A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Position Domain PD Control for Contour Tracking

For multi-axis motion control applications, contour tracking is one of the most common control problems encountered by industrial manipulators and robots. In this paper, a position domain PD control method is proposed for the purpose of improving the contour tracking performance. To develop the new control method, the multi-axis motion system is viewed as a master-slave motion system where the master motion is sampled equidistantly and used as an independent variable, while the slave motions are described as functions of the master motion according to the contour tracking requirements. The dynamic model of the multi-axis motion system is developed in the position domain based on the master motion by transforming the original system dynamic equations from the time domain to the position domain. In this control methodology, the master motion will yield zero tracking error for the position as it is used as reference, and only the slave motion tracking errors will affect the final contour tracking errors. The proposed position domain PD controller is successfully examined in a Cartesian robotic system for linear motion tracking and circular contour tracking.

Active Vibration Control for Milling Processes

In this paper, a study on the active control of vibration for peripheral milling is presented. Different from the control for the vibrations of cutting tool or workpiece, in this effort, the relative vibration between the workpiece and tool is selected as the control target. To reduce the relative vibration, a two-axis active work-holding stage, which is droved by two piezo-actuators, is designed and the control system synthesis method is used to determine the control gain. By this method, the dynamical stage is considered as plant while the complicated cutting process is treated as disturbance. The cutting vibration control can be considered as a robust disturbance rejection problem (RDRP), and the controller design is based on robust servo-mechanism method. Without the requirement on the model of disturbance, this method simplifies the vibration control problem and only the knowledge of frequencies of disturbance is required. Numerical results indicate the implemented system works well in cutting vibration cancellation.

Sensorless Simultaneous Rotary-Translational Axis Motion Error Measurement and Trace Based on Virtual Bar

Simultaneous rotary-translational (R-T) axis motion error has significant influence on multi-axis machine tool precision. To improve multi-axis machine tool precision, axis motion error measurement and trace method are investigated in this study. A sensorless R-T axis motion error measurement and trace technology based on virtual bar is proposed. Firstly, the fundamental sensorless test principle is discussed. Then, the virtual-bar-based test path of a circular test though a rotary axis and two translational axes motion is scheduled. The mathematical model of motion error is established. Furthermore, to identify the error source, spatial error charts and some advanced signal processing and feature extraction technologies, such as wavelet transform and frequency analysis, are used. The analysis of experimental results shows that it is practical and efficient to use the virtual bar and the sensorless information to estimate motion error.

Air Hybrid Engine Torque Control Using Adaptive Sliding Mode Control

In this work, a new air hybrid engine configuration is introduced in which two throttles are used to manage the engine load in three modes of operation i.e. braking, air motor, and conventional mode. A Mean Value Model (MVM) of the engine is developed at braking mode and a new Adaptive Sliding Mode Controller (ASMC), recently proposed in the literature, is applied to control the engine torque at this mode. The results show that the controller performs remarkably well in terms of the robustness, tracking error convergence and disturbance attenuation. Chattering effect is also removed by utilizing the ASMC scheme.

Configuration Optimization of a Boat Simulation Platform for a Mobile User

Motion simulation platforms are mechanical devices designed to replicate the dynamics of a given vehicle. These devices are very attractive for training individuals as drivers, pilots or passengers. In the case of river boats, the simulator consists of a section of the boat (hull) mounted over a 3 DOF parallel robot with a passive mass compensator (3UPS + PU). If users have mobility in the hull, an uncertainty in the position of the upper platform’s center of mass is produced. This variation may generate excessive loads on the robot that can be prevented by an adequate placement of the hull over the robot. Dynamic calculations, based on measurements of the real boat in motion, are computed by numerical simulations in SimMechanics. Three methodologies are presented for optimizing the configuration of a boat simulation platform. First, a manual procedure is developed in which critical cases are intuitively detected and evaluated. Then, two multi-variable optimization algorithms are used to systematically obtain the best position and orientation (pose) of the boat section: Genetic Algorithms and low discrepancy sequences. The pose is the design variable; the average forces are the objective functions and the maximum difference between the average forces is the fitness function. The article describes the design problem, the proposed optimization methodologies and simulation results for the optimal configuration.

Dynamic Mechanism of a Train Suspension System

Nonlinear dynamical behaviors of a train suspension system with impacts are investigated. The suspension system is modelled through an impact model with possible stick between a bolster and two wedges. Based on the mapping structures, periodic motions of such a system are described. To understand the global dynamical behaviors of the train suspension system, system parameter maps are developed. Numerical simulations for periodic and chaotic motions are performed from the parameter maps.

Distributed and Centralized H∞ Control of Large Segmented Telescopes

Next generation telescopes are to employ segmented mirrors to realize extremely large primary mirror surfaces. Most of the current ground-based telescopes has monolithic mirrors with radius upto 8 metres. Due to limitations segmentation is preferred for larger size mirrors. Segmentation of mirrors brings a challenging task of controlling the vast number of individual units. In this paper, the H∞ control of the primary mirror of the next generation telescopes are investigated. Both spatially-invariant distributed and centralized controllers are designed for simplified dynamic model of a 37 segment test unit. Firstly, the 37 segment system is modelled by adopting a nodal model. Secondly, an analytic calculation of a H∞ controller is presented. A centralized H∞ controller is, then, designed and simulated in MatLab-Simulink environment. Next, the simulation results are presented and the performance of the controller is evaluated. Thirdly, spatially-invariant distributed controller synthesis is described and a spatially-invariant distributed controller is designed for 37 segment system by controller truncation. The spatially-invariant distributed controller is simulated for the 37 segment system. The simulation results of the controller is presented and compared with the results from centralized scheme. It is shown that both centralized and spatially-invariant distributed controllers satisfy the imaging performance requirements.