Showing papers on "Rotary inertia published in 2015"

Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach

Abstract: The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced composite thick skew plates is studied. The CNTs are reinforced uniaxially aligned in the axial direction. Material properties of the nanocomposites are assumed to be graded in the thickness direction. The element-free IMLS-Ritz method is employed for the numerical analysis. The theoretical formulation has incorporated the effects of transverse shear deformation and rotary inertia through employing the first-order shear deformation theory (FSDT). A few numerical examples are chosen to demonstrate the numerical stability and accuracy of the IMLS-Ritz method. The validity of the IMLS-Ritz results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for various types of CNTs distributions, CNT ratios, skew plates, aspect ratios and thickness-to-height ratios under different boundary conditions. Some conclusions are drawn on the parametric studies with respect to the buckling characteristics.

Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method

Abstract: Flexural vibration analysis of beams made of functionally graded materials (FGMs) with various boundary conditions is considered in this paper. Due to technical problems during FGM fabrication, porosities and micro-voids can be created inside FGM samples which may lead to the reduction in density and strength of materials. In this investigation, the FGM beams are assumed to have even and uneven distributions of porosities over the beam cross-section. The modified rule of mixture is used to approximate material properties of the FGM beams including the porosity volume fraction. In order to cover the effects of shear deformation, axial and rotary inertia, the Timoshenko beam theory is used to form the coupled equations of motion for describing dynamic behavior of the beams. To solve such a problem, Chebyshev collocation method is employed to find natural frequencies of the beams supported by different end conditions. Based on numerical results, it is revealed that FGM beams with even distribution of porosities have more significant impact on natural frequencies than FGM beams with uneven porosity distribution.

Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells

Abstract: A geometrically non-linear theory is developed for shells of generic shape allowing for third-order thickness and shear deformation and rotary inertia by using eight parameters; geometric imperfections are also taken into account. The geometrically non-linear strain–displacement relationships are derived retaining full non-linear terms in all the 8 parameters, i.e. in-plane and transverse displacements, rotations of the normal and thickness deformation parameters; these relationships are presented in curvilinear coordinates, ready to be implemented in computer codes. Higher order terms in the transverse coordinate are retained in the derivation so that the theory is suitable also for thick laminated shells. Three-dimensional constitutive equations are used for linear elasticity. The theory is applied to circular cylindrical shells complete around the circumference and simply supported at both ends to study initially static finite deformation. Both radially distributed forces and displacement-dependent pressure are used as load and results for different shell theories are compared. Results show that a 6 parameter non-linear shell theory is quite accurate for isotropic shells. Finally, large-amplitude forced vibrations under harmonic excitation are investigated by using the new theory and results are compared to other available theories. The new theory with non-linearity in all the 8 parameters is the only one to predict correctly the thickness deformation; it works accurately for both static and dynamics loads.

Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach

Abstract: This paper presents the Kriging model approach for stochastic free vibration analysis of composite shallow doubly curved shells. The finite element formulation is carried out considering rotary inertia and transverse shear deformation based on Mindlin’s theory. The stochastic natural frequencies are expressed in terms of Kriging surrogate models. The influence of random variation of different input parameters on the output natural frequencies is addressed. The sampling size and computational cost is reduced by employing the present method compared to direct Monte Carlo simulation. The convergence studies and error analysis are carried out to ensure the accuracy of present approach. The stochastic mode shapes and frequency response function are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results using Kriging model and its performance.

Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge

Abstract: The free vibration characteristics of FGM cylindrical shells partially resting on elastic foundation with an oblique edge are investigated by an analytical method. The cylindrical shell is partially surrounded by an elastic foundation which is represented by the Pasternak model. An edge of an elastic foundation lies in a plane that is oblique at an angle with the shell axis. The motion of shell is represented based on the first order shear deformation theory (FSDT) to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shell is composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a four-parameter power law distribution in terms of volume fraction of the constituents. The equation of motion for eigenvalue problem is obtained using Rayleigh–Ritz method and variational approach. To validate the present method, the numerical example is presented and compared with the available existing results.

