Showing papers on "Rotary inertia published in 2007"
TL;DR: In this paper, the free vibration problem for micro/nanobeams modelled after Eringen's nonlocal elasticity theory and Timoshenko beam theory is considered and the governing equations and the boundary conditions are derived using Hamilton's principle.
Abstract: This paper is concerned with the free vibration problem for micro/nanobeams modelled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.
415 citations
TL;DR: In this article, the static, dynamic, and buckling behavior of composite members is investigated by taking into account for the influences of rotary inertia and shear deformations, and analytical solutions of the deflection are then found for the beam with uniformly distributing load under common boundary conditions.
148 citations
TL;DR: In this paper, the coupled thermo-mechanical and energy equations for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load were simultaneously solved for a functional graded axismmetric shell.
116 citations
TL;DR: In this article, the rotational inertia dampers combined with toggles are used to increase the vibration control effect of a structure with a small drift and a viscous or friction damping mechanism.
105 citations
Abstract: Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.
81 citations
TL;DR: In this article, the dynamic response of a rotating cantilever twisted and inclined airfoil blade subjected to contact loads at the free end is considered. And the Rayleigh-Ritz method is used to convert the set of coupled partial differential equations into equivalent classical mass, stiffness, damping, and gyroscopic matrices.
Abstract: In this paper, consideration is given to the dynamic response of a rotating cantilever twisted and inclined airfoil blade subjected to contact loads at the free end. Starting with the basic geometrical relations and energy formulation for a rotating Timoshenko beam constrained at the hub in a centrifugal force field, a system of coupled partial differential equations are derived for the combined axial, lateral and twisting motions which includes the transverse shear, rotary inertia, and Coriolis effects, as well. In the mathematical formulation, the torsion of the thin airfoil also considers a very general case of shear center not being coincident with the CG (center of gravity) of the cross section, which allows the equations to be used also for analyzing eccentric tip-rub loading of the blade. Equations are presented in terms of axial load along the longitudinal direction of the beam which enables us to solve the dynamic pulse buckling due to the tip being loaded in the longitudinal as well as transverse directions of the beam column. The Rayleigh-Ritz method is used to convert the set of four coupled-partial differential equations into equivalent classical mass, stiffness, damping, and gyroscopic matrices. Natural frequencies are computed for beams with varying "slenderness ratio" and "aspect ratio" as well as "twist angles." " Dynamical equations account for the full coupling effect of the transverse flexural motion of the beam with the torsional and axial motions due to pretwist in the airfoil. Some transient dynamic responses of a rotating beam repeatedly rubbing against the outer casing is shown for a typical airfoil with and without a pretwist.
78 citations
TL;DR: In this paper, free vibration analysis of a rotating, double tapered Timoshenko beam featuring coupling between flapwise bending and torsional vibrations is performed, and an efficient mathematical technique called the differential transform method (DTM) is used to solve the governing differential equations of motion.
69 citations
TL;DR: In this article, the vibration problem of initially stressed micro/nano-beams is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory.
Abstract: This paper is concerned with the vibration problem of initially stressed micro/nano-beams. The vibration problem is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of initial stress, transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. These equations are solved analytically for the vibration frequencies of micro/nano-beams with different initial stress values and boundary conditions. The effect of the initial stress on the fundamental frequency and vibration mode shape of the beam is investigated. The solutions obtained provide a better representation of the vibration behavior of initially stressed micro/nano-beams which are stubby and short, since the effects of small scale, transverse shear deformation and rotary inertia are significant and cannot be neglected.
63 citations
TL;DR: In this article, a spectral finite element method for two parallel beams connected to each other by the vertical springs uniformly distributed along the beam length is introduced, where the effects of the shear deformation and rotary inertia of the beams are accounted for.
51 citations
TL;DR: In this paper, a nine-noded isoparametric plate bending element has been used for the analysis of free undamped vibration of isotropic and fiber reinforced laminated composite plates.
