Heinz Köppe

Accurate Modeling of the Electric Field within Piezoelectric Layers for Active Composite Structures

The article considers thin-walled active structures, which utilize the piezoelectric patches as both sensor and actuator components. Most of the developed models for this type of application make an assumption of a constant electric field and, consequently, a linear distribution of the electric potential over the thickness of the piezopatches. Some recent papers use higher-order functions to model the mentioned electric quantities. In the study, it is demonstrated through an analytical deduction that a quadratic distribution of the electric potential and a linear distribution of the electric field are adequate for the piezoelectric patch that exhibits kinematics described by a first-order two-dimensional theory. A degenerated shell element is developed for modeling purposes and a set of numerical analyses is performed in order to demonstrate the additional stiffening effect caused by the refined functions for the electric quantities. The significance of the effect is discussed in detail.

Numerically Efficient Finite Element Formulation for Modeling Active Composite Laminates

Active systems have attracted a great deal of attention in the last few decades due to the potential benefits they offer over the conventional passive systems in various applications. Dealing with active systems requires the possibility of modeling and simulation of their behavior. The paper considers thin-walled active structures with laminate architecture featuring fiber reinforced composite as a passive material and utilizing piezoelectric patches as both sensor and actuator components. The objective is the development of numerically effective finite element tool for their modeling. A 9-node degenerate shell element is described in the paper and the main aspects of the application of the element are discussed through a set of numerical examples.

Active vibration control using optimal LQ tracking system with additional dynamics

This paper focuses on the vibration suppression task using an appropriate controller design for active control of structures with distributed piezoelectric actuators and sensors. The problem arises from the need to control undesired vibrations caused by disturbances or excitations acting upon a structure in an efficient and at the same time a simple way. A special class of disturbances/excitations (periodical, with frequencies equal or near to the eigenfrequencies of the controlled structure) may cause undesired resonant states. In order to reject such disturbances and suppress vibrations in the presence of excitations an optimal LQ controller based on tracking systems with additional dynamics is proposed for the vibration control problem. The controller was tested in the presence of excitations with different frequencies. Controller design is model-based, where for the numeric modelling of the structure the finite element approach was used. Besides, subspace-based model identification was used as well. Controller design, testing and implementation were performed on the funnel-shaped shell structure, the inlet part of the magnetic resonance tomograph. Simulation results as well as the real-time implementation of the controller as a part of the Hardware-in-the-Loop system show considerable vibration suppression in the presence of excitations and confirm the efficiency of the controller.

Aspects of Modeling Piezoelectric Active Thin-walled Structures

The objective of this article is to reconsider some important aspects of modeling piezoelectric active thin-walled structures. Hence, it is dealt here with thin-walled laminated structures involving piezoelectric patches. A recently developed shell type finite element is used for the purpose. The first aspect is adequate modeling of electric field within the piezoelectric patches polarized in the thickness direction. The influence of higher order functions for the electric field on the accuracy of the model is discussed. The second aspect is related to modeling geometrical non-linearities in the behavior of the considered structures and their significance on the accuracy of the predicted behavior. Both aspects are considered with respect to static and dynamic cases.

Vibration control of a funnel-shaped shell structure with distributed piezoelectric actuators and sensors

In this paper two approaches to vibration control of a funnel-shaped smart structure with distributed piezoelectric actuators and sensors are considered. They are based on different possibilities for the shell smart structure modeling. An optimal linear quadratic (LQ) tracking control system with additional dynamics is proposed as a model-based control solution for the vibration suppression of a funnel-shaped structure which is modeled using either of the two approaches suggested in this paper: a finite element method (FEM)-based approach and model identification based on the measured input–output signals. Another control approach is a direct robust model reference adaptive control (MRAC), which is based on the measurements of the plant input and output signals and desired behavior specified through a reference model. Both control approaches assume the state space realization of the controlled plant. Vibration suppression of the funnel-shaped inlet part of the magnetic resonance image (MRI) tomograph with distributed piezoelectric actuator and sensor patches is achieved applying proposed control concepts and verified through the Hardware-in-the-Loop experiments with dSPACE and through numeric simulations. The results of the vibration control show considerable suppression of the vibration magnitudes in the selected frequency range. (Some figures in this article are in colour only in the electronic version)

Degenerated shell element for geometrically nonlinear analysis of thin-walled piezoelectric active structures

Active piezoelectric thin-walled structures, especially those with a notably higher membrane than bending stiffness, are susceptible to large rotations and transverse deflections. Recent investigations conducted by a number of researchers have shown that the predicted behavior of piezoelectric structures can be significantly influenced by the assumption of large displacements and rotations of the structure, thus demanding a geometrically nonlinear formulation in order to investigate it. This paper offers a degenerated shell element and a simplified formulation that relies on small incremental steps for the geometrically nonlinear analysis of piezoelectric composite structures. A set of purely mechanical static cases is followed by a set of piezoelectric coupled static cases, both demonstrating the applicability of the proposed formulation.

