Dimensionless Frequency Parameter Research Articles

An analytical modelling of free vibration in porous FG-CNTRC plate resting on elastic foundations

This paper presents an analytical investigation of the vibrations of porous functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate resting on elastic foundations. The plates are reinforced with randomly oriented straight carbon nanotubes, featuring four distinct reinforcement distribution patterns along the thickness. Material properties of the porous FG-CNTRC are graded along the thickness, with both symmetric and asymmetric porosity distributions considered. Utilizing high-order shear deformation theory (HSDT), the equations of motion are derived from Hamilton’s energy principle, and Navier’s method is employed for the solutions. The simply supported plate is assumed to rest on Winkler/Pasternak elastic foundations. The study examines the effects of various parameters, including CNT volume fractions, CNT distribution patterns, thickness ratio (a/h), aspect ratio (a/b), porosity coefficient, and elastic foundation parameters, on the dimensionless frequency parameter.

Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

Heat transfer of pulsating water flow through aluminum-foam channel under asymmetric constant heat flux boundary condition

In the present study, the effect of pulsating inlet velocity condition on heat transfer in metal foam was investigated experimentally. Square wave shaped water velocity profiles with different amplitudes and frequencies were applied to the inlet of a rectangular channel filled with aluminum foam having 20 pores per inch and a porosity of 91.8%. A constant heat flux (12787 W/m2) was applied to one side of the porous channel. The non-heated surfaces were insulated. The surface temperatures, water inlet and outlet temperatures and volumetric flow rates were measured and recorded. The dimensionless flow frequency parameter (M) and dimensionless flow amplitude (Rem) parameter were changed in the ranges 4.8–7.3 and 492–1388, respectively. The results showed that there was a strong relationship between average Nusselt number and flow velocity amplitude. Generally, average Nusselt number was seen to increase with increasing frequency parameter and/or amplitude parameter. Correlations for the local time-averaged and surface-averaged Nusselt numbers are proposed. A meaningful comparison between steady-state and pulsating heat transfer is provided. It showed that heat transfer advantages of pulsating flow were only present for a certain low range of Reynolds number, beyond which pulsating flow heat transfer approached that of steady state.

Mechanism and modeling of Taylor bubble generation in viscous liquids via the vertical squeezing route

Bubble formation routes are vital to the application of microreactors, but a systematic understanding of the vertical squeezing remains lacking. Accordingly, this study focuses on the vertical squeezing bubble generation mechanism in viscous liquids in a T-junction microchannel. The results show there are the retraction, expansion, shrinking, and necking formation stages in the vertical squeezing route. A new formation stage, the retraction stage, is seen compared with horizontal squeezing. The influence of operating conditions on the generation mechanism was investigated from the gas–liquid interface behavior and force analysis, and the different formation mechanisms of satellite bubbles in the necking stage for two different squeezing routes were revealed. In addition, the complex bubble generation frequency rules were unified using a dimensionless frequency parameter. Finally, models for the generation frequency and bubble size were proposed. This work could provide some choice and design for the fundamentals of microreactors.

Modeling the effect of the inclination angle on the dynamic response of a biaxially pre-stressed plate

In this study, I report on an investigation of the forced vibrations procured by an arbitrary angled time-harmonic loading from a plate based on a rigid foundation. The study was formulated according to the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS). It was assumed throughout the investigation that there is a rigid clamped state between the system and the rigid ground; further, it was assumed that the plate was exposed to biaxially static initial stresses. Given this, a mathematical model was developed, and then solved using a three-dimensional finite element method (3D-FEM). Presented are numerical investigations that illustrate the influence of changes in the inclination of the force, as well as other important factors such as dimensionless frequency parameters, on the dynamic behavior of the system. In particular, the results indicate that the effect the initial stresses have on the dynamic stress distribution character increases with the aspect ratio but decreases with the thickness ratio.