Abstract: A nine-noded isoparametric plate-bending element has been used for the analysis of free undamped vibration of isotropic and fiber reinforced laminated composite plates. The effect of shear deformation has been incorporated in the formulation by considering the first-order shear deformation theory for the analysis. An effective mass lumping scheme with rotary inertia has been recommended. Two types of mass lumping schemes have been formed. In one lumping scheme rotary inertia has also been introduced. Numerical examples of isotropic and composite rectangular plates having different fiber orientations angles, thickness ratios, and aspect ratio have been solved. Examples of plates having internal cutout and uniformly distributed mass on the plates have also been studied. The results obtained have been compared with the available published literature. The present results are very close to the analytical solutions. Few examples have been presented as new results.
51 citations
TL;DR: In this article, the combined effects of non-Newtonian couple stresses and convective fluid inertia forces on the squeeze film motion between a long cylinder and an infinite plate are presented.
TL;DR: In this article, a free vibration analysis of composite cylindrical shells with different boundary conditions is presented using differential quadrature method (DQM), where the effects of shear deformation and rotary inertia terms are taken into account.
TL;DR: In this paper, the dynamic behavior of sandwich panels with a flexible core and debonded region with and without contact is studied using the high-order theory of Sandwich panels and considering geometrical nonlinear effects and the nonlinearity associated with the contact characteristics of the delaminated surfaces.
TL;DR: In this article, the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von Karman's assumptions, and the formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects.
TL;DR: In this paper, the mutual potential and the mutual gravitational torque of two bodies of arbitrary shape are derived based on Cartesian coordinates, inertia integrals with relation to the principal reference frames of each body, and the relative rotation matrix.
Abstract: The mutual gravitational potential and the mutual gravitational torque of two bodies of arbitrary shape are expanded to the fourth order. The derivations are based on Cartesian coordinates, inertia integrals with relation to the principal reference frames of each body, and the relative rotation matrix. The current formulation is convenient to utilize in high precision problems in rotational dynamics.
TL;DR: In this paper, the static and dynamic characteristics of composite thin-walled beams that are constructed from a single-cell box are investigated, and the effects of fiber orientation on static deflection and natural frequencies are considered.
Abstract: This paper investigates the static and dynamic characteristics of composite thin-walled beams that are constructed from a single-cell box. The structural model considered herein incorporates a number of nonclassical effects, such as material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia. The governing equations were derived using extended Hamilton's principle and solved using extended Galerkin's method. The effects of fiber orientation on static deflection and natural frequencies are considered and a number of important conclusions are outlined.
TL;DR: In this article, the authors presented a modified LTMM to determine the natural frequencies and the corresponding mode shapes of a multi-step Timoshenko beam with various boundary (supporting) conditions and carrying various concentrated elements with eccentricity of each lumped mass considered, by using the same formulation developed from a beam with free-free boundary conditions.
TL;DR: In this paper, the effects of the axial force, location, mass ratio, and the radius of gyration on the natural frequencies and mode shapes of DETF are investigated.
TL;DR: In this article, the effects of particle inertia on the rotary motion of a fiber in uniform flow fields are discussed. But the authors focus on the case of a slender fiber.
Abstract: The rotation of an inertialess ellipsoidal particle in a Newtonian fluid has been firstly analyzed by Jeffery [1]. He found that in the shear flow the particle rotates such that the end of its axis of symmetry describes a closed periodic orbit. The aim of this paper is to discuss the effects of particle inertia on the rotary motion of a fiber in uniform flow fields. We recall the equations of motion and the constitutive equation for the hydrodynamic moment in the case of a slender fiber. These equations are solved numerically for several flow fields. We demonstrate that for the plane flow fields with dominant vorticity (elliptic and rotational flows) the effect of inertia is the slow particle drift toward the flow plane.
TL;DR: In this article, the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load.
