Effects Of Rotary Inertia Research Articles

Retracted] Free Vibration Analysis of Thick Rectangular and Elliptical Plates with Concentric Cut‐Out

This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut‐out in which geometries of plate and cut‐outs are different, through a deflection matching condition by including shear deformation and rotary inertia effects, with less computational efforts and high accuracy. The modified Independent Coordinate Coupling Method (ICCM) is validated with FEM package (ANSYS) and applied to know the change in eigenvalues for a plate with cut‐out by varying various parameters like aspect ratios, cut‐out size, and thickness ratios. Trigonometric functions considered at the boundary level conditions of a simply supported plate should be satisfied. Free vibrational exploration on a thick isotropic plate with various aspect ratios and an elliptical plate with various sizes is carried out through the modified ICCM. Independent coordinates are applied for a plate domain and for a hole domain individually followed by equating the deflection condition of hole and plate, a reduced mass to express with cut‐out from which eigenvalues can be obtained. The deflection matching condition facilitates the analysis even though the geometries of plate and cut‐outs are different.

Dynamic modelling, simulation and experiments of a micro-cutter with applications to cell perforation

The nonlinear three-dimensional dynamic equations of motion of a micro-cutter driven longitudinally at ultrasonic operating frequencies are derived using Kane's method. The micro-cutter is assumed to be immersed in a fluid, and in contact with an oocyte, which is to be perforated by the micro-cutter. The micro-cutter is modelled as an Euler-Bernoulli cantilever beam attached to a moving base. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. It is assumed that there is no slip between the micro-cutter tip and the embryo membrane. The model presented demonstrates that the longitudinal excitation input of a micropipette results in excitation of out-of-plane, lateral motion due to the nonlinear dynamic coupling of the dynamics. Experimental results of membrane perforation are presented in the work supporting oocyte micro-cutter observations regarding suitable frequencies of excitation for effective oocyte membrane perforation.

Effects of Shear Deformation and Rotary Inertia on a Simple-free Anisotropic Plate on Vlasov Foundation Traversed by a Distributed Moving Mass

Effects of Shear Deformation and Rotary Inertia on a Simple-free Anisotropic Plate on Vlasov Foundation Traversed by a Distributed Moving Mass

Effect of localized edge loads on the buckling behaviour of hybrid fibre metal laminates

Buckling characteristics of hybrid fibre metal laminated (HFML) plate subjected to localized edge loads have been investigated in this work by developing finite element formulation. In the formulation, the plate is modelled by using 9-noded heterosis plate elements by considering the effect of shear deformation and rotary inertia. In the HFML configuration, carbon and glass fibre reinforced laminates have been considered as core materials and aluminium alloy as face sheets. The sequential layer effect on carbon and glass laminates is studied by considering cross-ply and angle-ply fibre orientations. In each type of ply-orientation, the effect of six different hybrid configurations of the material, load width, type of partial loads and boundary conditions have been considered to study the buckling behaviour HFML plates.

Free vibration of FGM conical–spherical shells

Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

Effects of different interlaminar hybridization and localized edge loads on the vibration and buckling behavior of fiber metal composite laminates

This investigation presents the effect of different interlaminar hybridization and localized in-plane edge loads on the vibration and buckling characteristics of hybrid fiber metal laminates (HFMLs) by developing finite element formulation. A 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. Since the stress distribution within the plate element is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems wherein two sets of boundary conditions are used, one for pre-buckling stresses and another for buckling load calculations. The present study consists of aluminum metal face sheets bound with four layered symmetric hybrid cross-ply and angle-ply laminate schemes. In each scheme, six different hybrid combinations have been considered. The performance of each hybrid combination is investigated under various loading combinations. Further, the effect of different parameters such as boundary condition, thickness of plate, width and position of localized edge loads, plate aspect ratio, and hybrid configurations are included in this work. The effect of each parameter is well investigated and explained by plotting mode shapes. It is revealed from the study that the hybrid configurations and localized edge loads significantly affect the vibration and buckling characteristics.

Free Vibration Analysis of Multi-Layer Rectangular Plate with Two Magneto-Rheological Fluid Layers and a Flexible Core

In the present article, the free vibration analysis of a multi-layer rectangular plate with two magneto-rheological (MR) fluid layers and a flexible core is investigated based on exponential shear deformation theory for the first time. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The displacement of the flexible core is modeled using Frostig’s second order model which contains a polynomial with unknown coefficients. MR fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they have the capability to change the stiffness and damping of a structure. The governing equations of motion have been derived using Hamilton`s principle. The Navier technique is employed to solve derived equations. To validate the accuracy of the derived equations, the results in a specific case are compared with available results in the literature, and a good agreement will be observed. Then, the effect of variation of some parameters such as magnetic field intensity, core thickness to panel thickness ratio and MR layer thickness to panel thickness ratio on natural frequency of the sandwich panel is investigated.