Quantification of a concentrated point mass by Haar wavelets and machine learning

The inverse problem of determining location and mass ratio of a concentrated point mass attached to the homogeneous Euler – Bernoulli beam was considered in this article. Under the assumption that the size of the point mass was small compared to the total mass of the beam, it was shown that the problem could be solved in terms of point-mass-induced changes in the natural frequencies or mode shapes. Predictions of the point mass location and its mass ratio were made by the artificial neural networks or the random forests. The dimensionless natural frequency parameters or the first mode shape transformed into the Haar wavelet coefficients were used at the inputs of the machine learning methods. The simulation studies indicated that the combined approach of the natural frequencies, Haar wavelets and neural networks produced accurate predictions. The results presented in this article could help in understanding the behaviour of more complex structures under similar conditions and provide apparent influence on design of beams.

Influence of CNTs grading and reinforcement on dynamic characteristics of composite Plates in thermal environment

This analytical work deals with the dynamic analysis of the functionally graded composite plate reinforced with single walled carbon nanotubes is discussed in this article. By using the extended rule of mixtures, the material properties were computed. The dimensionless frequency parameter was discovered by generating ABAQUS-solved eigenvalues and eigenvectors. The subspace process was used to produce buckling Eigenvalues for the plate. The purpose of the current research work was to analyse the influence of varying temperatures, CNTs and CNTs grading volume fractions on dimensionless frequencies and buckling factors or parameters. From the findings available in the literature, the results of this analysis have been established. CNTs volume percentage and its distribution were found to have a substantial impact on the dimensionless fundamental frequencies. Moreover, similar effect of these parameters on plate buckling were also been observed. Results reveal that the addition of CNT enhances the stiffness of the plate.

Semi-analytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells

This article is dedicated to predict the vibrational behavior of composite coupled conical-conical shell structures. The structural material is composed of two phases, including polymer epoxy matrix and Carbon NanoTube (CNT) fibers. To improve the vibrational structural behavior, the distributions of CNTs throughout the thickness of shells are assumed to be Functionally Graded. In order to enhance the research, five different patterns are considered for distribution of the CNT fibers within the matrix. The governing equations of motion associated with conical shells are obtained by using Donnell's theory and Hamilton method. In addition, the five-parameter shell theory is utilized in this article. As a result, five differential equations are achieved by using variation calculation. To solve the system of differential equations, an efficient and modified Generalized Differential Quadrature Method (GDQM) is employed. All the natural frequencies of shell structures are found for different states. By considering continuity conditions, the required modification is applied to GDQM. To validate the proposed formulation, some well-known benchmarks are solved. Moreover, several numerical examples and parametric studies are implemented to show the high accuracy and capability of the authors' scheme for analyzing coupled shells. To obtain accurate responses, 15 grid points are required for using in GDQM. Besides, it is observed that the minimum and maximum dimensionless frequency parameters are obtained by the patterns FG−O and FG−X, respectively.

СВОБОДНЫЕ И ВЫНУЖДЕННЫЕ КОЛЕБАНИЯ ОБОЛОЧЕК РАЗЛИЧНОЙ ФОРМЫ С УЧЕТОМ ПЕРЕМЕННОСТИ ТОЛЩИНЫ ИЗ НЕЛИНЕЙНО-УПРУГОГО МАТЕРИАЛА

the article considers issues of shell vibrations, which are widely used in various industries and construction. Shells serve as elements of building structures with large spans.
 The chapter “Introduction” discussed issues related to the use of shells in all areas of industry, in aviation, rocket and space technology, railway transport, in the oil and gas industry and provides examples of shells for use in ceilings of circuses, stations, hangars; in industry: shells of rotation used as tanks, containers, columns, reactors, etc. In the section “Materials and research methods” free and forced vibrations of shells of variable thickness made out of nonlinear elastic material reviewed. In shell calculations the Kirchhoff – Law hypothesis was used. It was found that, during vibrations, the shells experience relative deformation of elongation and shear of the surface with coordinates (x, y), as well as bending and torsion strains. It is established that vibrations in the shells lead to a rotation of the main directions of elasticity and regarding to the adopted coordinate axis to angle θ, and the elastic constants of the material depend on the elastic constant Biy – the main directions of the nonlinear elastic shells.
 When solving the system of equations of motion of the shell relative to the displacements arising in it during vibration, based on theory R and various methods. The values of the dimensionless frequency parameter for a spherical shell taking into account changes in its curvature, variability and thickness of elastic properties are obtained.

Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method

This study is dedicated to propose a numerical solution for free vibration analysis of nanocomposite conical shells. The First-order Shear Deformation Theory (FSDT) is used to achieve the governing equations. Then, an efficient numerical method, namely the Generalized Differential Quadrature Method (GDQM), is employed to solve the Donnell-type governing differential equations. The effects of the nanofillers aggregation are investigated throughout this research. It is considered that a single conical shell is composed of a variety of the constituent material. This type of material includes three phases: polymer matrix, macro-scale fibers and nano-scale Carbon Nano Tubes (CNTs). Two well-known approaches, namely Han and Chamis, are employed for the homogenization procedure to obtain the equivalent material properties. It is worth mentioning that the power pattern is employed for the functionally distribution of CNTs within the polymer matrix. Furthermore, the effects of different boundary conditions, geometric and material properties on the dimensionless frequency parameter of the multiscale nanocomposite conical shells are considered. Afterward, a parametric study is implemented to determine the deep influences of the volume fraction of the nanofillers throughout the inclusion on the vibrational behaviors of conical shells. It is found out that increasing the agglomeration parameter increases the frequency parameter of the conical structures. Moreover, increasing the power exponent of the volume fraction of FG-CNT material deals decrease of the frequency parameter of conical shells. Comparing the obtained results with the outputs of some well-known benchmarks proves the correctness, accuracy and high capability of the proposed formulation.

Free vibration analysis of multistepped nonlocal Bernoulli–Euler beams using dynamic stiffness matrix method

The free vibration of multistepped nanobeams is studied using the dynamic stiffness matrix method. The beam analysis is based on the Bernoulli–Euler theory, and the nanoscale analysis is based on the Eringen’s nonlocal elasticity theory. The nanobeam is attached to linear and rotational elastic supports at the start, end, and intermediate boundary conditions. The effect of the nonlocal parameter, boundary conditions, and step ratios on the nanobeam natural frequency is investigated. The results of the dynamic stiffness matrix methods are validated by comparing selected cases with the literature, which give excellent agreement with those literatures. The results show that the dimensionless natural frequency parameter is inversely proportional to the nonlocal parameters except in the first mode for clamped-free boundary conditions. Also, the gap between every two consecutive modes decreases with the increasing of the nonlocal parameter.

Vibration analysis of truncated spherical shells under various edge constraints

Abstract By means of combining Flugge's thin shell theory and energy method, a generalized approach to investigate vibration characteristic of truncated spherical shell subjected to various edge constraints is proposed. The truncated spherical shell is devided into different sections along the meridian line, in which the displacement function of truncated spherical shell along meridian and circumferential line are respectively represented by Jacobi polynomials and Fourier series. Various edge constraints can be simulated on the basis of virtual spring stiffness method in the current research. Finally, the solutions can be derived by meand of Ritz method. The dependability and exactness of current method have been proved by the comparison between current method, FEM and related literatures. The dimensionless frequency parameters of different truncated spherical shell under various edge constraints are displayed. In addition, the influence of geometric dimensions and boundary constraints on frequency parameters are also discussed.

Free vibration analysis of composite sandwich panels with hierarchical honeycomb sandwich core

Abstract The vibration characteristics of sandwich panels with a hierarchical composite honeycomb sandwich core were investigated in this study. An orthotropic constitutive model of the hierarchical composite honeycomb sandwich core was used to propose an equivalent model (two-dimensional model). Two-dimensional (2D) and the three-dimensional (3D) finite element models as well as modal tests were used to predict the natural frequencies and mode shapes of the sandwich panels. The prediction results obtained using the equivalent model were consistent with the experimental and 3D finite element analysis results. Subsequently, a redesigned sandwich panel, with a hierarchical cross-honeycomb sandwich core, was manufactured to implement the multifunctional characteristics such as fluid flow and installation of microelectronic devices. To compare the vibration characteristics of the panel with a hierarchical cross-honeycomb sandwich core with those of a panel with a hierarchical square-honeycomb sandwich core, a dimensionless frequency parameter, ω 1 / ω , was proposed. The frequency parameter had different sensitivities to the geometric parameters, i.e., the face-sheet thickness ratio, wall-sheet thickness ratio, and relative density of the filling foam.

