Number Of Half-waves Research Articles

Research on vibration response distorted similitude of cylindrical shells under modal distribution disorder

Similitude theory enables local-scale models to reflect the dynamic characteristics of full-scale models and is widely employed in engineering experimentation. However, shell structures, constrained by wall thickness, cannot undergo experiments through proportional downsizing. Existing similitude studies with retained wall thickness exhibit only minimal distortion, and accurate prediction of vibration responses is hindered by modal distribution disorder. To address these challenges, a method based on modified frequency response functions of natural frequencies and mode shapes is proposed. Scaling laws for natural frequencies and mode shapes of cylindrical shells with retained wall thickness are established. This method yields a maximum prediction error of 4.29 % for prototype natural frequencies, compared to 50.57 % for existing methods. Predicted prototype vibration acceleration responses correspond well with theoretical calculations in both frequency and amplitude, while existing methods fail entirely. The phenomenon of modal distribution disorder and the effectiveness of the proposed method in mitigating it are verified by modal experiments and response tests. Research reveals that the sensitivity of different modal frequencies to the wall thickness scaling factor varies, serving as the cause of modal distribution disorder. The modal distribution with the same circumferential wave number is unaffected by wall thickness. Modes above the bending frequency, with axial half-wavelength consistent with bending modes, are prone to disorder due to wall thickness distortion. During wall thickness distortion, a mode originally with the lowest frequency is surpassed towards lower frequency by the mode with larger circumferential wave number and the same axial half-wave number, leading to disorder. The proposed method addresses the challenge of minimal distortion in structural vibration response and poor performance, advancing the development of distorted similitude.

Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

This research proposes a computationally efficient methodology using a Constrained Variational Asymptotic Method (C-VAM) for non-linear buckling analysis on a hat-stringer panel with delamination defects. Starting with the geometrically non-linear kinematics, the VAM procedure reduces the three-dimensional (3-D) strain energy functional to an analogous 2-D plate model and evaluates the closed form warping solutions. Utilising the resulting warping solutions and recovery relations for the skin and the stringer, displacement continuity at the three-dimensional level is enforced between the stringer and the skin based on the pristine and delaminated interface regions. Consequently, the constrained matrices obtained from C-VAM is incorporated into an in-house developed non-linear finite element framework. Using the developed formulation, a stiffened panel with delamination of 40 mm between the stringer and the skin is analysed under compression. The results have been validated locally and globally, employing experimental data and 3-D finite element analysis (FEA). Experiments are carried out on the co-cured panel by applying quasi-static loading with displacement-controlled conditions, and 3-D FEA is carried out in Abaqus. Load-response plots have been obtained to validate the results at the global level, and they are in excellent agreement with experiments and 3-D FEA. Subsequently, out-of-plane displacement contour plots are obtained; the number of half waves and wave intensity in 3-D FEA and C-VAM are comparable, although there are minor differences compared to the experimental findings. The proposed framework is shown to be computationally efficient by over 55% as compared to 3-D FEA for performing non-linear buckling analysis on the stiffened composite structure considered in the current work.

Buckling analysis of rectangular plates with rotationally restrained edges subjected to linearly varying in-plane loading

This study addresses a comprehensive procedure for the buckling behavior of rectangular plates with rotationally restrained edges. They are subjected to uniaxial in-plane load that varies linearly from compression to bending. The load is applied to opposite edges with variable boundary conditions, ranging from simply supported to clamped. The other edges can also be free, guided, or between them. For the first time, the generalized integral transform technique (GITT) is applied to the buckling equation of such a plate. The integral kernel perfectly satisfies the plate boundary conditions and its constituent terms are limited to the approximate range of ±1 which prevents the numerical instability. The transformed equation is a set of linear algebraic equations which establish an eigenvalue problem. The plate buckling coefficient, and corresponding mode shape (contours of the buckled plate, the number of half-waves in each direction, etc.) are presented according to variations of the edge relative stiffness as well as the plate aspect ratio, the loading shape, and Poisson's ratio. The latter parameter has a significant effect on the buckling behavior when at least one of the edges is free, guided, or between them. This portion is developed for auxetic materials (negative Poisson's ratios), and it was concluded that the minimum buckling load mostly occurs as the Poisson's ratio tends to zero.

