Showing papers on "Rotary inertia published in 2012"

Nonlocal Timoshenko beam theory for vibration of carbon nanotube-based biosensor

Abstract: This article studies vibration of carbon nanotube (CNT)-based biosensor A CNT-based biosensor is modeled as a nonlocal Timoshenko beam made of multiwall CNT carrying a spherical nanoscale bio-object at the free end, and the influence of the rotary inertia of the bio-object itself is considered The fundamental frequencies are computed via the transfer function method The effects of the attached spherical bio-object's rotary inertia and mass, the length-to-diameter of the CNT on the natural frequencies are discussed If the nonlocal parameter is neglected, the frequencies for four possible cases are compared Obtained results show that the rotary inertia decreases the fundamental frequency, while an increase in the diameter of the attached bio-object reduces the natural frequency, but causes frequency shift to rise The mass sensitivity of biosensor can be improved for short CNTs used The rotary inertia of the attached bio-object has a strong effect on the natural frequencies and cannot be simply neglected The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short CNT biosensors Obtained results are helpful to the design of micro-cantilevered resonator as atomic-resolution mass sensor or biosensor

Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory

Abstract: This article deals with the small-scale effect on the nonlinear free vibration of orthotropic single-layered graphene sheets using the nonlocal elasticity plate theory. The formulations are based on the Mindlin plate theory, and von Karman-type nonlinearity is considered in strain displacement relations. Virtual work principle is used to derive the nonlinear nonlocal plate equations in which the effects of rotary inertia and transverse shear are included. The differential quadrature method is employed to reduce the governing nonlinear partial differential equations to a system of nonlinear algebraic eigenvalue equations. The efficiency and accuracy of the method are demonstrated by comparing the developed result with those available in literature. The methodology is capable of studying large-amplitude vibration characteristics of nanoplates with different sets of boundary conditions. The effects of various parameters on the nonlinear vibrations of nanoplates are presented.

Free vibration of tapered isotropic rectangular plates

Abstract: In this paper, free vibration analysis of isotropic rectangular plates with linearly varying thickness in one direction has been investigated using a high-order triangular element. The first order shear deformation theory is used to include the effect of transverse shear deformation. The element has 18 nodes on the sides and six internal nodes. The geometry of element is expressed by three linear shape functions of area coordinates. The formulation is displacement-based. The element has 51 degrees-of-freedom, which can be reduced to 39 degrees-of-freedom by Guyan reduction, mass condensation, or eigenvalue economization scheme for the degrees-of-freedom associated with the internal nodes. Rotary inertia has been included in the consistent mass matrix. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Isotropic plates with different thickness ratios (varies from 0.01 to 0.2), tapered ratios, aspect ratios and boundary conditions are analyzed. The results ...

Exact analytical solution for free vibration of functionally graded thin annular sector plates resting on elastic foundation

Abstract: This article introduces an exact analytical method for free vibration analysis of functionally graded (FG) thin annular sector plates resting on Winkler and Pasternak elastic foundations. The annular sector plate has simply supported radial edges and arbitrary boundary conditions along the circular edges. Based on the displacement field of Kirchhoff plate theory, the governing equations of motion are obtained considering the in-plane displacements and rotary inertia. Using a set of functions, the three coupled governing equations of motion are converted into two decoupled equations. By applying the boundary conditions at inner and outer radii, an eigenvalue problem for finding the natural frequencies is obtained. The nine distinct cases are considered involve all possible combinations of boundary conditions along the circular edges. Accurate non-dimensional frequency is presented for over a wide range of sector angles, some inner to outer radii (aspect ratio) and different powers of functionally graded ma...

Two-step in-orbit recognition rotary inertia estimation method for combined spacecraft

Abstract: The invention discloses a two-step in-orbit recognition rotary inertia estimation method for a combined spacecraft, and belongs to the technical field of navigation control for spacecrafts. The method includes the following steps: the normalization treatment for the rotary inertia of the spacecraft is performed through analyzing the satellite attitude kinetics equation and selecting the rotary inertia in a certain direction of the spacecraft as a criteria, so as to obtain a special rotary inertia ratio matrix of the spacecraft, a combined spacecraft attitude kinetics model, a system state equation and a measuring equation are established to obtain the system state quantity of the combined spacecraft, and the recognition for the rotary inertia ratio matrix of the combined spacecraft can be performed through the EKF filtering estimation; and a least square equation is built through the obtained rotary inertia ratio matrix and the controlling force exerted by the active spacecraft, and the selected the rotary inertia in a certain direction is estimated so as to finally realize the optimum estimation on the rotary inertia of the combined spacecraft. The method combines the EKF algorithm and the least squares algorithm, and has the advantages of high estimation accuracy, short recognition process time, less consumed fuel and strong engineering applicability.