On Finite Element Analysis of Piezoelectric Controlled Smart Structures

The increasing engineering activities in the development and industrial application of piezoelectric smart structures require effective and reliable simulation and design tools [9]. Even if significant progress has been observed over the past years most of such developments are restricted to special requirements and applications [2]. In our opinion the finite element method (FEM) is an excellent basis to develop overall software tools which meet the engineering requirements. Consequently, such a general purpose software tool has been designed by the authors and realized step by step over the last few years [1], [3], [4]. Recently, this tool was completed by new thin shell type elements as well as a data interface to connect controller design tools with our finite element analysis tool. In the paper the focus is on these new developments. First the theoretical basis of our finite element software tool is presented briefly. Then the new electromechanical coupled layered thin shell elements are prescribed which are very efficient to simulate the global structural behavior of thin-walled structures controlled by piezoelectric wafers and fibers. After that our concept to connect finite element analysis and controller design is given which result in an computer based overall design and simulation strategy for smart structure. Finally, the active vibration suppression of an excited plate structure is presented as a test example to demonstrate the applicability of our finite element based overall design and simulation software.

Numerical and Experimental Investigations of Adaptive Plate and Shell Structures

In many branches of engineering lightweight design has become very important to reduce the mass and the energy consumption and to increase simultaneously the safety, integrity and environmental compatibility of a system. To meet these opposite objectives adaptive structural concepts have attracted increasing attention. These concepts are characterized by a synergistic integration of active (smart) materials, structures, sensors, actuators, and control electronic to an adaptive system. The potential uses of such concepts cover the entire range from mechanical engineering, aerospace engineering and civil engineering to manufacturing, transportation, robotics, medicine etc. The use of plate and shell structures as basic components of such adaptive systems is very common. Such smart material systems often consist of different layers of passive and active materials, e.g. steel or aluminium sheets attached with piezoceramics, fiber reinforced composites with embedded piezoelectric wafers etc. [1], [2], [4], [6]. The global behavior of piezoelectric smart structures can be modeled with sufficient accuracy by the linearized coupled electromechanical constitutive equations. However, it is generally recognized that analytical solutions of the coupled electro-mechanical field equations are limited to relatively simple geometry and boundary conditions. In practical applications, finite element (FE) techniques provide the versatility in modeling, simulation, analysis and optimal design of real engineering adaptive structures.

Entwurf intelligenter Strukturen unter Einbeziehung der Regelung (Design of Intelligent Structures Including Control)

Im Beitrag wird ein Konzept für den Entwurf und die Simulation intelligenter (adaptiver, smarter) Leichtbaustrukturen vorgestellt, die in der Lage sind, selbsttätig störende Schwingungen infolge äußerer Erregungen zu unterdrücken. Dazu werden piezoelektrische Folien- oder Fasermodule als Sensoren und/oder Aktuatoren in die Struktur integriert und über einen Regler so verbunden, dass das gewünschte Strukturverhalten erreicht wird. Das vorgestellte Entwicklungskonzept basiert auf einer Verknüpfung von numerischen Methoden der Strukturmechanik (Finite-Element-Methode) und Methoden der Reglerauslegung zu einem ganzheitlichen Entwurfskonzept.

A software platform for the analysis of porous die-cast parts using the finite cell method

Due to the die-cast technology the manufactured parts contain unavoidable imperfections such as cavities and pores with a length scale much smaller than the size of the produced parts. Such imperfections can reduce the load bearing capacity as well as the lifetime of a part and, consequently, have to be taken into consideration during the design process. But, to include the huge amount of small scale pores in a classical finite element simulation requires an extremely refined mesh and results in a computational effort, which may exceed the capacity of todayt’‘s computer hardware. An alternative approach is the application of the finite cell method (FCM), which can operate with non body-fitted hexahedral or tetrahedral meshes, meaning that the finite element mesh does not have to be aligned to the geometry of the structural part. The pores are taken into account in form of a STL data set (STL: standard tessellation language) coming from computed tomography (CT) or other sources, such as from a cast simulation procedure.