping ratio, and the results showed great accuracy compared to the study results. Hyperparameter tuning is employed for better optimizing the predictive models.

Designing regression approach for mode frequency prediction of empty and filled steel silos

In this study the primary objective is to design prediction model for the free vibration analysis of thin circular cylindrical steel silos having various aspect ratios in empty and varying filled conditions for different types of closures. A finite element method (FEM) is used to carry out the free vibration analysis of steel silos. It is found that the effect of different aspect ratios slender, intermediate slender and squat steel silos is very significant for dynamic response of silo. The silos are considered having open, flat and cone type of closures at its top end. The clamped-free (cantilever) boundary condition is taken for this approach as actual silos are fixed at flat-base. The structural mass of thin cylindrical shell steel silo is made constant for a particular height and diameter. The eigenvalues of the thin cylindrical shell steel silos are extracted by using block Lanczos method. The free vibrations of thin cylindrical shell steel silo with different aspect ratios, radius to thickness ratio are studied. From the present studies it is seen that as aspect ratio increases the fundamental frequency is reduced in empty silo. It is more in the case of squat silo. It can be seen that the fundamental frequency is less in the case of flat closure in all the aspect ratios of the silo. The frequency values are more in the case of cone closure is observed. Also as the mode number increases the modal frequency value increases. Further, as the filling level is increased the modal frequency also increases. Finally, regression approach is adopted for predicting the mode frequency of empty and filled silos for wide range of aspect ratios.

Dynamic modal analysis of pristine single-walled carbon nanotubes

Carbon nanotubes (CNTs) exhibit exceptional mechanical properties, making them highly promising for various applications. This study conducts dynamic modal analysis on single-walled carbon nanotubes (SWNTs) to explore their vibrational behavior and natural frequencies. Findings indicate a consistent decrease in natural frequencies with increasing nanotube length under cantilever and bridge boundary conditions, attributed to increased mass requiring more vibrational energy. In contrast, nanotube diameter shows inconsistent effects on natural frequency. Results suggest that SWNT natural frequency is more influenced by length than diameter. The study provides valuable insights for designing devices and structures using SWNTs, proposing short SWNTs for high-frequency resonators and long SWNTs for high-performance applications. Overall, this research enhances our understanding of SWNT dynamic characteristics, offering crucial information for the development of innovative nanoscale technologies.

Identification of microbes using single-layer graphene-based nano biosensors.

Graphene based nano sensors have huge potential in an era of sensor technology. The objective of this study is to create a sensor by investigating the vibration responses of cantilever and bridged boundary conditioned single layer graphene sheets (SLGS) with various attached microorganisms on the tip and at the centre of the sheet. The Parvoviridae, Flaviviridae, and Polyomaviridae biological substances have been comprehensively investigated here. For the Parvoviridae, Polyomaviridae, and Flaviviridae categories of targeted microbes, the sizes are 21nm, 40nm, and 45nm, respectively. The Parvoviridae family has a maximum frequency of 1.87x107 Hz with a cantilever condition and a mass of 4.2441 Zg, and for a bridged condition, it demonstrates a maximum frequency of 1.23x108 Hz with the same mass on armchair SLG (5 5). The data analysis shows that 3.0041 Zg mass of the Mimivirus has the lowest frequency. It demonstrates explicitly that the rate of frequency decreases as the value of mass increases. When compared to chiral SLG, the armchair single layer graphene sheet performs better. The research indicates that the dynamic properties are significantly influenced by the mass of various biological organisms. The application of this sensor will enable the detection of microorganisms or viruses that can be connected to SLG. In this research, the application of Single Layer Graphene (SLG) as a virus sensing device is explored. Atomistic finite element method (AFEM) has been used to carry out the dynamic analysis of SLG. Molecular dynamic analysis and simulations have been performed to see how SLG behaves when employed as sensors for biological entities and when they are exposed to bridged and cantilever boundary conditions. The frequency analysis was performed using ANSYS APDL software. SLG of various chirality has been utilised in the investigation. By altering the applied mass of a biological object, the difference in frequency observed. The idea behind mass detection employing nano biosensors is built on the concept that the stiffness of a biomolecule changes as its mass changes, making the resonant frequency extremely sensitive to that change. A shift in the resonance frequency results from a change in the associated mass on the graphene sheet. The main challenge in mass detection is estimating the variation in resonant frequency driven by the mass of the connected molecule. The SLG-based biosensor has a specific application in the early identification of diseases. The biosensor investigated in this article is novel, whereas the biosensors that are presently on the market operate using the ionization method. The simulations result shows SLG based biosensor's sensitivity considerably faster than an existing one.

