Specifity of Including of Structural Nonlinearity in Model of Dynamics of Cable-Driven Robot

The paper deals with a problem of modeling of the dynamics of a parallel cable-driven robot with the inclusion of structural nonlinearity of cables in a mathematical model. Mathematical model is implemented in a computer model with the possibility of using of symbolic calculations. Parallel cable robots as a type of robotics have been developing in the last two or three decades. The research in the theoretical field was being carried out and the mathematical model of the cable system was being refined with the spread of the practical use of cable robots. This is a non-trivial task to draw up a dynamic model of a cable-driven robot. Cable-driven robots are highly nonlinear systems, because of the main reason for the nonlinearity is the properties of the cable system. As an element of a mechanical system, the cable or the wire rope is a unilateral constraint, since the cable works only for stretching, but not for compression. Thus, the cables are structurally nonlinear elements of the system. On the other hand, cables have the property of sagging under their own weight. Thus, the cables are geometrically nonlinear elements of the system. Under the condition of a payload mass that is utterly greater than the mass of each cable, the cables can be considered strained without sagging and geometric nonlinearity can be neglected. Since symbolic computations can be used in a computer model which implements a mathematical model of the dynamics of a robot, in such a way it must provide the possibility of symbolic computations with the condition of structural nonlinearity. The main aim of this work is to develop a method that ensures the inclusion of the structural nonlinearity of the cable system in the mathematical model. It is supposed to consider the possibility of implementation of the computer model with symbolic computations. The problem of including a mathematical model of cables as unilateral constraints in the model of highly loaded cable robots is considered. The justification for including the activation functions in a system of differential equations of dynamics of cable-driven robot is formulated. A model of wire ropes as unilateral constraints is represented via including the activation functions in a system of differential equations. With using of the proposed method, numerical solution of a problem of forward dynamics has been obtained for high-loaded parallel cable-driven robot.

An investigation of the structural nonlinearity effects on the building seismic risk assessment under mainshock–aftershock sequences in Tehran metro city

This research attempts to investigate the effects of neglecting the nonlinear behavior of structures on the estimated seismic risk assessment of buildings under mainshock–aftershock (MA) sequences. In this regard, the Tehran metro city is selected as a building site due to its high seismicity level. Three separate 5-, 10-, and 15-story buildings are considered and designed based on international design codes. The earthquake hazard scenarios containing mainshock–aftershock sequences are modeled randomly using a synthetic stochastic methodology for this region. Next, by implementing the Monte Carlo simulation method, buildings performances are obtained for a large number of different scenarios, and consequently, the lifetime direct losses imposed on the buildings are evaluated. To investigate the effect of structural nonlinearity, the described process is performed in two distinct scenarios: one of them assumes that the buildings behave linearly, while the other one allows the structures to respond nonlinearly. Finally, the level of dependency of calculated lifetime seismic risk to this parameter and also the contribution of different sources of losses, including physical damage, business interruption, and casualty losses, are investigated considering the aftershocks effect.

Nonlinear vibration response of a complex aeroengine under the rubbing fault

Rolling bearing and squeeze film damper will introduce structural nonlinearity into the dynamic model of aeroengine. Rubbing will occur due to the clearance reduction design of the engine. The coupling of structural nonlinearity and fault nonlinearity will make the engine present rich vibration responses. This paper aims to analyze the nonlinear vibration behavior of the whole aeroengine including rolling bearing and squeeze film damper under rubbing fault. Firstly, the dynamic model of a turboshaft engine with nonlinear support and rubbing fault is established; The rolling bearing force, the oil film force and the rubbing force are introduced into a dual-rotor-casing model with six support points. Secondly, the linear part of the model is verified by the dynamic characteristics of the three-dimensional finite element model. Finally, the varying compliance vibration, the damping effect and the bifurcation mechanism are analyzed in detail in which the bearing clearance, speed ratio and rubbing stiffness are considered. Results show that the rubbing fault in the nonlinear support case will excite more significant varying compliance vibration in the low-speed region and expand the rotating speed range of the chaotic region in the high-speed region compared with that in the linear support case.

Curved Ballasted Track-Vehicle Dynamic Interaction: Effects of Curve Radius and Track Structural Nonlinearity

In this work, a model for characterizing the ballasted track-vehicle interaction is presented. The vehicle is modelled as a multi-rigid-body system consisting of a car body, two bogie frames and four wheelsets, and the track is modelled by finite elements including the rail, the sleeper and the track bed. All bodies are connected by spring-dashpot elements. With novelty, the geometric nonlinearity of curved rail beam and mechanical nonlinearity of ballasted bed lateral resistance have been fully considered. Besides, numerical solution procedures including iteration and increment have been also developed to accurately clarify the dynamic nonlinear performance of vehicle-track systems. Apart from model validations in statics and dynamics, the influence of track nonlinearity and curved track radius on vehicle-track dynamic performance has been revealed in detail.