Abstract: In this paper, the response of a circular cylindrical thin shell made of the functionally graded material based on the generalized theory of thermoelasticity is obtained. The governing equations of the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. Thermoelasticity with second sound effect in cylindrical shells based on the Lord–Shulman model is compared with the Green–Lindsay model. A second-order shear deformation shell theory, that accounts for the transverse shear strains and rotations, is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain is used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The effects of temperature field for linear and non-linear distributions across the shell thickness are examined. The results are validated with the known data in the literature. Copyright © 2006 John Wiley & Sons, Ltd.
TL;DR: In this article, the non-axisymmetric vibration and stability problem of a rotating annular plate is analyzed by using the finite element method, and the effects of various properties, such as orthotropic properties of face layers and the viscoelastic core layer stiffness and thickness are discussed.
TL;DR: In this paper, the authors studied numerical solutions for the hydroelastic problems of bodies directly in the time domain using Neumann-Kelvin formulation, where the exact initial boundary value problem is linearized using the free stream as a basis flow, replaced by the boundary integral equation applying Green theorem over the transient free surface Green function.
19 Nov 2007
TL;DR: In this paper, an analytical approach, as well as a calculation method for determining the dynamic response of Timoshenko beams under uniform partially distributed moving masses, using the so-called discrete element technique (DET).
Abstract: The current article presents an analytical approach, as well as a calculation method for determining the dynamic response of Timoshenko beams under uniform partially distributed moving masses, using the so-called discrete element technique (DET). It is shown that the proposed methodology offers a compact and computationally efficient way of conducting parametric studies to evaluate the dynamic response of the beam-like structures with arbitrary boundary conditions such as railway and road bridges. First, a formulation is presented in a matrix form for beams under partially distributed masses. The results have been validated against analytical formulations, finite difference, and finite element results. A number of parametric studies were conducted to assess the effects of the moving mass velocity and moving mass length on the beam deflection. A major aspect of the work is the study of successive travelling masses for which the transient effects are important. Both analytical and DET results showed...
TL;DR: In this article, a finite element discretization of the rotor using a Rayleigh beam model is considered, which includes rotary inertia and gyroscopic moments leading to nonself-adjoint systems.
Abstract: We focus on the reduction of the vibration level of rotors by optimizing the shape of the body. The target is to reduce rotor weight and rotor vibrations leading to higher efficiency and less noise. We consider a finite element discretization of the rotor using a Rayleigh beam model which includes rotary inertia and gyroscopic moments leading to nonself-adjoint systems. We present a general algebraic framework for this case. The mass function is the objective function of the optimization problem and constraints are set on the nonlinear and nonconvex functions of critical speed and unbalanced response. For the numerical solution, algorithms belonging to the class of sequential convex programming are applied for the example of a turbocharger. A remarkable reduction of mass of an initially given prototype could be achieved while significantly reducing the unbalanced response and raising the critical speeds.
TL;DR: In this article, the Timoshenko beam theory and the effects of shearing deformations and rotary inertia were considered to suppress the inherent divergent rigid body modes by using a dual-level control approach.
TL;DR: In this paper, the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method were investigated.
Abstract: Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying "multiple" spring-mass systems is rare, particular that regarding the "exact" solutions. As to the "exact" solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated.
TL;DR: Using the technical computing program Mathematica, the dynamic stiffness matrix for the spatially coupled free vibration analysis of thin-walled curved beam with non-symmetric cross-section on two-types of elastic foundation is newly presented based on the power series method.
TL;DR: In this paper, a theoretical method was developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia.
Abstract: A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia. Heat conduction equation across the shell thickness is used to determine the temperature distribution. Material properties are assumed to be graded across the shell wall thickness of according to a power-law, in terms of the volume fractions of the constituents. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied. The obtained results have been compared with the analytical results of other researchers, which showed good agreement. The new features of thermal vibrati...
TL;DR: In this paper, the authors considered the inertial forces and moments of the tip mass and rotary inertia as the boundary conditions at the tip end of the beam and found that the approximate solution for the last problem may be achieved by two techniques: Method 1 and Method 2.
TL;DR: In this article, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples, which can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.