Study on Free Vibration Analysis of a Rotating Fibre-Graphene-Reinforced Hybrid Polymer Composites Pre-Twist Shel

The present work aims to develop a computational procedure for investigating the vibration behaviour of pre-twisted laminated composite shell containing graphene inclusions in their matrix. According to nanoscopic empirical equations, graphene's mechanical properties are determined by its size dependence. It has been demonstrated that the orthotropic mechanical properties of composite laminates made from carbon fibres and hybrid matrix can be evaluated. Based on pre-twist and geometric configurations, finite element methods have been used to model hybrid materials shells that include carbon fibre, graphene, and graphene-fibre reinforcement. As part of the validation process, the proposed method is compared with other methods when possible. Finally, the vibrational behaviour of the composite shell is extracted by imposing a twisted angle on a cantilever boundary condition. An analysis of vibrations for each configuration is presented in this paper, as well as the effects of graphene inclusions on natural frequencies. As graphene volume fractions in the matrix increase, the natural frequencies of every mode also increase. When the hub radius and rotational speed are increased, the frequency parameter increases with an increase in graphene volume in the hybrid polymer composite pre-twisted shell.

Nanoresonator vibrational behaviour analysis of single- and double-layer graphene with atomic vacancy and pinhole defects

Nanosensors and actuators are frequently made of graphene. Any defect in the graphene's manufacturing has an impact on its sensing performance and on its dynamic behaviour. Using a molecular dynamics technique, the influence of pinhole defects and atomic defects on the performance parameters of single-layer graphene sheets (SLGSs) and double-layer graphene sheets (DLGSs) with various boundary conditions and lengths is explored. In contrast to the perfect nanostructure of a graphene sheet, defects are described as holes formed by atomic vacancies. As the number of defects increases, the simulation results show that the presence of defects has the greatest impact on the resonance frequency of SLGSs and DLGSs. The influence of pinhole defect (PD) and atomic vacancy defect (AVD) on armchair, zigzag, and chiral SLGSs and DLGSs was investigated in this article using molecular dynamics simulation. The influence of both types of defects is largest when it is adjacent to the fixed support for all three different types of graphene sheets, i.e. armchair, zigzag, and chiral. The structure of the graphene sheet has been created using ANSYS APDL software. In the structure of the graphene sheet, atomic and pinhole defects have been generated. SLG and DLG sheets are modelled using a space frame structure that is identical to a three-dimensional beam. Dynamic analysis of single-layer and double-layer graphene sheets performed with different lengths using the atomistic finite element method. The interlayer separation in the form of Van der Waals interaction is modelled using characteristic spring element (Combin14). The upper and lower sheets of DLGSs are described as elastic beams connected by a spring element. With atomic vacancy defect for the bridged boundary condition, the highest frequency of 2.86 × 108 Hz was found for zigzag DLG (20 0) and with same boundary condition for pinhole defect 2.79 × 108 Hz frequency achieved. In a single-layer graphene sheet with an atomic vacancy and cantilever boundary condition, the maximum efficiency was 4.13 × 103 Hz for SLG (20 0), while in a pinhole defect, it produced 2.73 × 107 Hz. Moreover, the elastic parameters of beam components are calculated using the mechanical properties of covalent bonds between carbon atoms in the hexagonal lattice. The model has been tested against previous research. The focus of this research is to develop a mechanism for determining how defects affect graphene frequency band in application as nano resonators.

