Transient analysis of flexible multi-body systems. Part I: Dynamics of flexible bodies

The formulation for the dynamic analysis of undamped linear structural systems using the finite element method results in two element matrices; the mass and stiffness matrices, that describe the element inertia and stiffness properties. However, these matrices are not sufficient to describe the dynamics of structures that undergo large rigid-body motion. Other element matrices, in addition to the mass and stiffness matrices, are required to account for the inertia coupling between gross motion and elastic deformation. These matrices are time-invariant and can be generated and assembled in the same manner as the mass and stiffness matrices are assembled in linear structural dynamics. An inherent relation between these matrices and the deformable body mean axes exists. This paper is the first of two parts. It presents the two-dimensional and three-dimensional formulation of the system equations of motion of inertia-variant flexible bodies. In particular, Euler parameters are employed to describe the rotations of the body reference in the spatial analysis. In Part II [13], this formulation is applied to the impact analysis of a large-scale constrained flexible aircraft which are modeled as a multi-body system consisting of interconnected rigid and flexible components.     

Hybrid control of flexible multi-body systems

In constrained systems of rigid and flexible bodies, the gross rigid body motion and elastic deformation cannot be controlled independently because of the coupling between these two motions. A hybrid control method for suppressing the vibration of a geometrically nonlinear flexible multi-body system is proposed in this paper. This method utilizes both the passive and active control concepts. In the passive control strategy, flexible components in the system are manufactured from fiber-reinforced composite laminates which have high strength-to-weight and stiffness-to-weight ratios. On the other hand, the active control scheme used in this paper utilizes measurable velocity and acceleration signals to produce the command signals required to activate the actuator forces. A small number of sensors and controllers with constant gain factors are used in order to obtain a low-cost and simple control system. The generalized active control forces associated with the system generalized coordinates are developed using the virtual work and are written in terms of the coupled set of reference and elastic coordinates. The system differential equations of motion are developed using Lagrange's equation and the Jacobian matrix of the nonlinear algebraic constraint equations describing mechanical joints in the system is used to identify a set of independent generalized coordinates. The associated independent differential equations are identified and are written in the state space formulation. The characteristics of the proposed hybrid control are evaluated through computer simulations of a seven-body flexible vehicle. The performance characteristics of the hybrid control are also compared to the performance characteristics of the passive and active controls.     

Dynamic analysis of flexible multi-body systems using mixed modal and tangent coordinates

This paper presents a mixed modal and tangent coordinate technique for computer aided analysis of flexible mechanical systems whose components undergo large translations and large rotations. In this model the configuration of a flexible component is identified by using two sets of generalized coordinates, namely rigid body and elastic coordinates. The rigid body coordinates define the location and orientation of a body axis, whereas the elastic coordinates define the displacement field of a component with respect to its body axis. The elastic coordinates are introduced by using finite element discretization to model flexible components with complex geometries. A modal analysis technique is used to identify the elastic mode shapes and to eliminate insignificant higher frequency modes. An orthonormalization of constraint Jacobian matrix associated with rigid body coordinates is used to identify the rigid body tangent coordinates. The resulting modal and tangent coordinates are used to develop an automated numerical integration scheme to solve the system differential and algebraic equations. Two numerical examples are considered to show the feasibility of dynamic analysis of flexible mechanical systems using this scheme.     

Structural load alleviation using distributed delay shaper: Application to flexible aircraft

Lightweight flexible aircraft suffers from unwanted oscillatory vibrations during aircraft manoeuvres. A recently developed distributed-delay signal (DZV) shaper is therefore proposed to be applied as a feedforward controller to alleviate the manoeuvre loads, as an alternative to traditional structural filters used routinely in this context. Structural filters are essentially linear low-pass filters with bandwidth below the significant flexible modes, applied to control signals generated either by the pilot’s direct input or by the flight control system. It has been showed that if instead a properly tuned signal shaper is used, better performance can be achieved: first, the target modes are significantly attenuated while the responsiveness of the aircraft is less compromised and secondly, the oscillatory nature of the vibrations are reduced. The high fidelity simulation results on a full scaled dynamic model of a highly flexible blended wing–body (BWB) aircraft show that in comparison to traditional structural filters, signal shapers significantly reduce the wing root loading (forces and moments) which provides potential structural benefits.     