The Beneficial Role of Piles on the Seismic Loading of Structures

We examine the kinematic response of fixed-head vertical floating piles embedded in continuously nonhomogeneous soils and subjected to upward propagating seismic waves. The problem is explored numerically by means of a rigorous finite element (FE) model of the soil-pile system to quantify the kinematically induced reduction of the horizontal free-field spectral acceleration. Soil stiffness varies continuously with depth according to a generalized power law function. We show that kinematic pile response in the harmonic regime is controlled by a unique dimensionless frequency parameter involving the active pile length in a generalized nonhomogeneous soil. A new, simplified expression for the horizontal kinematic interaction factor Iuis proposed for practical time-domain applications while a novel physical interpretation of the filtering action of piles is reported by introducing the role of pile stiffness in averaging soil motion over an effective pile length. Following a parametric study under transient motion, we propose a set of novel, ready-to-use formulae for a rapid assessment of the pile-induced filtering action. An application of the proposed formulae to clayey soils is finally presented, leading to useful indications for the selection of the pile diameter associated with the maximum filtering potential.

Propagation of Love-type wave in functionally graded pre-stressed magneto-visco-elastic fiber-reinforced composite structure

ABSTRACT A theoretical model is established to analyze the propagation behavior of Love-type wave in a composite structure which is comprised of two different functionally graded pre-stressed magneto-visco-elastic fiber-reinforced media as layer and substrate. Traction free surface along with the common interface of layer and substrate are of sinusoidal type. The closed form expressions of displacement components have been deduced for both the layer and substrate adopting the perturbation technique. The derived expression for displacement component consists of two-part in which the first part corresponds to the case of plane boundaries whereas the remaining part appears due to non-zero curvature of the boundaries. The influence of the sinusoidal type of curved boundaries on the displacement of a particle in a functionally graded pre-stressed magneto-visco-elastic fiber-reinforced media due to the propagation of Love-type wave has been unraveled explicitly. The substantial influence of dimensionless undulation frequency parameter, undulation amplitude parameter, functionally gradient parameter, initial stress, viscoelasticity and magneto-elasticity on displacement components are distinctly traced out through numerical simulations and graphical illustrations. Furthermore, the deduced results are validated with the classical and pre-established results.

Electromagnetic radiation force on a perfect electromagnetic conductor (PEMC) circular cylinder

Unlike isotropic dielectric objects, the interaction of incident electromagnetic (EM) or optical waves with a material allowing rotary polarization produces coupled polarized internal and scattered fields. The aim of this investigation is to examine theoretically a novel physical effect, which concerns the contributions of the co-polarized and cross-polarized fields to the radiation force (per-length) experienced by an infinitely long perfect electromagnetic conductor (PEMC) cylinder having a circular cross-section and illuminated by TM-polarized plane progressive waves propagating perpendicularly to its axis. The multipole partial-wave series expansion method in cylindrical coordinates is used to derive exact series expansions for the co-polarized and cross-polarized components of the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation). In contrast with the perfect electric or magnetic conductors (PECs or PMCs), or the dielectric cylinder case, numerical illustrative results for the radiation force function (which is the radiation force per unit energy density and cross-sectional surface) clearly demonstrate the contribution of the cross-polarized component of the radiation force for a PEMC cylinder allowing rotary polarization. The results show that the cross-polarized component of the radiation force function can be positive or negative as the dimensionless frequency parameter ka varies (where k is the wavenumber in the medium of wave propagation and a is the radius of the cylinder). Moreover, it vanishes for ka = 0.67946 regardless of the admittance of the PEMC cylinder. Notice that the total force (i.e. the sum of the co-polarized and cross-polarized components) is always repulsive (i.e., positive). It is also verified that the results are in complete agreement with the law of energy conservation applied to scattering. The present analysis generalizes the classical radiation force investigations by introducing extra new terms in the series expansion for the longitudinal radiation force function for cylindrical materials allowing rotary polarization.