Dynamic Snap-Through and nonlinear vibrations of bistable asymmetric Cross-Ply composite laminated cantilever shell under external excitation

The bistable asymmetric composite laminated structures have the broad applications in the design of the deformable aircrafts and energy harvester due to the unique nonlinear dynamic snap-through characteristics. This paper studies the dynamic snap-through phenomena and nonlinear vibrations of the bistable asymmetric cross-ply composite laminated cantilever shell under the external excitation. Reddy’s third-order shear deformation theory and Hamilton principle are applied to establish the differential dynamic governing equation of the bistable asymmetric composite laminated cantilever shell. Two-degree-of-freedom nonlinear dynamic system is obtained by employing Galerkin approach. The curvature-displacement relationship is given for the bistable asymmetric composite laminated cantilever shell. Chebyshev-Ritz is utilized to obtain both natural frequencies and mode shapes of the bistable asymmetric composite laminated cantilever shell. Considering the cantilever boundary condition, the free vibrations are analyzed by considering different factors of the bistable asymmetric composite laminated cantilever shell, such as the curing temperature, numbers of the layers and geometry parameters. It is observed that the dynamic snap-through behaviors and chaotic vibrations are found under varying the frequency and amplitude of the external excitation. Several validations are carried out among the obtained results with these of other references. The results of the numerical simulation and finite element software ABAQUS are in good agreement with these of the vibration experiment.

Nonlinear dynamics analysis of a graphene laminated composite plate based on an extended Rayleigh–Ritz method

Linear and nonlinear vibration characteristics of the graphene platelet-reinforced composite (GPLRC) laminated plates are investigated. Based on the first-order shear theory and von Karman geometric nonlinearity, the energy expressions of the GPLRC laminates are established. The boundary elastic potential energy is established by penalty function method to simulate different boundary conditions. The linear and nonlinear frequencies of the GPLRC laminated plate are calculated by introducing boundary potential energy into Rayleigh–Ritz method. The convergence and accuracy of the method are verified by numerical examples, and the effects of different parameters on frequency are analyzed. Considering the cantilever boundary conditions, the nonlinear motion governing equations of the GPLRC laminated plate are obtained by Hamilton principle. The two-degree-freedom ordinary differential motion equations of the laminates are derived by Galerkin method. Considering the fundamental parameter resonance and 1:1 internal resonance, the amplitude–frequency response curves of the structure under transverse excitation are obtained. The effects of transverse excitation and damping coefficient on nonlinear vibration characteristics of the GPLRC laminated plates are investigated by numerical simulation.

Natural vibration of cantilever porous twisted plate with variable thickness in different directions

In this paper, the blade is assumed to be a rotating variable thickness cantilever twisted plate structure, and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied. It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction, respectively, and it changes in both directions. The classical thin shell theory, the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate, in which the centrifugal force potential due to high rotational speed is included. Then, according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions, the dynamic system expressed by equations of motion is reduced to an eigenvalue problem. By numerical simulation, the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters. A series of comparison studies are performed to verify the accuracy of the present formulation and calculations, in which compared data come from experimental, finite element method and theoretical calculation, respectively. The influence of pre-twist angle, three different forms of thickness taper ratio and rotational speed on natural vibration, mode exchange and frequency veering phenomenon of the system is discussed in detail. In addition, the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.

Nonlinear and chaotic vibrations of rotating functionally graded GPL reinforced composite pre-twisted blade subjected to aerodynamic force