Dynamics of a Delaminated Timoshenko Beam Subjected to a Moving Oscillatory Mass

Abstract: This paper presents dynamic response of a delaminated composite beam under the action of moving oscillatory mass. The Poisson's effect, shear deformation and rotary inertia have been considered in this analysis. We have used the constrained mode model to simulate the behavior between the delaminated surfaces. Based on this model, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes for the delaminated beam. Then, the forced response is determined by employing the modal series expansion technique. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literature. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the oscillator velocity, different ply configuration and the size, depth and spanwise location of the single delamination on the dynamic response of the beam are discussed in detail in the parametric study. Fu...

Method for automatically estimating inertia in a mechanical system

Abstract: Systems and methods for estimating an inertia and a friction coefficient for a controlled mechanical system are provided. In one or more embodiments, an inertia estimator can generate a torque command signal that varies continuously over time during a testing sequence. The velocity of a motion system in response to the time-varying torque command signal is measured and recorded during the testing sequence. The inertia estimator then estimates the inertia and/or the friction coefficient of the motion system based on the torque command data sent to the motion system and the measured velocity data. In some embodiments, the inertia estimator estimates the inertia and the friction coefficient based on integrals of the torque command data and the velocity data.

Vibration of Timoshenko beams using non-classical elasticity theories

Abstract: This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases.

Fluidic Electrodynamics: On parallels between electromagnetic and fluidic inertia

Abstract: The purpose of the present work is to trace parallels between the known inertia forces in fluid dynamics with the inertia forces in electromagnetism that are known to induce resistance forces on masses both due to acceleration and at constant velocity. It is shown that the force exerted on a particle by an ideal fluid produces two effects: i) resistance to acceleration and, ii) an increase of mass with velocity. These resistance forces arise due to the fluid dragged by the particle, where the bare mass of the particle at rest changes when in motion ("dressed" particle). It is demonstrated that the vector potential created by a charged particle in motion acts as an ideal space flow that surrounds the particle. The interaction between the particle and the entrained space flow gives rise to the observed properties of inertia and the relativistic increase of mass. Parallels are made between the inertia property of matter, electromagnetism and the hydrodynamic drag in potential flow. Accordingly, in this framework the non resistance of a particle in uniform motion through an ideal fluid (D'Alembert's paradox) corresponds to Newton's first law. The law of inertia suggests that the physical vacuum can be modeled as an ideal fluid, agreeing with the space-time ideal fluid approach from general relativity.

Frequency analysis of carbon-nanotube-based mass sensor using non-local Timoshenko beam theory

Abstract: The characteristic equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using non-local Timoshenko beam theory. The relationship between the resonant frequency of the sensor and the attached mass can be obtained from the equation. The result shows that the effects of shear deformation and rotary inertia on the frequency of the sensor obviously increase when the mode number increases and the attached mass is small relative to the sensor. When the value of aspect ratio of the sensor is small, the effects of shear deformation and rotary inertia on the frequency are large particularly at high-order modes. In addition, the variation of frequency shift with the attached mass on the sensor is compared with the previous studies when the non-local effect is not taken into account.

Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models

Abstract: The transverse vibration of a single-walled carbon nanotube (SWCNT) with light waviness along its axis is modeled by the nonlocal Euler-Bernoulli and Timoshenko beam theory. Unlike the Euler-Bernoulli beam model (EBM), the effects of transverse shear deformation and rotary inertia are considered within the framework of the Timoshenko beam model (TBM). The surrounding elastic medium is described as both Winkler-type and Pasternak-type foundation models. The governing equations are derived using Hamilton’s principle, and the Galerkin method is applied to solve these equations. According to this study, the results indicate that the frequency calculated by TBM is lower than that obtained by EBM. Detailed results show that the importance of transverse shear deformation and rotary inertia become more significant for stocky SWCNTs with clamped-clamped boundary conditions. Moreover, the influences of the amplitude of waviness, nonlocal parameter, medium constants, boundary conditions and aspect ratio are analyzed and discussed. It is shown that waviness in the curved SWCNT causes an obvious increase in the natural frequency in comparison with the straight SWCNT, especially for a compliant medium, pinned-pinned boundary condition, short SWCNT and large nonlocal coefficient.

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

Abstract: This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler–Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler–Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.

Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditions

Abstract: This paper investigates the large-amplitude free vibration of a double-walled carbon nanotube (DWCNT) surrounded by an elastic medium in the presence of temperature change. Based on continuum mechanics, a nonlocal elastic beam model is employed in which nanotubes are coupled together via the van der Waals (vdW) interlayer interactions. The Pasternak foundation model and a nonlinear vdW model are utilized to describe the surrounding elastic medium effect and the vdW interlayer interactions, respectively. DWCNTs with different boundary conditions are analyzed utilizing the Timoshenko beam theory that considers the shear deformation and rotary inertia effects. The governing equations are derived from Hamilton’s principle; the Galerkin method is utilized to discretize the governing equations. The influences of the nonlocal parameter, spring constant, carbon nanotube aspect ratio, and temperature change on the nonlinear free vibration characteristics of a double-walled carbon nanotube with different boundary conditions are thoroughly investigated. It is deduced that the nonlocal parameter, spring constant, and the aspect ratio play significant roles for the value of the nonlinear frequency. Also, the temperature change and the type of boundary conditions have an effect on the nonlinear frequency.

Frequency shift of a nanomechanical sensor carrying a nanoparticle using nonlocal Timoshenko beam theory

Abstract: The frequency shift of a nanomechanical sensor carrying a nanoparticle is studied. A bridged single-walled carbon nanotube (SWCNT) carrying a nanoparticle is modeled as a clamped micro-beam with a concentrated micro-mass at any position. Based on the nonlocal Timoshenko theory of beams, which incorporates size effects into the classical theory, the natural frequencies of the nanomechanical sensor are derived using the transfer function method. The effects of the mass and position of the nanoparticle on the frequency shift are discussed. In the absence of the nonlocal effect, the frequencies are reduced to the results of the classical model, in agreement with those using the finite element method. The obtained results show that when the mass of the attached nanoparticle increases or its location is close to the beam center, the natural frequency decreases, but the shift in frequency increases. The effect of the nonlocal parameter on the frequency shift is significant. Decreasing the length-to-diameter ratio also increases the frequency shift. The natural frequencies and shifts are strongly affected by rotary inertia, and the nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short nanomechanical sensors. The obtained results are helpful in the design of SWCNT-based resonator as nanomechanical mass sensor.

Flow-induced vibration and stability analysis of multi-wall carbon nanotubes

Abstract: The free vibration and flow-induced flutter instability of cantilever multi-wall carbon nanotubes conveying fluid are investigated and the nanotubes are modeled as thin-walled beams. The non-classical effects of the transverse shear, rotary inertia, warping inhibition, and van der Waals forces between two walls are incorporated into the structural model. The governing equations and associated boundary conditions are derived using Hamilton’s principle. A numerical analysis is carried out by using the extended Galerkin method, which enables us to obtain more accurate solutions compared to the conventional Galerkin method. Cantilevered carbon nanotubes are damped with decaying amplitude for a flow velocity below a certain critical value. However, beyond this critical flow velocity, flutter instability may occur. The variations in the critical flow velocity with respect to both the radius ratio and length of the carbon nanotubes are investigated and pertinent conclusions are outlined. The differences in the vibration and instability characteristics between the Timoshenko beam theory and Euler beam theory are revealed. A comparative analysis of the natural frequencies and flutter characteristics of MWCNTs and SWCNTs is also performed.

Dynamic analysis of shear deformable plates using the Dual Reciprocity Method

Abstract: The Dual Reciprocity Method is a popular mathematical technique to treat domain integrals in the boundary element method (BEM). This technique has been used to treat inertial integrals in the dynamic thin plate bending analysis using a direct formulation of the BEM based on the elastostatic fundamental solution of the problem. In this work, this approach was applied for the dynamic analysis of shear deformable plates based on the Reissner plate bending theory, considering the rotary inertia of the plate. Three kinds of problems: modal, harmonic and transient dynamic analysis, were analyzed. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation.

Feed-forward friction and inertia compensation for improving backdrivability of motors

Abstract: Backdrivability is an important property in applications like haptics, where force or torque is exerted by the user onto the motor. Gears cause higher friction, which results in a reduction of the backdrivability. This paper investigates how the backdriving torque can be reduced without the additional use of expensive force-torque sensors. The friction compensation uses a predetermined mapping, that adapts the motor's supporting torque depending on the measured velocity. The inertia compensation depends on the acceleration multiplied by the motor's moment of inertia. The method was objectively evaluated by using a robot. Kinetic friction compensation with inertia compensation significantly reduced the backdriving torque by 66.67 % over all median, and 23.58 % over all average values from measurements with different velocity and acceleration profiles. However, the variance and torque peaks were increased. The inertia compensation showed slight benefits in comparison to kinetic compensation alone, but not throughout all measurements.