Buckling behavior of interlaminar hybrid fiber metal laminate (HFMLs) subjected to uniaxial compressive loading

The aerospace industry witnessed the rapid increase in the usage of Fiber Metal Laminate (FMLs) for its higher load carrying capacity and many other advantages. The core material of FMLs made up of either glass or carbon fibers based on the type of application. One can achieve superior material property and economic in design by combining glass and carbon interlayer as a core material and the top and bottom by aluminum sheets, which forms a hybrid fibre metal laminates (HFMLs). In this investigation, the effect of different hybrid combinations on the vibration and buckling behavior of interlayer HFMLs have been studied by developing finite element formulation. The 9-noded heterosis plate element has been used to model the plate by incorporating the effect of shear deformation and rotary inertia. Sixteen different hybrid combinations have been considered to investigate the effect of ply orientation, boundary condition and aspect ratios of HFMLs. In each combination cross-ply, angle-ply and quasi isotropic layup schemes are considered to investigate the different parameters in detail and the results are discussed below.

Nonlinear vibration suppression of laminated composite conical shells on elastic foundations with magnetostrictive layers

Nonlinear vibration control of laminated composite conical shells surrounded by elastic foundations through magnetostrictive layers is presented in this paper. The shell modeled via the consideration of the effects of shear deformation and rotary inertia while von Karman theory of nonlinearity is also employed. In order to suppress the nonlinear vibration, velocity feedback control method is adopted. Modified Galerkin method is exerted to obtain the nonlinear ordinary differential equation of the system from equations obtained via Hamilton principle. The results of this study are acquired with a combination of modal analysis and multiple scales method. The asymptotical stability of the system around zero equilibrium point is investigated based on Lyapunov’s indirect method. The results for damping coefficients of nonlinear system and fundamental linear frequency as well as the curves of amplitude versus nonlinear frequency and nonlinear frequency ratio are obtained for different values of several parameters.

Buckling analysis of functionally graded materials by dynamic approach

Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions.

Effect of initial stresses on vibration behavior of functionally graded materials

Abstract Functionally Graded Materials (FGM) is the result of continuous gradation of two or more constituent materials over a certain volume. This type of material overcomes many problems, particularly delamination, cracking and damages which are very frequently found in laminated composite materials. The FGMs are commonly found in space structures, and these structural elements are subjected to various kinds of loadings during its service period, in which in-plane loading is the one which significantly affects the vibration characteristics of the structural elements. In this investigation, the effect of tensile and compressive stresses on vibration characteristics of FG panels has been studied by using finite element technique (FE). For mathematical modelling Poisson's ratio is assumed constant and Young’s modulus of elasticity is assumed to vary according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded isoparametric element by considering the effect of transverse shear deformation and rotary inertia. The effect of different factors such as volume fraction index, the thickness of the panel, boundary condition and tensile as well as compressive edge loads are considered to study the vibration behaviour of the FGM plate under tensile and compressive uniaxial edge loads.

Dynamic behaviour of perforated laminated panels under biaxial non-uniform edge loads based on FE approach

Buckling loads of laminated panels are calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-planes edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with the different sized cutouts. The aim of this work is to investigate the effect of biaxial non-uniform in-plane edge loads on the vibrations and buckling behaviour of panel with and without circular cutouts by using finite element technique. Further, the effect of different ply-orientations, boundary conditions and cutout sizes are also addressed in this work. Towards this, a nine-noded heterosis plate element has been adopted to model the panel by incorporating the effect of shear deformation and rotary inertia. Finally, it is shown that the non-uniform edge loading, boundary condition and cutout sizes have a remarkable effect on the vibration and buckling behavior of panel.

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.

Frequency study on panel type of FG-CNTRC joined conical-conical structures

In this paper, frequency behavior of the joined conical-conical panels is investigated while the structures are reinforced with uniform or functionally graded (FG) embedment of carbon nanotubes (CNTs). To consider both rotary inertia and in-plane effects, the formulation is developed upon FSDT considerations. By means of Hamilton’s principle the dynamic equations for two cones are derived. To attach two individual panels accurately, continuity conditions is performed at the junctions to satisfy the compatibility of displacements and stress resultants. After imposing simply supported boundary conditions at the straight edges, the set of governing equations are discretized meridionally on the basis of generalized differential quadrature (GDQ) technique. The proposed discretization approach is applicable for arbitrary boundary types imposed on the two curved edges at the initiating and terminating points of the structure. The validation of results is primarily assessed via some comparisons between present data and those previous researches in the favor of individual conical panels and also finite element model for joined conical-conical type. Thereafter, the significant roles of semi-vertex angle, embrace angle, CNT parameters and boundary types on the vibrational features are discussed.