Data-driven analysis of structural instabilities in electroactive polymer bilayers based on a variational saddle-point principle

In this work, we use a data-driven approach to model the onset of wrinkling in composite dielectric elastomer (DE) bilayer structures that are subjected to combined electro-mechanical loading conditions. Specifically, the critical surface-charge density required to activate wrinkling and the resulting number of half-waves are determined as functions of the tunable geometrical and material features of the DE bilayer using supervised machine learning (ML) models. The required data for the ML surrogates is generated using a finite-element-based framework for structural stability analysis of the DE bilayer, which is rooted in a variational saddle-point formulation for non-linear electro-elastostatics. Within the considered broad design space for the DE bilayer, the data points are sampled according to a Latin-hypercube-type design, following which training and test datasets containing the values of the target variables for the sampled input-feature vectors are generated using the adopted finite-element framework. Subsequently, we implement and compare the capabilities of different ML models to capture accurately the non-linear dependence of the wrinkling characteristics on the tunable features of the DE bilayer.

Quantum correlations beyond entanglement between two moving atoms interacting with a coherent cavity

Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter.

Study on Sinusoidal Post-Buckling Deformation of Coiled Tubing in Horizontal Wells Based on the Separation Constant Method

In this paper, a set of partial differential equations considering the dynamic effects of the coiled tubing (CT) is established based on the bending theory of slender beams considering the axial loads. The analytical solution of sinusoidal deformation with the time term is obtained. The critical load of coiled tubing during sinusoidal buckling and the change of half-wave number during sinusoidal post-buckling are studied through the introduction of the necessary conditions, solution and the separation constant. The contact force of coiled tubing with sinusoidal post-buckling on the horizontal well wall is analyzed. The results show that the critical load for sinusoidal buckling of fixed-size CT is related to the section angular acceleration coefficient. The half-wave number produced by the sinusoidal post-buckling bending of the CT gradually decreases during compression. The contact force of the deformed CT to the borehole wall is related to the compression speed of the CT. By introducing the dynamic term and the separation constant, this research model can provide a theoretical basis for studying the transformation of the CT from sinusoidal buckling to helical buckling.

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

The cylindrical shell made of metal rubber has a strong ability to reduce and absorb vibration, which widens its application in the industrial field. Therefore, it is of great significance to study the vibration characteristics of metal-rubber cylindrical shells (MRCSs). However, there is relatively little research on this aspect. Based on this, the dynamic properties of MRCS are investigated in this paper based on viscoelastic theory, the Rayleigh–Ritz method, and the Gram–Schmidt orthogonal polynomials. The correctness of the proposed model was verified by comparison with the literature and experimental verification. The results show that the preloading state and boundary conditions have significant effects on the natural frequency and modal loss factor of MRCS. The effect of the Pasternak elastic foundation on the natural frequency and modal loss factor of MRCS varies with the change of the axial half wave number m. The effect of the Pasternak elastic foundation on higher-order vibrations is similar to that of the artificial spring technique.

Antenna source of radio-frequency emission in ion-proton pulsars

ABSTRACT The growth of a longitudinal or quasi-longitudinal Langmuir mode in the outward-moving beam of ions and protons that forms the open sector of an ion-proton pulsar magnetosphere radiates as an analogue of an end-fed high-impedance horizontal straight-wire antenna an integral number of half-waves in length. The radiation has, broadly, the energy flux, linear polarization, and spectral index that are widely observed: also, the notch phenomenon seen in some integrated pulse profiles occurs naturally. The new field of pulsar observations below 100 MHz may lead to productive tests of the radio emission mechanism.

Free vibration characteristics of cord-reinforced air spring with winding formation under preload conditions

A precise transfer matrix was employed to analyze the free vibration characteristics of a cord-reinforced air spring with winding formation under preload conditions. The air spring was abstracted as a rotary combined shell structure with variable winding trajectory characteristics. The rotary structure, which consisted of cylindrical and toroidal shells, was analyzed for its shell pre-stress under preload conditions. The shell pre-stress was combined with the theory of thin shells to create the rotary shell vibration control equations under preload effect. The Helmholtz equation was used to analyze the influence of sound pressure inside shells under the fluid–structure coupling boundary conditions. The rotary shell transfer matrix was derived from the variable winding trajectory equation, geometrical equation, and physical equation of shells. Under the continuous conditions of state vector between the cylindrical and toroidal shells, the shells were combined into a rotary combined shell structure to obtain its total free vibration equation. The shell boundary conditions were considered to solve the natural frequency of the air spring. The calculation results were compared with the prototype test and simulation results to verify the effectiveness and accuracy of the theoretical model. On this basis, we explored the influence of axial half wave number, circumferential wave number, geometrical structure, and material characteristics on the free vibration characteristics of the air spring. The research findings would provide important and significant guidance for the structural design of cord-reinforced air springs with winding formation.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