Global/local analysis of composite light aircraft crash landing

The objective of this paper is to present the implementation of so-called global/local approach to crash landing analysis of the light composite aircraft. The analyses and experimental verifications have been performed for PZL I-23 aircraft, designed jointly by Institute of Aviation and PZL Swidnik aircraft factory. Some criteria for designing the light composite aircraft, according to the “safe-crash” rule have been formulated.     

Application of generalised neural network for aircraft landing control system

 It is observed that landing performance is the most typical phase of an aircraft performance. During landing operation the stability and controllability are the major considerations. To achieve a safe landing, an aircraft has to be controlled in such a way that its wheels touch the ground comfortably and gently within the paved surface of the runway. The conventional control theory found very successful in solving well defined problems, which are described precisely with definite and clearly mentioned boundaries. In real life systems the boundaries can't be defined clearly and conventional controller does not give satisfactory results. Whenever, an aircraft deviates from its glide path (gliding angle) during landing operation, it will affect the landing field, landing area as well as touch down point on the runway. To control correct gliding angle (glide path) of an aircraft while landing, various traditional controllers like PID controller or state space controller as well as maneuvering of pilots are used, but due to the presence of non-linearities of actuators and pilots these controllers do not give satisfactory results. Since artificial neural network can be used as an intelligent control technique and are able to control the correct gliding angle i.e. correct gliding path of an aircraft while landing through learning which can easily accommodate the aforesaid non-linearities. The existing neural network has various drawbacks such as large training time, large number of neurons and hidden layers required to deal with complex problems. To overcome these drawbacks and develop a non-linear controller for aircraft landing system a generalized neural network has been developed.     

舰载机前起落架突伸的动力学响应分析

为研究舰载机前轮拖拽弹射起飞技术,基于多体系统动力学理论,建立模拟舰载机前起落架突伸的4自由度多体动力学模型,推导出系统的动力学微分方程.利用该模型,用数值方法仿真舰载机前起落架的突伸运动,得出突伸过程中舰载机的重心位置、俯仰角和前起落架空气弹簧力等参数的动态响应特性.仿真结果可为舰载机及其起落架设计提供参考.     

Substructure synthesis methods for dynamic analysis of multi-body systems

The formulation for the dynamic analysis of flexible multi-body systems that undergo large rigid body motion, leads to geometrically non-linear inertia properties due to large rotations. These inertia non-linearities that represent the coupling between gross rigid body motion and small elastic deformation, are dependent on the assumed displacement field. As alternatives to the finite element methods, deformable body shape functions and shape vectors are commonly employed to describe elastic deformation of linear structures. In this paper, substructure shape functions and shape vectors are used to describe elastic deformation of non-linear inertia-variant multi-body systems. This leads to two different representations of inertia nonlinearities; one is based on a consistent mass formulation, while the other is a lumped mass technique. The multi-body systems considered are collections of interconnected rigid and flexible bodies. Open and closed loop systems are permitted.     

Transformational design of real-time systems. Part II: From program specifications to programs

In the two parts of this article we present a transformational approach to the design of real-time systems. The overall starting point are requirements formulated in a subset of Duration Calculus called implementables and the target are programs in an OCCAM dialect PL. In the first part we have shown how the level of program specifications represented by a language SL can be reached. SL combines regular expressions with action systems and time conditions. In this part we show the transformation from SL to PL. It relies on the ‘Expansion strategy’ by which certain transformations can be applied in an almost automatic fashion. In many places transformations consist of algebraic reasoning by laws for operations on programs. Both parts of our transformational calculus rely on the mixed term techniques in which syntax pieces of two languages are mixed in a semantically coherent manner. In the first part of the article mixed terms between implementables and SL have been used, in the present part mixed terms between SL and PL are used. The approach is illustrated by the example of a computer controlled gas burner from part I again. Received 23 July 1996 / 13 February 1998     

Modeling multibody systems with uncertainties. Part II: Numerical applications

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects”.In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set.The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties.     