A shear deformable cylindrical shell model based on couple stress theory

Abstract: In this paper, formulation of the thin cylindrical shell via the modified couple stress theory by taking account of shear deformation and rotary inertia is obtained. To do this, the study developed the first shear deformable cylindrical shell theory by considering the size effects via the couple stress theory and the equations of motion of shell with classical and non-classical boundary conditions were extracted through Hamilton’s principle. In the end, as an example, free vibrations of the single-walled carbon nanotube (SWCNT) were investigated. Here, the SWCNT was modeled as a simply supported shell, and the Navier procedure was used to solve the vibration problem. The results of the new model were compared with those of the classical theory, pointing to the conclusion that the classical model is a special case of the modified couple stress theory. The findings also demonstrate that the rigidity of the nano-shell in the modified couple stress theory compared with that in the classical theory is greater, resulting in the increase in natural frequencies. In addition, the effect of the material length scale parameter on the vibrations of the nano-shell in different lengths and thickness was investigated.

Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation

Abstract: Nonlinear and linear free vibration of symmetrically laminated magneto-electro-elastic doubly-curved thin shell resting on an elastic foundation is studied analytically The shell is considered to be simply-supported on all edges and the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces To obtain the equations of motion, the Donnell shell theory in the presence of rotary inertia effect is used Moreover, Gauss' laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior The nonlinear partial differential equations of motion are reduced to a single nonlinear ordinary differential equation by introducing a force function and using the single-term Galerkin method The resulting equation is solved analytically by Lindstedt-Poincare perturbation method After validation of the present study, several numerical studies are done to investigate the effects of foundation parameters, geometrical properties of the shell, and electric and magnetic potentials on the linear and nonlinear behavior of these smart shells

Free vibration of four-parameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions

Abstract: The objective of this work is to present a Haar Wavelet Discretization (HWD) method-based solution approach for the free vibration analysis of functionally graded (FG) spherical and parabolic shells of revolution with arbitrary boundary conditions. The first-order shear deformation theory is adopted to account for the transverse shear effect and rotary inertia of the shell structures. Haar wavelet and their integral and Fourier series are selected as the basis functions for the variables and their derivatives in the meridional and circumferential directions, respectively. The constants appearing in the integrating process are determined by boundary conditions, and thus the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations. The proposed approach directly deals with nodal values and does not require special formula for evaluating system matrices. Also, the convenience of the approach is shown in handling general boundary conditions. Numerical examples are given for the free vibrations of FG shells with different combinations of classical and elastic boundary conditions. Effects of spring stiffness values and the material power-law distributions on the natural frequencies of shells are also discussed. Some new results for the considered shell structures are presented, which may serve as benchmark solutions.

A nonlocal timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method

Abstract: This article presents the solution for free vibration of nanobeams based on Eringen nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is considered in the first theory, and the transverse shear deformation effects as well as rotary inertia are taken into account in the latter one. Through variational formulation and the Hamilton principle, the governing differential equations of free vibration of the nonlocal Timoshenko beam and the boundary conditions are derived. The obtained equations are solved by the differential transformation method (DTM) for various frequency modes of the beams with different end conditions. In addition, the effects of slenderness and on vibration behavior are presented. It is revealed that the slenderness affects the vibration characteristics slightly whilst the small scale plays a significant role in the vibration behavior of the nanobeam.

Isogeometric vibration analysis of free-form Timoshenko curved beams

Abstract: In this paper, the finite free-form curved beam element is formulated by the isogeometric approach based on the Timoshenko Rcurved beam theory to investigate the free vibration behavior of the curved beams with arbitrary curvature. The non-uniform rational B-splines (NURBS) functions which define the geometry of the curved beam are used as the basis functions for the finite element analysis. In order to enrich the basis functions and to increase the accuracy of the solution fields, the h-, p-, and k-refinement techniques are implemented. The geometry and curvature of free-form curved beams are modelled in a unique way based on NURBS. The gap between the free vibration analysis of the curved beams with constant curvature and those with variable curvature is eliminated. All the effects of the axis extensibility, the shear deformation, and the rotary inertia are taken into consideration by the present isogeometric model. Results of the parabolic and elliptic curved beams for non-dimensional frequencies are compared with other available results in order to show the accuracy and efficiency of the present isogeometric approach. Furthermore, the free vibration analysis of the elliptic thick rings is presented. Particularly, the Tschirnhausen’s cubic curved beam is considered to study the dynamic behavior as an example of free-form curved beams.