The nonlinear and chaotic vibrations of the rotating functionally graded graphene platelet reinforced composite (FG-GPLRC) pre-twisted blade subjected to the aerodynamic force are investigated by taking into account the cantilever boundary condition. The rotating FG-GPLRC pre-twisted blade is simplified to a rotating FG-GPLRC pre-twisted cylindrical panel. The graphene platelets (GPLs) are dispersed uniformly and oriented randomly in every layer while the GPL volume fractions vary from the layer to layer, which leads to four different GPL distribution patterns. Based on the strain–displacement relationship of the pre-twisted cylindrical panel derived by Green strain tensor, the natural frequencies of the rotating FG-GPLRC pre-twisted cylindrical panel are obtained by using the first-order shear deformation theory and Chebyshev–Ritz method. Lagrange’s formulation is used to derive the nonlinear ordinary differential equations of motion. The complex chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel are investigated by performing numerical simulations on the basis of Runge–Kutta algorithm. The bifurcation diagrams, Lyapunov exponents, time histories, phase portraits and Poincare maps are depicted to detect the periodic and chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel with different parameters, such as Coriolis force, GPL distribution pattern, steady-state rotating speed, perturbation rotating speed and aerodynamic force. The double-parameter maximum Lyapunov exponent is regarded as an effective method to detect the chaotic regions of the rotating FG-GPLRC pre-twisted cylindrical panel.

Analytical solutions for bending, buckling and vibration of nanobeams on Winkler–Pasternak foundation

The nonlocal elasticity theory and the Euler–Bernoulli (EB) beam theory are used to present closed-form analytical expressions for static bending, axial buckling, and free vibration of nanosized beams resting on an elastic foundation. The differential constitutive relations of Eringen are utilized to represent the small-scale effects of the nanobeam’s mechanical response. The governing equation of motion is derived by employing Hamilton’s principle. Utilizing the Laplace transform approach, analytical expressions of the bending displacements, the critical buckling force, and the vibration frequency of nanobeams with simply supported (S-S), clamped, cantilevered, and propped cantilevered boundary conditions are produced. In order to confirm the correctness of the offered closed-form equations, their outputs are compared to those of the available numerical method solutions. The effects of the Winkler parameter, the Pasternak parameter and the nonlocal parameter on bending, buckling, and vibration characteristics of nanobeams have been explained. Presented analytical expressions and graphical representations demonstrate how increasing Winkler and Pasternak parameters reduce bending displacements while raising the critical buckling load and the natural frequency of nonlocal nanobeams. Benchmark numerical results are also presented to investigate and discuss the effects of all parameters on bending deflections, buckling loads, and natural frequencies of nanobeams.

Effect of defects and boundary conditions on the vibrational behavior of carbon nanotube and graphene: A molecular dynamics perspective

The presence of defects has a significant effect on the mechanical and vibrational properties of carbon nanotubes (CNTs) and graphene. The vibrational properties of single-layered graphene sheets (SLGS) and single-wall carbon nanotubes (SWCNT) have been investigated in this research. Molecular dynamics simulations have been conducted on pristine and defective zigzag and armchair CNTs, with clamped-free (C-F) boundary conditions as well as pristine and defective armchair graphene sheets with different boundary conditions to investigate the effect of various parameters such as chirality, aspect ratio, boundary conditions, and types and number of defects on the longitudinal and transverse vibrational behavior of CNTs and graphene sheets. It was observed that for the cantilever boundary condition, shorter tubes give better vibrational sensitivity as compared to the larger ones for a constant diameter of the tube. The chirality has not a considerable effect on the natural frequency of CNTs. Regarding graphene sheets, it was observed that increasing the size of the graphene sheet decreased the fundamental natural frequency of SLGS. As compared to Stone-Wales defects, the vacancy defects were found to have more impact on the degradation of the natural frequency of CNTs and GS.

Analysis and active control of bending and vibration responses of the MRE multifunctional grid composite sandwich plates

This paper investigates the active control effect on the bending and vibration responses of the magnetorheological elastomer (MRE) multifunctional grid composite sandwich plates (MREMGCSPs), which consist of top and bottom carbon fibre/epoxy panels and one MRE-based grid functional core with many grid functional components (GFCs) and several grid frame beams (GFBs). First, based on the first-order shear deformation theory, the energy principle, the Ritz method, the Duhamel integral approach, etc., the solution to bending and the pulse vibration responses of such a structure under cantilever boundary condition are successfully obtained. Thereafter, to verify the current model as well as evaluate the bending and vibration resistance, a MREMGCSP structure is fabricated and measured with different measuring points and magnetic field magnitudes. Finally, the influence of critical geometric and control parameters on static and dynamic properties is discussed to summarize some practical conclusions for engineering applications. This study provides a useful model for estimating both static and dynamic behaviors of the MREMGCSPs, which can assist researchers in designing, manufacturing, and optimisation of similar multifunctional structures with MRE.