Free vibration analysis of tapered Rayleigh beams using the transfer matrix method

In this study, an exact transfer matrix method is developed to analyze the effect of rotatory inertia and tapering on the free vibration characteristics of tapered Rayleigh beams. The beam model developed addresses practical cross sections, including single-tapered and double-tapered beams. The governing differential equation is solved using the Frobenius method for power series solutions, and then, the transfer matrix is formulated to transform the state vectors defined from the displacements, bending moment, and shear force at the start and end points. To investigate the effect of rotatory inertia and taper ratio on the natural frequencies and mode shapes of beam structures, the length-to-height ratios of tapered beams with four classical boundary conditions and various taper ratios are examined. The accuracy of the developed method is demonstrated using the comparative results predicted in previous studies. Through a parametric study, the numerical results that are useful in practical applications are offered, and relevant conclusions not discussed in previous studies are proposed. Furthermore, the results discussed can serve as a benchmark solution.

Evaluation of optimum length scale parameters in longitudinal wave propagation on nonlocal strain gradient carbon nanotubes by lattice dynamics

Longitudinal wave propagation in carbon nanotubes has been investigated by using Rayleigh-Bishop rod model and nonlocal strain gradient elasticity theory in the present study. Size dependent governing equation of motion has been obtained with variational formulation. Validation of the proposed model has been achieved with developed lattice dynamics model which considers neighborhood interaction. Least squares approach has been used in addition to the traditional calibration methodology. Number of atomic interactions, shear strain and rotary inertia effects have important effects on the calibration of scale parameters. Present results could help to continuum modeling of carbon nanotubes with accurate scale parameters.

Effect of position of partial load on buckling and vibration characteristics of composite panels with circular cutouts

Abstract In this, the effect of different positions of partial ledge loads on buckling behavior of laminated panels with the centrally placed circular cutout is studied by developing finite element formulation using 9 - noded heterosis element. The formulation includes the effect of shear deformation and rotary inertia. The effect of various parameter such as cutout size, ply-orientation and thickness of the panel included in this work to study the buckling behavior of each parameter in detail. It is observed that the buckling resistance of the panel decreases with the increase in cutouts size irrespective of position of partial load. However, the position of partial load at extreme ends show higher buckling resistance as compared to that of centrally placed edge loads, irrespective of cutout size. Further, cross-ply symmetric laminates show extremely higher and least buckling resistance, when partial load acting at the extreme edges and at the center of the partial edges respectively, as compared to all other layup schemes.

Supersonic Aeroelasticity and Dynamic Instability of Functionally Graded Porous Cylindrical Shells Using a Unified Solution Formulation

This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

Dynamic Analysis of Plates with Cut-Out Carrying Concentrated and Distributed Mass

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

Effect of porosity distribution on natural frequencies of thin and thick cylinders based on Mirsky–Hermann’s shear deformation theory

In this paper, the effect of the porosity coefficient and its distribution on the natural frequencies and mode shapes of a thin and thick cylindrical shell made of asymmetric porous materials is investigated analytically. The mechanical properties of the porous shell are non-uniform in the thickness and isotropic in the circumferential directions. The displacement field is assumed based on the first-order Mirsky–Hermann theory by considering the effects of transverse normal strain and rotary inertia. For more accurate stress resultants, the trapezoidal shape factor is considered in the formulation. The constitutive relations follow Biot’s theory for the porous materials and the kinematic of the problem is linear. The governing equations include four coupled partial differential equations that are solved using an analytical method and they are compared with the finite element analysis. By the sensitivity analysis, the effects of porosity distribution and geometry of the cylinder on the natural frequencies and mode shapes are studied. The results show that the largest frequency corresponds to the material which has the maximum density inside of the cylinder. Abbreviations: FSDT, first-order shear-deformation theory; 2D, two-dimensional; 3D, three-dimensional; FG, functionally graded; FGM, functionally graded materials; DQ, differential quadrature; MDEW, maximum density in outer (external) wall; MDIW, maximum density in inner wall; C.C, complex conjugate (of proceeding terms)