A hybrid analytical method for predicting vibrations in vacuum and water of the sandwich plate with z-direction reinforcements and cavities

This paper presents a multi-functional sandwich plate with z-direction reinforcements and cavities that has the potential to meet the pressure resistance and the acoustic stealth requirement of the underwater equipment in deep sea. In order to predict its free and forced vibrations in both vacuum and water, a hybrid analytical method is proposed by combining a multi-level homogenization model and a layerwise model. The core with z-direction reinforcements and cavities is homogenized and effective elastic constants are calculated by the Mori-Tanaka formula. Vibration equations of the sandwich plate are derived utilizing the layerwise model based on the first-order shear deformation theory. The water effect is taken into account by the Euler's equation. Vibration results are solved under simply supported boundaries. Validation studies and parameter analyses are then conducted. It is found that different from the existing theoretical approach based on the equivalent single-layer model that is only applicable for the sandwich with a hard core material, the present hybrid analytical method is well suitable for vibration predictions of the sandwich plate with z-direction reinforcements and cavities, no matter the hard or soft core. Besides, due to the homogenization of the three-phase core and the neglecting of local vibrations in the layerwise model, the present analytical method only predicts accurate free vibrations when the half wave numbers are less than numbers of cavities in x and y directions, and also just shows the high precision in force vibration calculations as the maximum analysis frequency is less than the natural frequency of the mode corresponding to numbers of cavities.

About natural frequencies and forms of electroelastic vibrations of ring piezoceramic plates

The general solution of problem non-axisymmetric electromechanical vibrations of piezoceramic ring plate is obtained. For the plates with radial cuts of electrode covering and for boundary conditions rigid clamping — free edge, free edge — rigid clamping the spectra of natural frequencies of vibrations are mode shapes for the first harmonics in the circumferential coordinate are identified are numerically determined and analyzed. The comparative analysis of natural frequencies and forms of piezoelectric vibrations of polarized on thickness ring piezoceramic plates is executed under various boundary conditions. One of the important characteristics of the forms of oscillations is the number and location of nodal lines. From the obtained results for the frequency equations and asymptotic formulas for frequencies, it follows that the number of nodes and the nature of the forms under all types of boundary conditions can be determined by the asymptotic approximation. Under different boundary conditions, an integer number of half-waves can be placed on the width of the ring (the forms n = 1,2,3,4 at have the number of nodes n –1); or an odd number of quarter waves is placed on the width of the ring (forms have the number of nodes); or an odd number of quarter waves is placed on the width of the ring (forms have the number of nodes); or an integer number of half-waves is placed on the width of the ring (forms have the number of nodes). These findings are better confirmed for natural frequencies and forms with higher numbers.

Applicability and Limitations of Ru’s Formulation for Vibration Modelling of Double-Walled Carbon Nanotubes

In this paper, a comparison is conducted between two different formulations of the van der Waals interaction coefficient between layers, as applied to the vibrations of double-walled carbon nanotubes (DWCNTs); specifically, the evaluation of the natural frequencies is achieved through Ru’s and He’s formulations. The actual discrete DWCNT is modelled by means of a couple of concentric equivalent continuous thin cylindrical shells, where Donnell shell theory is adopted to obtain strain-displacement relationships. In order to take into account the chirality effect of DWCNT, an anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and the Rayleigh–Ritz method is used to obtain approximate natural frequencies and mode shapes. A parametric analysis considering different values of diameters and numbers of waves along longitudinal and circumferential directions is performed by adopting Ru’s and He’s formulations. From the comparisons, it is evident that Ru’s formulation provides unsatisfactory results for relatively low values of diameters and relatively high numbers of circumferential waves with respect to the more accurate He’s formulation. This behaviour is observed for every number of longitudinal half-waves. Therefore, Ru’s formulation cannot be used for the vibration modelling of DWCNTs in a large range of diameters and wavenumbers.