FOLDED ANGLE DEPENDENT MODAL ANALYSIS OF THE FLAT AND FOLDED PLATES

The effect of folded angle and boundary condition differences on the natural frequency, which is one of the dynamic characteristics of isotropic thin plates, is investigated. Modal analyzes of flat and folded structures are performed with ANSYS under cantilever and two-side-fixed boundary conditions. The validation of the free vibration results of the structures is performed with Solidworks. The first five natural frequencies of each structure are obtained, and the values in terms of non-dimensional natural frequency parameters are interpreted with the tables and graphics. While both an increase and a decrease can be observed depending on the increase in the folded angle in the first five natural frequencies for the cantilever boundary condition, the effect of the increase in the folded angle on the natural frequencies in the two-sided-fixed structures is much less in the higher folded angle values. It is seen that the reason for the sudden changes in the folded angle - non-dimensional natural frequency graphs is the mode shape change.

Effects of stacking sequences and longitudinal parameter on the dynamic characteristics of multilayer glass epoxy composite

In the current scenario, the structures made of composites are drawing attention due to their high spring rate, capacity to withstand high force, reinforcement and optimized mass. Up till now, several materials have been designed and manufactured. The components as well as structures made of these composite materials do expose to dynamic loading during their functions which leads to the failure of the respective component/structure. The dynamic characteristics depend on the material properties, physical dimension, no. of layers, orientation of the fibers and end conditions. Here an analysis is performed to determine the vibration characteristics of multilayer composite beams made of glass epoxy composite. The Cantilever boundary condition is considered. Ten layers are considered. Various stacking are considered with the different fiber orientations. The natural frequency of a multilayer composite beam is sensitive to the length and fiber orientations. As the length and number of layer increase, the natural frequency decreases. The natural frequency for fiber orientation at 900 is minimum as compared to other fiber orientations irrespective of the length while the natural frequencies for the 00 fiber orientation is more compared to other orientations for out of plane vibrations irrespective of the geometrical dimensions. The natural frequencies for other orientations are more compared to 00 orientation for specific modes due to high stiffness in the torsional direction.

Torsional analysis of open thin-walled doubly symmetric beams under torsion and bimoment

The present paper investigated the static analysis for the coupled torsional-warping response of open thin-walled doubly symmetric beams subjected to various twisting moments and bimoments. The static equilibrium torsional-warping coupling differential equations and associated boundary conditions for the thin-walled beams are derived using total potential energy variational principle. The exact closed-form solutions for the beams having a cantilever, simply-supported, fixed-fixed and fixed-fork boundary conditions and under various torsional and warping moments are determined. The present solution is shown to successfully capture the coupled torsional-warping static response of the thin-walled beams with various boundary conditions and by excluding and including axial static force effects. The validity and the accuracy of the numerical results based on the present solution are accomplished throughout the numerical examples presented and compared with well-established ABAQUS finite beam model solution and other exact solution available in the literature.

An analysis for bi-stability characteristics of lateral buckled beams with energy dissipation features

In this paper, a concave-shaped unit composed of two thin-walled beams with cantilever boundary conditions is designed and fabricated. Forces are introduced through the two cantilever ends of the beams whose constraints are hinged joints to get a bi-stable axial or lateral buckled unit. Initial buckling deformations of the concave-shaped units are analyzed theoretically and numerically. Experimental and numerical methods are used to investigate the post-buckling deformations and snap-through behaviors, when the concave-shaped units are axial buckled or lateral buckled. In the case of completing downwards and upwards snapping processes, there is a hysteresis loop in the force–displacement curve for the bi-stable lateral buckled unit, while is not for the bi-stable axial buckled unit. Finally, the influence of transverse displacements and dimension parameters on the snap-through behaviors of the bi-stable lateral buckled units is studied by the simulation method.