Mechanics and Model-Based Control of Smart Materials and Structures

Frontmatter

1. Energy Absorption of Axially-Impacted Column Controlled by Transverse Impact

Abstract

Energy absorption of a column under an axial impact was controlled by a transverse impact which attributed instantaneous reduction of the structural stiffness. It was found that the absorption of the axial impact energy increased due to the post-buckling deformation being enlarged by transverse impact, though the axial impact load decreased. The experiment showed that the time elapsed from the beginning of the axial impact to the transverse impact significantly influenced the energy absorption. A transverse impact applied simultaneously with an axial impact produced the highest energy absorption. The method suggested in this paper could increase the energy absorption without loosing any stiffness and static strength.

Tadaharu Adachi

2. Seismic Performance of Tuned Mass Dampers

Abstract

In a fundamental parametric study the seismic performance of Tuned Mass Dampers(TMDs) is investigated. Earthquake excited vibration-prone structures are modeled as elastic single-degree-of-freedom oscillators and they are equipped with a single TMD. The TMD performance is assessed by means of response reduction coefficients, which are generated from the ratio of the structural response with and without TMD attached. It is found that TMDs are effective in reducing the dynamic response of seismic excited structures with light structural damping. The results of the presented study are based on a set of 40 recorded ordinary ground motions

Christoph Adam, Thomas Furtmüller

3. Problems in Fast Moving Non-Holonomic Elastic Systems

Abstract

The Central Equation of Dynamics allows a unified view on existing methods and reveals them as a specific view on one and the same classical mechanics. Thereby, the particular methods exhibit special advantages and disadvantages according to the aim of investigation. For the derivation of the motion equations, the analytical methods display some drawbacks: the use of non-holonomic velocities needs an enormous effort and non-holonomic constraints can not à-priori be considered. Due to the directional derivatives w.r.t. the angular velocities, the obtained linearized equations do not represent the motions w.r.t. the co-rotational frame(and any orthogonal frame, resp.) as usually requested. This fact may lead to severe misinterpretations. In elastic multi body systems, the calculation effort increases dramatically. All these drawbacks are removed when using the Projection Equation

Hartmut Bremer

4. Using GPS sensors in Structural Mechanics

Abstract

Distributed sensor networks are conceived for a simple installation all around the free boundary of deformable media. The impact on current structural engineering technology depends on some requisites which are preliminarily discussed in this chapter: wireless communication between sensors and storage unit(s), reliability of the acquisition, low power consumption. Within this framework, non contact displacement sensors should be preferred in view of reconstructing the stress and strain fields inside the medium. GPS(Global Positioning System) sensors would be adequate, but they suffer some drawbacks which suggest the study of land GPS configurations. Assuming that the milestones listed above have all been reached, the design of the sensors dislocation is identified as the core structural-mechanics optimization problem.

Fabio Casciati, Zhicong Chen

5. Hybrid Control Procedures in Mitigating Cable Vibrations

Abstract

Cable vibration control is an active research field in the technical literature. Yet, a robust and effective control strategy for cable dynamics is still missing. Indeed, cables exhibit a complex behavior, mainly due to internal resonances and nonlinear couplings. Moreover, most of the control solutions already known in the literature are affected by damper/actuator localization, which significantly impairs their overall control effectiveness. To overcome these drawbacks, the authors have recently proposed a hybrid solution combining wrapped shape memory alloy(SMA) wires and an open-loop actuation. These control solutions have shown promising vibration mitigation capabilities when the motion was essentially dominated by the first in-plane mode. Here, a particular attention is posed to controlling the second in-plane modal amplitude which is known to entail serious control difficulties and proved to be considerably relevant in technical situations. To this end, the effectiveness of the passive(SMA wires), open-loop active and hybrid control solutions are investigated by means of a campaign of laboratory tests. The results extend the previous theoretical/experimental study and confirm the potentialities of the proposed hybrid approach

Lucia Faravelli, Clemente Fuggini, Filippo Ubertini

6. Thermal Stress Analysis in a Functionally Graded Material Considering Finite Thermal Wave Speed

Abstract

Three-dimensional generalized thermoelasticity based on the Lord and Shulman's theory and the Green and Lindsay's theory is analyzed by use of the state space approach and integral transform techniques(Laplace and Fourier transforms). The functionally graded material is approximated to a multi-layered medium. Each layer is homogeneous and isotropic. The surfaces are traction free and subjected to a partial heating. The numerical calculations for temperature and thermal stresses are carried out

Toshio Furukawa

7. Numerical homogenization and optimization of smart composite materials

Abstract

The paper presents a numerical homogenisation approach to calculate the effective properties of fibre and particle reinforced materials including smart and multifunctional materials with a focus on piezoelectric fibre composites applied to control vibration and noise radiation of structures. This finite element based homogenisation is used to optimise the material distribution at the micro-scale by applying an evolutionary approach to receive a desired global behaviour of a structure at the macro-scale.

