Yeping Xiong

A general linear mathematical model of power flow analysis and control for integrated structure-control systems

Abstract Generalized integrated structure–control dynamical systems consisting of any number of active/passive controllers and three-dimensional rigid/flexible substructures are investigated. The developed mathematical model assessing the behaviour of these complex systems includes description of general boundary conditions, the interaction mechanisms between structures, power flows and control characteristics. Three active control strategies are examined. That is, multiple channel absolute/relative velocity feedback controllers, their hybrid combination and an existing passive control system to which the former control systems are attached in order to improve overall control efficiency. From the viewpoint of continuum mechanics, an analytical solution of this generalized structure–control system has been developed allowing predictions of the dynamic responses at any point on or in substructures of the coupled system. Absolute or relative dynamic response or receptance, transmissibility, mobility, transfer functions have been derived to evaluate complex dynamic interaction mechanisms through various transmission paths. The instantaneous and time-averaged power flow of energy input, transmission and dissipation or absorption within and between the source substructure, control subsystems and controlled substructure are presented. The general theory developed provides an integrated framework to solve various vibration isolation and control problems and provides a basis to develop a general algorithm that may allow the user to build arbitrarily complex linear control models using simple commands and inputs. The proposed approach is applied to a practical example to illustrate and validate the mathematical model as well as to assess control effectiveness and to provide important guidelines to assist vibration control designers.

A power flow mode theory based on a system's damping distribution and power flow design approaches

A power flow mode theory is developed to describe the natural power flow behaviour of a dynamic system based on its inherent damping distribution. The systems characteristic-damping matrix is constructed and it is shown that the eigenvalues and eigenvectors of this matrix identify natural power flow characteristics. These eigenvectors, or power flow mode vectors, are chosen as a set of base-vectors spanning the power flow space and completely describe the power flow in the system. The generalized coordinate of the velocity vector decomposed in this space defines the power flow response vector. A time-averaged power flow expression and theorems relating to its estimation are presented. Based on this theory, power flow design approaches are proposed to identify energy flow patterns satisfying vibration control requirements. The mode control factor defines the measure of the correlation between a power flow mode and a natural vibration mode of the system. Power flow design theorems are presented providing guidelines to construct damping distributions maximizing power dissipation or to suppress/retain a particular vibration mode and/or a motion. The developed damping-based power flow mode theory is compared with a mobility-based power flow model. It is shown that the proposed power flow model provides insight into the power flow dissipation mechanisms in dynamic systems. Examples are presented to demonstrate the applicability of the power flow mode theory and the power flow design approach. These examples demonstrate the generality of the theory, including non-symmetric damping matrices, and illustrate power flow design applications through modifications of the systems damping distribution using passive and/or active control components.

Hybrid active and passive control of vibratory power flow in flexible isolation system

A hybrid active and passive vibration control strategy is developed to reduce the total power flows from machines, subject to multiple excitations, to supporting flexible structures. The dynamic interactions between machines, controllers, and receiving structures are studied. A force feedback control process governed by a proportional control law is adopted to produce active control forces to cancel the transmitted forces in the mounts. Computational simulations of a simple and a multiple dimensional hybrid vibration isolation system are performed to study the force transmissibility and the total power flows from vibration sources through active and passive isolators to the supporting structures. The investigation focuses on the effects of a hybrid control approach to the reduction of power flow transmissions and the influence of the dynamic characteristics of the control on power flow spectra. The hybrid control mechanism is synthesised from the power flow analysis. Conclusions and control strategies, well supported by numerical simulations, are deduced providing very useful guidelines for hybrid vibration isolation design.

Vibration Characteristics of Sandwich Beams with Steel Skins and Magnetorheological Elastomer Cores

Magnetorheological elastomer (MRE) cored sandwich beams with steel skins offer potentially advantageous features when used in the context of structural dynamics. Modelling of the dynamic behaviour is undertaken in this investigation by adopting a higher order sandwich beam theory. Frequency responses from the theoretical modelling are compared with experimental results on MRE cored sandwich beams. The experimental responses are generated from a specially designed test rig to study dynamic behaviour, damping effects, localised magnetic field effects and energy dissipation with varying topology. A numerically based parametric study is conducted to find the optimum geometry for skins and core material to enhance damping performance. Under the same magnetic field strength, sandwich beams with thinner skins and thicker MRE core dissapate more vibration energy. Correlation between the experimental results and numerical studies has been found to be reasonably good.

Nonlinear dynamic behaviors of rotated blades with small breathing cracks based on vibration power flow analysis

Rotated blades are key mechanical components in turbomachinery and high cycle fatigues often induce blade cracks. Accurate detection of small cracks in rotated blades is very significant for safety, reliability, and availability. In nature, a breathing crack model is fit for a small crack in a rotated blade rather than other models. However, traditional vibration displacements-based methods are less sensitive to nonlinear characteristics due to small breathing cracks. In order to solve this problem, vibration power flow analysis (VPFA) is proposed to analyze nonlinear dynamic behaviors of rotated blades with small breathing cracks in this paper. Firstly, local flexibility due to a crack is derived and then time-varying dynamic model of the rotated blade with a small breathing crack is built. Based on it, the corresponding vibration power flow model is presented. Finally, VPFA-based numerical simulations are done to validate nonlinear behaviors of the cracked blade. The results demonstrate that nonlinear behaviors of a crack can be enhanced by power flow analysis and VPFA is more sensitive to a small breathing crack than displacements-based vibration analysis. Bifurcations will occur due to breathing cracks and subharmonic resonance factors can be defined to identify breathing cracks. Thus the proposed method can provide a promising way for detecting and predicting small breathing cracks in rotated blades.

