Showing papers on "Rotary inertia published in 2013"

Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes

Abstract: The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

Stick–slip and slip–slip operation of piezoelectric inertia drives. Part I: Ideal excitation

Abstract: Piezoelectric inertia motors, also known as “stick–slip drives”, use the inertia of a body to drive it in small steps by means of a friction contact. While these steps are classically assumed to involve stiction and sliding, the motors can also operate in “slip–slip” mode without any phase of static friction. This contribution provides a systematic investigation and performance comparison of different stick–slip and slip–slip modes of operation. Different criteria for comparing the motional performance of inertia motors are defined: Steady state velocity, smoothness of motion, and start-up time. Using the example of a translational inertia motor excited by an ideal displacement signal, it is found that the maximum velocity reachable in stick–slip operation is limited principally, while continuous slip–slip operation allows very high velocities. For the investigated driving signals, the motor velocity is proportional to the square root of the actuator stroke. The motor performance with these ideal signals defines an upper boundary for the performance of real motors.

Axisymmetric nonlinear free vibration of size-dependent functionally graded annular microplates

Abstract: In this paper, a non-classical microplate model is developed for the axisymmetric nonlinear free vibration analysis of annular microplates made of functionally graded materials (FGMs) based on the modified couple stress theory, Mindlin plate theory and von Karman geometric nonlinearity. This non-classical model is capable of incorporating the microplate model with the length scale parameter, geometric nonlinearity, transverse shear deformation and rotary inertia. By using Hamilton's principle, the higher-order governing equations and boundary conditions for the problem are derived. The differential quadrature (DQ) method is employed to discretise the governing equations, which are then solved by a modified iterative method to obtain the nonlinear frequencies of FGM microplates with different boundary conditions. Numerical results are then presented in both tabular and graphical form to investigate the effects of the length scale parameter, gradient index, inner-to-outer radius ratio and radius-to-thickness ratio on the nonlinear free vibration characteristics of FGM microplates. It is found that unlike homogeneous microplates, the FGM microplates display different vibration behavior at positive and negative amplitudes due to the presence of bending-extension coupling.

Nonlinear dynamics of an axially moving Timoshenko beam with an internal resonance

Abstract: This paper investigates the nonlinear forced dynamics of an axially moving Timoshenko beam. Taking into account rotary inertia and shear deformation, the equations of motion are obtained through use of constitutive relations and Hamilton’s principle. The two coupled nonlinear partial differential equations are discretized into a set of nonlinear ordinary differential equations via Galerkin’s scheme. The set is solved by means of the pseudo-arclength continuation technique and direct time integration. Specifically, the frequency-response curves of the system in the subcritical regime are obtained via the pseudo-arclength continuation technique; the bifurcation diagrams of Poincare maps are obtained by means of direct time integration of the discretized equations. The resonant response is examined, for the cases when the system possesses a three-to-one internal resonance and when not. Results are shown through time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The results indicate that the system displays a wide variety of rich dynamics.

Free vibration of axial-loaded multi-step Timoshenko beam carrying arbitrary concentrated elements using continuous-mass transfer matrix method

Abstract: The continuous-mass transfer matrix method (CTMM) is one of the few practical approaches to yield the “exact” solutions for free vibrations of a non-uniform beam carrying any number of concentrated elements. However, most of the existing CTMM does not consider the effects of shear deformation (SD), rotary inertia (RI), joint action term of SD and RI, and axial load. Thus, the objective of this paper is to present a simple formulation so that one can easily obtain the “exact“ natural frequencies and the associated mode shapes of a multi-step beam carrying arbitrary various concentrated elements (including eccentric lumped masses with rotary inertias, linear springs, rotational springs and spring-mass systems) in various boundary conditions with all the above-mentioned effects considered by using the modified CTMM. In addition to comparing with the existing relevant data, most of the numerical results obtained from the modified CTMM are also compared with those of the conventional finite element method (FEM) and good agreements are achieved.

Robot control method, robot control device, and robot control system

Abstract: A CPU of a robot control device calculates load torque based on the inertia force, centrifugal force or Coriolis force, gravity force, friction torque, and actuator inertia torque applied to a joint axis of each link, each time an orientation parameter indicative of the link position and orientation allowed by a redundant degree of freedom is sequentially changed, under a constraint of end-effector position and orientation as target values. The CPU obtains the link position and orientation at which the ratio of the load torque to the rated torque of a rotary actuator provided for each joint is minimized, while the orientation parameter is being changed, and provides a feed-forward value that gives rise to each load torque obtained when the ratio of the load torque to the rated torque of the rotary actuator is minimized, to a control command generated to the rotary actuator of each joint axis for achieving the end-effector position and orientation as target values.

