Showing papers on "Rotary inertia published in 2005"

Flexural wave propagation in single-walled carbon nanotubes

Abstract: The paper presents the study on the flexural wave propagation in a single-walled carbon nanotube through the use of the continuum mechanics and the molecular dynamics simulation based on the Terroff-Brenner potential. The study focuses on the wave dispersion caused not only by the rotary inertia and the shear deformation in the model of a traditional Timoshenko beam, but also by the nonlocal elasticity characterizing the microstructure of carbon nanotube in a wide frequency range up to THz. For this purpose, the paper starts with the dynamic equation of a generalized Timoshenko beam made of the nonlocal elastic material, and then gives the dispersion relations of the flexural wave in the nonlocal elastic Timoshenko beam, the traditional Timoshenko beam and the Euler beam, respectively. Afterwards, it presents the molecular dynamics simulations for the flexural wave propagation in an armchair (5,5) and an armchair (10,10) single-walled carbon nanotubes for a wide range of wave numbers. The simulation results show that the Euler beam holds for describing the dispersion of flexural waves in the two single-walled carbon nanotubes only when the wave number is small. The Timoshenko beam provides a better prediction for the dispersion of flexural waves in the two single-walled carbon nanotubes when the wave number becomes a little bit large. Only the nonlocal elastic Timoshenko beam is able to predict the decrease of phase velocity when the wave number is so large that the microstructure of carbon nanotubes has a significant influence on the flexural wave dispersion.

Terahertz vibration of short carbon nanotubes modeled as timoshenko-beams

Abstract: Short carbon nanotubes of smaller aspect ratio (say, between 10 and 50) are finding significant application in nanotechnology. This paper studies vibration of such short carbon nanotubes whose higher-order resonant frequencies fall within terahertz range. Because rotary inertia and shear deformation are significant for higher-order modes of shorter elastic beams, the carbon nanotubes studied here are modeled as Timoshenko beams instead of classical Euler beams. Detailed results are demonstrated for double-wall carbon nanotubes of aspect ratio 10, 20, or 50 based on the Timoshenko-beam model and the Euler-beam model, respectively. Comparisons between different single-beam or double-beam models indicate that rotary inertia and shear deformation, accounted for by the Timoshenko-beam model, have a substantial effect on higher-order resonant frequencies and modes of double-wall carbon nanotubes of small aspect ratio (between 10 and 20). In particular, Timoshenoko-beam effects are significant for both large-diameter and small-diameter double-wall carbon nanotubes, while double-beam effects characterized by noncoaxial deflections of the inner and outer tubes are more significant for small-diameter than large-diameter double-wall carbon nanotubes. This suggests that the Timoshenko-beam model, rather than the Euler-beam model, is relevant for terahertz vibration of short carbon nanotubes.

Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end

Abstract: Consideration is given to the dynamic response of a Timoshenko beam under repeated pulse loading. Starting with the basic dynamical equations for a rotating radial cantilever Timoshenko beam clamped at the hub in a centrifugal force field, a system of equations are derived for coupled axial and lateral motions which includes the transverse shear and rotary inertia effects, as well. The hyperbolic wave equation governing the axial motion is coupled with the flexural wave equation governing the lateral motion of the beam through the velocity-dependent skew-symmetric Coriolis force terms. In the analytical formulation, Rayleigh–Ritz method with a set of sinusoidal displacement shape functions is used to determine stiffness, mass and gyroscopic matrices of the system. The tip of the rotating beam is subjected to a periodic pulse load due to local rubbing against the outer case introducing Coulomb friction in the system. Transient response of the beam with the tip deforming due to rub is discussed in terms of the frequency shift and non-linear dynamic response of the rotating beam. Numerical results are presented for this vibro-impact problem of hard rub with varying coefficients of friction and the contact-load time. The effects of beam tip rub forces transmitted through the system are considered to analyze the conditions for dynamic stability of a rotating blade with intermittent rub.

Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects

Abstract: A general theory is proposed for the shear deformable thin-walled beam with non-symmetric open/closed cross-sections and its exact dynamic and static element stiffness matrices are evaluated. For this purpose, an improved shear deformable beam theory is developed by introducing Vlasov's assumption and applying Hellinger–Reissner principle. This includes the shear deformations due to the shear forces and the restrained warping torsion and due to the coupled effects between them, rotary inertia effects and the flexural–torsional coupling effects due to the non-symmetric cross-sections. Governing equations and force–deformation relations are derived from the energy principle and a system of linear eigenproblem with non-symmetric matrices is constructed based on 14 displacement parameters. And then explicit expressions for displacement parameters are derived and the exact dynamic and the static stiffness matrices are determined using force–deformation relationships. In order to verify the validity and the accuracy of this study, the numerical solutions are presented and compared with other numerical solutions available in the literature and results using the thin-walled beam element and the shell element. Particularly the influences of the coupled shear deformation on the vibrational and the elastic behavior of non-symmetric beams with various boundary conditions are investigated.