Stochastic natural frequency of composite conical shells

Abstract: The present study portrays the stochastic natural frequencies of laminated composite conical shells using a surrogate model (D-optimal design) approach. The rotary inertia and transverse shear deformation are incorporated in probabilistic finite element analysis with uncertainty due to variation in angle of twist. A sensitivity analysis is carried out to address the influence of different input parameters on the output natural frequencies. Typical fiber orientation angle and material properties are randomly varied to obtain the stochastic natural frequencies. The sampling size and computational cost are exorbitantly reduced by employing the present approach compared to direct Monte Carlo simulation. Statistical analysis is presented to illustrate the results. The stochastic natural frequencies obtained are the first known results for the type of analyses carried out here.

Influences of shear stresses and rotary inertia on the vibration of functionally graded coated sandwich cylindrical shells resting on the Pasternak elastic foundation

Abstract: In this study, the behavior of vibration of sandwich cylindrical shells covered by functionally graded coatings and resting on the Pasternak elastic foundation considering combined influences of sh...

Eringen's Length-Scale Coefficients for Vibration and Buckling of Nonlocal Rectangular Plates with Simply Supported Edges

Abstract: For the nonlocal theory of structures, Eringen's small length-scale coefficient e0 may be identified from atomistic modeling or experimental tests. In this study, Eringen's small length-scale coefficients are presented for the vibration and buckling of nonlocal rectangular plates with simply supported edges. The coefficients are calibrated by comparing the vibration frequency and buckling loads obtained from a nonlocal plate and a microstructured beam-grid model with the same characteristic length. The beam-grid model is composed of rigid beams connected by rotational and torsional springs. It is found that the small length-scale coefficient e0 varies with respect to the initial stress, rotary inertia, mode shape, and aspect ratio of the rectangular plate.

The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia

Abstract: The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that th ...

Buckling and postbuckling of single‐walled carbon nanotubes based on a nonlocal Timoshenko beam model

Abstract: In this research, the axial buckling and postbuckling configurations of single-walled carbon nanotubes (SWCNTs) under different types of end conditions are investigated based on an efficient numerical approach. The effects of transverse shear deformation and rotary inertia are taken into account using the Timoshenko beam theory. The nonlinear governing equations and associated boundary conditions are derived by the virtual displacements principle and then discretized via the generalized differential quadrature method. The small scale effect is incorporated into the model through Eringen's nonlocal elasticity. To obtain the critical buckling loads, the set of linear discretized equations are solved as an eigenvalue problem. Also, to address the postbuckling problem, the pseudo arc-length continuation method is applied to the set of nonlinear parameterized equations. The effects of nonlocal parameter, boundary conditions, aspect ratio and buckling mode on the critical buckling load and postbuckling behavior are studied. Moreover, a comparison is made between the results of Timoshenko beam model and those of its Euler-Bernoulli counterpart for various magnitudes of nonlocal parameter.

Free vibration of moderately thick functionally graded plates by a meshless local natural neighbor interpolation method

Abstract: Using a meshless local natural neighbor interpolation (MLNNI) method, natural frequencies of moderately thick plates made of functionally graded materials (FGMs) are analyzed in this paper based on the first-order shear deformation theory (FSDT), which is employed to take into account the transverse shear strain and rotary inertia. The material properties of the plates are assumed to vary across the thickness direction by a simple power rule of the volume fractions of the constituents. In the present method, a set of distinct nodes are randomly distributed over the middle plane of the considered plate and each node is surrounded by a polygonal sub-domain. The trial functions are constructed by the natural neighbor interpolation, which makes the constructed shape functions possess Kronecker delta property and thus no special techniques are required to enforce the essential boundary conditions. The order of integrands involved in domain integrals is reduced due to the use of three-node triangular FEM shape functions as test functions. The natural frequencies computed by the present method are found to agree well with those reported in the literature, which demonstrates the versatility of the present method for free vibration analysis of moderately thick functionally graded plates.