Analytical determination of non-local parameter value to investigate the axial buckling of nanoshells affected by the passing nanofluids and their velocities considering various modified cylindrical shell theories

We analytically determine the nonlocal parameter value to achieve a more accurate axial-buckling response of carbon nanoshells conveying nanofluids. To this end, the four plates/shells’ classical theories of Love, Flügge, Donnell, and Sanders are generalized using Eringen’s nonlocal elasticity theory. By combining these theories in cylindrical coordinates, a modified motion equation is presented to investigate the buckling behavior of the nanofluid-nanostructure-interaction problem. Herein, in addition to the small-scale effect of the structure and the passing fluid on the critical buckling strain, we discuss the effects of nanoflow velocity, fluid density (nano-liquid/nano-gas), half-wave numbers, aspect ratio, and nanoshell flexural rigidity. The analytical approach is used to discretize and solve the obtained relations to study the mentioned cases.

On nonlinear free vibration of externally compressible fluid-loaded sandwich cylindrical shells: Curvature nonlinearity in bending and impermeability condition

A nonlinear fluid–structure interaction (FSI) model is presented for nonlinear vibration analysis of sandwich cylindrical shells subjected to an external compressible flow by considering the curvature nonlinearity in impermeability condition and bending. The sandwich shells are made of two face sheets and a central core of advanced materials including functionally graded (FG), metal foam, and anisogrid lattice composite. Based on the Kirchhoff–love hypotheses with the geometric nonlinearities in the normal strain and curvature of mid-surface, one decoupled nonlinear integral–differential equation is obtained for axisymmetric bending vibration of sandwich cylindrical shells. For the first time, the nonlinear impermeability condition is developed in order to take into account the large deformation of thin structures in FSI modeling. In both subsonic and supersonic regimes of steady irrotational compressible flow, a closed-form expression for nonlinear pressure distribution is presented according to the conservation of mass and generalized Bernoulli equation of extended potential theory. Using the Galerkin’s method in conjunction with the multiple-scale perturbation technique, the decoupled equation is solved to obtain nonlinear frequency and time–history response. Finally, parametric studies are carried out to investigate the effects of geometric ratios, boundary conditions, fluid specifications, and material variation on the responses of sandwich shells with different layups such as [Al; FG core; ZrO2], [Al; foam core; ZrO2], [Al; lattice core; Al]. Significant differences in pressure variation due to curvature nonlinearity are observed for short shells with larger vibration amplitude and larger number of half-waves in the axial direction. Therefore, the linear vibration analysis is inadequate for analyzing short sandwich cylindrical shells surrounded by an external fluid flow especially in the case of movable ends.

Buckling stability analysis of underpinning piles during basement excavation beneath existing buildings

In the present paper, the pile-soil system’s total potential energy equation of underpinning piles was established based on the Winkler elastic foundation beam theory. This energy equation was used to explore the effect of basement excavation beneath existing buildings on the underpinning pile’ buckling stability. Utilizing the minimum potential energy theory, the expression of the critical buckling load for underpinning piles’ stability during the excavation project was obtained. Moreover, the influencing factors of the critical buckling load were investigated. It was found that the underpinning pile’s critical load converged with the augment of half-wave number. Moreover, the pile skin friction and deadweight had an insignificant influence on it. In addition, the critical load of underpinning piles decreased sharply with the increasing excavation depth and gradually increased with the augment of pile diameter. The results of this study provides a basis for the design of adding piles in similar projects and reduces the hidden danger of excavation instability.

Modeling and analysis of forced vibration of the thin-walled cylindrical shell with arbitrary multi-ring hard coating under elastic constraint

In this paper, a parameterized multi-partitioning method is presented for modeling arbitrary multi-ring hard coating treatment for the thin-walled cylindrical shell under different ring numbers and coating ratios, while the Rayleigh–Ritz method and the Chebyshev orthogonal polynomials of the second kind are employed to derive the governing equations of motion and the admissible displacement, respectively. Moreover, a unified formulation of external load based on the trigonometric and Chebyshev series is developed for forced vibration analysis of the shell with arbitrary axial half-wave number and circumferential wave number. Based on the experimental resonant frequencies, an improved inverse identification procedure is proposed in which the genetic algorithm and pattern search algorithm are sequentially employed to identify the stiffness coefficients of elastic constraint. Good agreement between the experimental and numerical resonant frequencies and responses exhibits the reliability and effectiveness of both the stiffness identification method and semi-analytical model. The identified results happen to find that the constraint stiffness may have the inherent property of frequency dependence due to the existence of micro sliding which would further result in soft nonlinearity in frequency response curve as shown in experimental results. Additionally, the influences of ring number and coating ratio on vibration and damping characteristics of the thin-walled cylindrical shell are investigated by introducing the average strain energy density and average modal loss factor.