Modal characteristics of micro-perforated sandwich beams with square honeycomb-corrugation hybrid cores: A mixed experimental-numerical study

Modal performance of micro-perforated sandwich beams with honeycomb-corrugation hybrid cores was investigated. Finite element methods and modal analysis techniques have been used to predict their vibration characteristics (i.e. their natural frequencies and mode shapes). It is shown that the natural frequencies of sandwich beam with micro-perforation are slightly lower than those of corresponding order of sandwich beam without micro-perforation based on the experimental and three-dimensional finite element calculated results. To reveal the effect of micro-perforation diameters on the natural frequencies of sandwich beams, a dimensionless frequency parameter ϖ was proposed. The results demonstrate that the frequency parameter of sandwich panels decrease near-linearly with the increase of micro-perforation ratio. In addition, the frequency parameter ϖ is sensitive not to such parameters as the face sheet thickness ratio, the slenderness ratio of corrugated member and the relative density of filling honeycomb, but to the configuration of micro-perforation.

Experimental and numerical investigation of axial heat transfer enhancement by oscillatory flows

In the current study, axial heat transfer enhancements by laminar oscillatory flow between cold and hot reservoirs connected by a bundle of tubes are examined experimentally and numerically. The dimensionless frequency parameter, Womersley number Wo, ranged from 0.1 to 100 with different tidal displacements. Exceeding its molecular counterpart by about five orders of magnitude, the oscillatory thermal conductivity was enhanced with quadratic scaling on the tidal displacement or pressure-gradient amplitude, and the square root of the frequency of oscillation. Two correlations were suggested for the oscillatory thermal conductivity enhancement as a function of Wo and tidal displacement. The correlations showed that the axial heat transfer rate scaled in proportion to Wo1.62 for Wo > 3 and behaves exponentially for low Wo with different scales depending on pressure gradient amplitude. The study has proposed a classification for the oscillatory flow by partitioning the flow into four different regions varying from low tidal displacement to bulk convective exchange. The results also showed that for unsteady flow the unsteady axial conduction is negligible for Wo > 3, but becomes significant as it goes below Wo = 3. This criterion invalidates the previous studies’ assumption for Wo < 3 by ignoring the unsteady axial conduction. Finally, more than ten times of enhancement in axial heat transfer rate was observed in tubes with sufficient wall thickness. This non-zero thermal diffusivity at the interface between the fluid and the tube wall has improved the storage-release process through the Stokes layer.

Finite element analysis of the axial dynamic response and efficiency of pile groups

ABSTRACT Dynamic pile group effect can either increase or decrease the response of pile-supported structures. This paper presents the results of a three-dimensional finite element model of the pile-to-pile interaction that considers the effect of the surrounding soil to determine the dynamic stiffness and damping for vertical end bearing pile groups subjected to a vertical harmonic loading. The results were generated for a wide range of the dimensionless frequency parameter (ao ) for a 9 × 9-pile group with three different spacings: two-, four- and six-pile diameter. Both the stiffness and the damping showed an oscillatory behaviour with the dimensionless frequency parameter ao , as well as with the soil shear modulus. In addition, the group efficiency was determined as a function of the pile spacing and the soil shear modulus. The efficiency factor for the stiffness can be as high as 1.15 and as low as 0.7 and for the damping as high as 3.75 and as low as 0.4 as a function of the dimensionless frequency parameter ao .

Effects of low-Re pulsatile flow on friction characteristics in bare square array rod bundles

Interest in unsteady flow in floating systems has increased in recent times. This paper presents the results of the experimental investigation on the resistance characteristics of pulsating flow through square array bare rod bundles with P/D = 1.326 and W/D = 1.268 conducted in the range of time-averaged Reynold’s number Reta = 1–7 × 103 and dimensionless acceleration (α) of 0.001–0.013. Pulsatile flow affects the time-averaged friction factor because it changes the velocity field close to the wall. The dimensionless frequency parameter (ω′) relates the frequency to the viscous effects while the dimensionless acceleration (α) is the product of the velocity amplitude (Au), diameter (D) of the channel and the frequency (ω) normalized by the mean velocity (Um). Ratios (Cλ) of the time-averaged friction factor (λp) in pulsatile flow to the friction factor (λs) in a steady flow and (Cp) of their average pressure drops were used to compare the two flows. Cλ and Cp increase with an increase in Au, ω′ and α; but decreases with increase in Reta. The dynamics of the extra turbulence generated as a result of pulsation was also analyzed in the subchannels.