Vibration analysis of embedded nanotubes using nonlocal continuum theory

Abstract: Vibration of nanotubes embedded in an elastic matrix is investigated by using the nonlocal Timoshenko beam model. Both a stress gradient and a strain gradient approach are considered. The Hamilton’s principle is adopted to obtain the frequencies of the nanotubes. The dependencies of frequency on the stiffness and mass density of the surrounding elastic matrix, the nonlocal parameter, the transverse shear stiffness and the rotary inertia of the nanotubes are obtained. The results show a significant dependence of frequencies on the surrounding medium and the nonlocal parameter. The frequencies are over-predicted by using the Euler beam model that neglects the shear stiffness and rotary inertia of the nanotubes. It is also found that the lower bound and the upper bound for the frequencies of nanotubes are, respectively, provided by the strain gradient model provides and the stress gradient theory. Explicit formulas for the frequency are obtained and therefore are easy to use by material scientists and engineers for the design of nanotubes and nanotubes based composites.

Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory

Abstract: Nonlinear free vibration and instability of fluid-conveying double-walled boron nitride nanotubes (DWBNNTs) embedded in viscoelastic medium are studied in this paper. The effects of the transverse shear deformation and rotary inertia are considered by utilizing the Timoshenko beam theory. The size effect is applied by the modified couple stress theory and considering a material length scale parameter for beam model. The nonlinear effect is considered by the Von Karman type geometric nonlinearity. The electromechanical coupling and charge equation are employed to consider the piezoelectric effect. The surrounding viscoelastic medium is described as the linear visco-Pasternak foundation model characterized by the spring and damper. Hamilton’s principle is used to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is employed to discretize the nonlinear higher-order governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequency and critical fluid velocity of fluid-conveying DWBNNTs with clamped-clamped (C-C) boundary conditions. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, spring and damping constants of surrounding viscoelastic medium and fluid velocity on the nonlinear free vibration, instability and electric potential distribution of DWBNNTs. This study might be useful for the design and smart control of nano devices.

Semi-analytical solution for the free vibration analysis of generally laminated composite Timoshenko beams with single delamination

Abstract: A rather new semi-analytical method towards investigating the free vibration analysis of generally laminated composite beam (LCB) with a delamination is presented. For the first time the combined effects of material couplings (bending–tension, bending–twist, and tension–twist couplings) with the effects of shear deformation, rotary inertia and Poisson’s effect are taken into account. The semi-analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the method of Lagrange multipliers. To verify the validity and the accuracy of the obtained results, they were compared with the results from other available references. Very good agreements were observed. Furthermore, the effects of some parameters such as slenderness ratio, the rotary inertia, the shear deformation, material anisotropy, ply configuration, and delamination parameters on the dynamic response of the delaminated beam are examined.

Inertia from an asymmetric Casimir effect

Abstract: The property of inertia has never been fully explained. A model for inertia (MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is due to Unruh radiation and 2) this radiation is subject to a Hubble-scale Casimir effect. This model has no adjustable parameters and predicts the cosmic acceleration, and galaxy rotation without dark matter, suggesting that Unruh radiation indeed causes inertia, but the exact mechanism by which it does this has not been specified. The mechanism suggested here is that when an object accelerates, for example to the right, a dynamical (Rindler) event horizon forms to its left, reducing the Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces an imbalance in the radiation pressure on the object, and a net force that always opposes acceleration, like inertia. A formula for inertia is derived, and an experimental test is suggested.

Investigation of the dynamic characteristics of a dual rotor system and its start-up simulation based on finite element method

Abstract: Recently, the finite element method (FEM) has been commonly applied in the engineering analysis of rotor dynamics. Gyroscopic moments, rotary inertia, transverse shear deformation and gravity can be included in computational models of rotor-bearing systems. In this paper, a finite element model and its solution method are presented for the calculation of the dynamics of dual rotor systems. A typical structure with two rotor shafts is discussed and the procedure for obtaining the coupling motion equations of the subsystems is illustrated. A computer program is developed to solve critical speeds and to simulate the transient motion. The influence of gyroscopic moments on co-rotation and counter-rotation is analyzed, and the effect of the speed ratio on critical speed is studied. The dynamic characteristics under different conditions of increasing speed during start-up are demonstrated by comparison with transient nodal displacements. The presented model provides a complete foundation for further investigation of the dynamics of dual rotor systems.

Free vibration analysis of laminated composite plates with elastically restrained edges using FEM

Abstract: The application of FEM is shown for free vibration analysis of moderately thick laminated composite plates with edges elastically restrained against translation and rotation. The governing equations employed are based on the first order shear deformation theory including the effects of rotary inertia. Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Angle-ply and cross-ply laminates with different thickness-to-length ratios are examined. Comparisons are made with results for thin as well as moderately thick laminated plates.