Continuous/discrete modeling and analysis of elastic planar multi-body systems

The modeling and analysis of continuous/discrete multi-body systems are described, with emphasis on applications to elastic planar closed-loop systems. Whereas the continuous formulations presented can be applied to simplified models (with less effort) to help isolate the dominant factors for parametric evaluations in preliminary analysis studies, on the other hand, the finite element formulations described are, in general, applicable for more complex geometries and larger problems. In this regard, an explicit self-starting velocity-based time integration architecture is employed for the numerical simulation of multi-body dynamics with several inherent attractive features. Numerical test cases for planar multi-body dynamic situations employing the Timoshenko beam theory are presented from a generalized viewpoint in conjunction with the present formulations to validate the applicability of the proposed formulations.     

Algorithmic analysis of polygonal hybrid systems,Part II: Phase portrait and tools

Polygonal differential inclusion systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. The reachability problem as well as the computation of certain objects of the phase portrait is decidable. In this paper we show how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs. We also present the tool SPeeDI⁺, which implements a reachability algorithm and computes phase portraits of SPDIs.     

An introduction to distribution theory for signals analysis.: Part II. The convolution

This article continues the exposition in Part I [D.C. Smith, An introduction to distribution theory for signals analysis, Digital Signal Process. 13 (2003) 201–232] of certain key concepts from distribution theory which are essential for understanding signal theory. In this second part, we demonstrate the power of distribution theory by focusing on distributional convolution and some of its applications to signals analysis. The well-known classical convolution theorem (CCT) states that the Fourier transform of a convolution of integrable functions is the product of their Fourier transforms, and is essential in signals processing, by providing a method for removing noise and undesirable spectral artifacts from signals. Unfortunately, signal processing texts routinely apply this theorem nonrigorously, with questionable results, e.g., in attempts to apply it to singular functions in derivations of the Hilbert conjugate and the analytic signal, in attempts to recover an unknown causal impulse response modeling a data channel, and in derivations of the Sampling Theorem [D.C. Smith, An introduction to distribution theory for signals analysis, Digital Signal Process. 13 (2003) 201–232]. Fortunately, many inadequacies of the CCT are overcome by its generalizations to the tempered distributions. In this article we discuss three distributional convolution theorems (DCTs), each of which has important theoretical and practical consequences for signal theory. We demonstrate that when the Cauchy principal value distribution is used to properly define the Hilbert conjugate, the first DCT may be applied to rigorously derive the analytic signal. The second DCT is particularly useful for applications involving compactly supported distributions, including the Dirac delta. The third DCT concerns the lesser-known distributional Laplace transform, which is shown by example to be superior to either the classical or distributional Fourier transform for recovering an unknown impulse response modeling a causal linear time-invariant system. This article upholds the style of Part I, by avoiding unnecessary abstraction and supplying very detailed proofs in hopes of appealing to a wider audience.     

Developmental systems with finite axiom sets Part II. systems with interactions

In this paper the notion of a developmental system with interactions is generalized to include a finite number of (rather than one) axioms. It is shown that whereas this generalization considerably enlarges the class of languages generated, the main properties of the larger class of languages are basically the same as those of the smaller class     

Information systems support for healthcare quality: Part II

In the second and final part of his series of quality management, healthcare information systems consultant Peter Spitzer, M.D., describes how I/S can support quality healthcare services by improving the care-delivery process and by providing the data needed for quality support, monitoring and management.     

Reanalysis-based fast solution algorithm for flexible multi-body system dynamic analysis with floating frame of reference formulation

Multibody System Dynamics - In order to improve the computational efficiency of flexible multi-body system dynamic analysis with floating frame of reference formulation (FFRF), a reanalysis-based...