Effect of cable corrosion on nonlinear elastic stability of girder in Cable-Stayed bridges with floating systems

This paper presents an investigation of the influence of cable corrosion on the nonlinear elastic stability of long-span cable-stayed bridges based on the energy method and the theory of the beam on elastic foundation (TBEF). The corrosion-induced fluctuations in vertical support rigidity and the non-uniform distributions of axial forces between girder segments are considered by a discretized model based on the energy method. The classical TBEF model is applied to evaluate the number of half-waves through the identification of the weakest section in a girder, prior to the numerical solution to the buckling eigenvalue equations derived from the discretized model. The feasibility and reasonability of the proposed procedures are validated by two ideal beams and a case study on a real long-span cable-stayed bridge with assumed corrosion scenarios, through the comparison with the results from elastic finite element analysis considering geometric nonlinearities. The case study has indicated that cable corrosion exerts a significant influence on critical buckling load, exhibiting an approximate linear relation with corrosion ratio. However, corrosion does not seem to put a significant effect on the number of half-waves of buckling mode of the girder. The possibility of failure modes switch is found to depend primarily on the spacing of cables and the depth of girder. Cable-stayed bridges having densely distributed cables and relatively shallow girder possess a higher possibility of failure modes switch when severe corrosion takes place.

Active control of a sandwich plate with reinforced magnetostrictive faces and viscoelastic core, resting on elastic foundation

The current study presents a vibration investigation of a laminated plate considering a viscoelastic core with embedded magnetostrictive layers. The simply-supported plate is supported via Pasternak’s substrate medium. Based on different plate theories and employing Hamilton’s principle, the system of governing differential equations is derived. The mechanical properties of the viscoelastic core are described depend on the time varies based on Kelvin–Voigt model. Actuating magnetostrictive layers are utilized to control the vibration damping process of the system with the assistance of feedback and constant gain distributed control. The analytical solution is obtained to investigate the influence of half wave numbers, thickness ratios, core thickness, aspect ratios, lamination schemes, elastic foundation parameters, damping coefficient, feedback coefficient magnitude, magnetostrictive layers location, on the vibrational behavior of laminated plate. Some observations about the vibration damping process of the present plate are displayed. The results refer to that the vibration suppression rate depends on the thickness of the plate, the feedback control value, the foundation constants, and the viscoelastic structural damping significantly. Moreover, the study can be providing benchmark tests to validate future contributions on the viscoelastic smart structural issues and developing the design of smart viscoelastic structures and control of their vibrations.

Information-Measuring Complex to Detect High Frequency Gravitational Waves

The gravitational waves predicted by the general theory of relativity and detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) have typical frequencies in the range of 30 ... 300 Hz. Current theories of gravity predict the existence of high-frequency gravitational waves with frequencies of 10 ... 100 MHz, including those of cosmological origin, induced by quantum fluctuations of the scalar field at the stage of cosmological inflation in the early Universe.Multi-beam optical resonators, in particular the Fabry-Perot interferometers, can be used to detect high-frequency gravitational waves. When using multi-beam optical resonators, it is possible to use the phenomenon of low-frequency optical resonance, which allows us to have a selective response to the gravitational wave effect. The gravitational-optical resonance in a multi-beam interferometer occurs if the condition is fulfilled that an integer number of half-waves of gravitational radiation is along the length of the resonator.The use of a multi-beam interferometer to detect high-frequency gravitational waves does not require the creation of a complex system for decoupling mirrors used for gravitational antennas operating in the low-frequency part of the spectrum. This is due to the fact that the frequency of mechanical vibrations of the interferometer mirrors is significantly less than the frequency of the gravitational wave.The paper considers possible optical schemes of a high-frequency gravitational antenna: based on the traditional Michelson interferometer, in the arms of which two Fabry-Perot interferometers are available, and on the basis of the Mach-Zehnder optical scheme, where Fabry-Perot interferometers can be made in the form of two perpendicular arms, with reflecting mirrors at the bend of the beam. The advantage of the second scheme is that three photo-detectors, one being main and two others being auxiliary, can be used, and there is a possibility to detect radiation transmitted by Fabry-Perot interferometers.To prove that detection of high-frequency gravitational waves is possible, a potential sensitivity of the high-frequency gravitational antenna has been estimated in the paper.