Local and Global Damped Vibrations of Plates with a Viscoelastic Soft Flexible Core: An Improved High-order Approach:

Abstract: An improved high-order theory is presented to investigate the dynamic behavior of thin and thick fiber-reinforced plastic (FRP) plates with a soft viscoelastic flexible core. Shear deformation theory is used for the face sheets while three-dimensional elasticity theory is used for the soft core. The analysis permits nonlinear distortions of the cross-sectional plane of the core as well as changes in its height. The analysis determines the damped natural frequencies, loss factors, and local and global mode shapes of plates. Some of the results are hitherto not reported in the literature based on a higher-order plate theory (HSAPT). Transverse shear and rotary inertia effects of face sheets are taken into consideration. For simply supported boundary condition, closed-form solutions are obtained by Navier’s technique. Numerical results are presented and compared with the experimental and theoretical results found in literature.

On vibration of functionally graded plates according to a refined trigonometric plate theory

Abstract: The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lame's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM

Abstract: A differential quadrature (DQ) procedure is developed for free vibration analysis of variable thickness moderately thick plates with edges elastically restrained against translation and rotation. The governing equations are based on the first order shear deformation theory and the rotary inertia effects are considered. Comparisons with known thin plate and uniform thickness Mindlin plate solutions are carried out to verify the applicability and accuracy of the analysis. Plates with linear or nonlinear varying thickness in one or two directions can be considered. It is demonstrated that using this DQ procedure, classical boundary conditions such as simply supported, clamped and free edges for variable thickness, thin as well as moderately thick plates can be simulated without any numerical difficulties. The effects of different combinations of constraints at edges, aspect ratio, thickness-to-length ratio, and stiffness parameter values on accuracy and convergence behaviors of the plates are presented. Some new results are presented for bi-linearly variable thickness plates with elastically restrained edges.

First-Order Shear Deformation, p-Version, Finite Element for Laminated Plate Nonlinear Vibrations

Abstract: A p-version, hierarchical finite element for moderately thick composite laminated plates is presented, where the effects of the rotary inertia, transverse shear, and geometrical nonlinearity are taken into account. The time-domain free-vibration equations of motion are obtained by applying the principle of virtual work. Those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor-corrector procedure. The linear natural frequencies of vibration of several plates are determined, and the convergence properties of the element are investigated. It is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy. The influences of the plate's thickness, of the width to length ratio, and of the fiber orientation on nonlinear free vibrations are investigated.

Free in-plane vibrations of highly buckled beams carrying a lumped mass

Abstract: Free undamped in-plane vibrations of shear undeformable beams around their highly buckled configurations are investigated neglecting rotary inertia effects. The beams are inertially nonuniform since a lumped mass is rigidly clamped along the span. Two mechanical models are considered depending on the boundary conditions in the post-buckling phases. First, the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end, a roller support, both in the buckling and post-buckling phases. In the second model, the beam is extensible in the post-buckling phase because the roller support boundary is changed into a fixed hinged end. Free undamped vibrations are governed, in the first case, by a homogeneous integral-partial-differential equation and, in the second case, by two coupled partial-differential equations with variable coefficients. The solutions of the associated eigenvalue problems are found employing two approaches: a semi-analytical method based on Galerkin discretization and a finite element method. A close agreement in the outcomes is found. The leading differences relating to the natural frequencies and linear normal modes of the two pre-stressed curved beam models are discussed; in particular, the occurrence of the veering phenomenon and the crossovers are outlined.

A finite thin circular beam element for out-of-plane vibration analysis of curved beams

Abstract: In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.

Human-powered generator system with active inertia and simulated vehicle

Abstract: A human-powered generator system for electric watercycles with a control means whereby the perceived mechanical properties of the pedal mechanism and electric pedal-powered generator are adjustable by the operator. The invention provides a means whereby the rotational inertia and damping of the input pedal mechanism, including generator, as perceived by the operator can be increased or decreased as desired. The control means with further properties such that the input pedal mechanism as perceived by the operator can be made to mimic that of bicycle; i.e., with large inertia when pedaling in the forward direction, a very low inertia when pedaling in the reverse direction, and a freewheeling clutch mechanism whereby the large inertia is disengaged when not pedaling in the forward direction with a forward torque. The control means further enable the electric watercycle to be perceived as coasting through the water when the operator takes a momentary break from pedaling, much like that of a bicycle coasting.

Rotation Control Device and Construction Machine

Abstract: To rotate a rotary body at a constant velocity, a swing control device 50 of an electric rotary excavator controls the rotation of the rotary body with a small first torque command value T1. Thus, when inertia moment of the rotary body is changed due to extension or retraction of a boom and an arm, the change of the inertia moment affects the rotation velocity of the rotary body, and an operator can perform a rotation operation with the same feeling as in a hydraulically-driven excavator. In contrast, when operating a swing lever 10 for acceleration, the rotation is controlled with a large second torque command value T2. Accordingly, a good and quick operational feeling is obtained without a delay in acceleration or deceleration, and the degradation of workability can be avoided.

Measuring the moment of inertia of the human body by a rotating platform method

Abstract: An apparatus has been constructed for the demonstration and measurement of the moment of inertia of a human body The apparatus consists of a turntable that is free to rotate under the action of a falling weight The mechanical features of the apparatus are presented together with a theoretical model of its operation The apparatus has been used to measure the moment of inertia of the human body in a number of different positions using motion-analysis video equipment to measure the rotational speed of the turntable continuously