System-Level Coupled Modeling of Piezoelectric Vibration Energy Harvesting Systems by Joint Finite Element and Circuit Analysis

A practical piezoelectric vibration energy harvesting (PVEH) system is usually composed of two coupled parts: a harvesting structure and an interface circuit. Thus, it is much necessary to build system-level coupled models for analyzing PVEH systems, so that the whole PVEH system can be optimized to obtain a high overall efficiency. In this paper, two classes of coupled models are proposed by joint finite element and circuit analysis. The first one is to integrate the equivalent circuit model of the harvesting structure with the interface circuit and the second one is to integrate the equivalent electrical impedance of the interface circuit into the finite element model of the harvesting structure. Then equivalent circuit model parameters of the harvesting structure are estimated by finite element analysis and the equivalent electrical impedance of the interface circuit is derived by circuit analysis. In the end, simulations are done to validate and compare the proposed two classes of system-level coupled models. The results demonstrate that harvested powers from the two classes of coupled models approximate to theoretic values. Thus, the proposed coupled models can be used for system-level optimizations in engineering applications.

Melnikov-method-based broadband mechanism and necessary conditions of nonlinear rotating energy harvesting using piezoelectric beam

Nonlinearity can be used to enhance broadband rotating piezoelectric vibration energy harvesting, but how to construct a proper nonlinear rotating harvester is a challenging problem in engineering applications. This article presents a Melnikov-theory-based method to explore broadband mechanism and necessary conditions of nonlinear rotating piezoelectric vibration energy harvesting system. First, a perturbed state-space representation of nonlinear rotating energy harvesting system is built based on its dynamic model. It can be seen that bi-stability of the unperturbed nonlinear system is the physical basis of achieving broadband and low-frequency rotating energy harvesting. Second, the Melnikov function is defined to derive two necessary conditions of homoclinic bifurcation and chaotic motions. Then simulations are performed to identify the key parameters and their effects on the Melnikov conditions, including distance, rotating frequency, and excitations. It can be seen that homoclinic bifurcation and chaotic motions can occur in nonlinear rotating energy harvesting systems under single-frequency and broadband excitations. Finally, the experiments are carried out to validate the two necessary conditions. The results demonstrate that the proposed method can provide important guidelines for optimally designing nonlinear rotating piezoelectric energy harvesters in practice.

Investigations on a Nonlinear Energy Harvesting System Consisting of a Flapping Foil and an Electro-Magnetic Generator Using Power Flow Analysis

A nonlinear energy harvesting system consisting of a flapping foil and an electro-magnetic generator excited by incompressible quasi-steady air flows is investigated. Due to stiffness nonlinearities in pitch and/or heave degrees of freedom, the system behaves a stable limit cycle oscillation when flow velocity exceeds the critical flutter speed, so that the mechanical energy imported from air flow is converted into electricity by the coupled electro-magnetic generator. The power flow equations and variables, including the input, dissipated, transmitted and harnessed powers, of the system are formulated. A fourth-order Runge-Kutta method is used to obtain the system’s dynamical response as well as power flow variables. It shows that increasing the nonlinear stiffness in heave motion or decreasing in pitch motion benefits power generation. The research demonstrates the capability of this nonlinear system to harvest natural energy without extra operation cost. Discussions and planed further research works are given for engineering applications

Power flow response based dynamic topology optimization of bi-material plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

Weld root magnification factors for semi-elliptical cracks in T-butt joints

Many researchers have focused their efforts on fatigue failures occurring on weld toes. In recent years, more and more fatigue failures occur on weld roots. Therefore, it is important to explore the behaviour of weld root fatigues. This paper investigates numerically the Magnification factors (Mk) for types of semi-elliptical cracks on the weld root of a T-butt joint. The geometry of the joint is determined by four important parameters: crack depth ratio, crack shape ratio, weld leg ratio and weld angle. A singular element approach is used to generate the corresponding finite element meshes. For each set of given four parameters of the semi-elliptical root crack, the corresponding T-butt joint is numerically simulated and its Mk at the deepest point of the weld root crack is obtained for the respective tension and shear loads. The variation range of the four parameters covers 750 cases for each load, totaling 1500 simulations are completed. The numerical results obtained are then represented by the curve to explore the effects of four parameters on the Mk. To obtain an approximate equation representing Mk as a function of the four parameters for each load, a multiple regression method is adopted and the related regression analysis is performed. The error distributions of the two approximate equations are compared with the finite element data. It is confirmed that the obtained approximate functions fit very well to the database from which they are derived. Therefore, these two equations present a valuable reference for engineering applications in T-butt joint designs.