Ulrich Gabbert, Sreedhar Kari, Niels Bohn, Harald Berger

8. Hybride Bell Tower Like Structures in Earthquake Environment

Abstract

Dynamic actions of bell movement are characteristic aspects in bell towers and thus show significant influences on the response of the main structure. In case of strong motions the oscillation of the bell exhibits(moderately) large rotations and nonlinear analysis becomes essential to understand the nature of the system and its dynamic process. The bell is modeled as rigid pendulum and the equations of motion of the hybrid structure follow from the formulation according to Lagrange equations. A coupled 2DOF system is used to study the dominant geometrically nonlinear influence of the bells rotation in frequency domain. Numerical nonlinear computer simulations are performed for MDOFs studying the influence of the higher modes of the main structure on the behavior of the pendulum. Parameter studies are performed for two different types of support excitations, i.e., time-harmonic, stationary random process

Rudolf Heuer, S. Mehdi Yousefi

9. Tracking of Stresses: A Further Step Towards Ageless Structures

Abstract

The present paper deals with the derivation of distributions of smart actuators, which enforce a structure to follow a desired stress trajectory everywhere and at all times. A particular case is the complete cancellation of force-induced stresses, a topic of particular interest in the context of ageless structures. Our formulation is derived within the framework of the linear dynamic theory of elasticity, and is based on the characterization of the initial boundary value problem of elasticity in terms of stresses. Smart actuation is represented by actuation stresses. We derive conditions, under which the desired stresses can be tracked exactly by the actuation stresses, and we present an easy to solve initial value problem for computing the actuation stresses

Hans Irschik, Michael Krommer, Markus Gusenbauer

10. Non-Linear Dynamic Deformation of a Piezothermoelastic Laminate

Abstract

This paper presents an analysis on the nonlinear transient behavior of a piezothermoelastic laminate. For the analytical model, a laminated beam is considered to be composed of elastic structural and piezoelectric layers that are subjected to mechanical, thermal, and electrical loads as disturbances or intended control procedures. The deformation of the laminate is analyzed using the classical laminate theory and the von Kármán strain. Equations of motion in terms of the displacements are obtained and analyzed through the Galerkin method. As a result, the dynamic deflection of the laminate is found to be governed by the equation for a polynomial oscillator, and the transient large deformation due to mechanical, thermal, and electrical loads are obtained. Through these results, the characteristics of the transient deformation of the laminate are discussed in detail

Masayuki Ishihara, Yasuhiro Watanabe, Naotake Noda

11. Determining Liquid Properties Using Mechanically Vibrating Sensors

Abstract

Miniaturized sensors for physical liquid parameters can be utilized in applications where liquids in industrial processes are monitored in order to maintain the quality of a process or the associated product. Due to the adverse properties commonly associated with chemical interfaces(lacking reversibility, drift, etc.), sensing physical parameters as indicators for the state of the liquid, in particularly density, viscosity(or more general rheological properties), and infrared absorption is an attractive alternative to conventional chemical sensors. The miniaturization of suitable sensor principles on the one hand facilitates the implementation of these devices online. On the other hand, scaling effect have to be taken into account, which, e.g., in case of viscosity sensors, lead to issues when it comes to applications in complex liquids such as suspensions. In our paper we provide an overview on our recent work discussing the device design, the associated modeling, and the application of the devices

Bernhard Jakoby, E. K. Reichel, F. Lucklum, B. Weiss, C. Riesch, F. Keplinger, R. Beigelbeck, W. Hilber

12. Mathematical Analysis of Flexural Vibration for a Functionally Graded Material Plate and Vibration Suppression by Flexural Wave Control

Abstract

In this paper, flexural vibrations of rectangular plates and beams which are consisted of functionally inhomogeneous materials due to cyclic loadings of external force and temperature change are analyzed mathematically. Interference between the flexural vibration due to cyclic loading and that due to cyclic heating is discussed. The amplification effect by loading frequency is also discussed for the deflection and stresses of the beam and the plate. Furthermore, a control problem of the flexural vibration of the FGM beam by the method of wave control is considered. In order to remove progressive wave in flexural waves excited by cyclic loading, intensity and phase lag of control force are derived on the basis of the active sink method. Then, the validity of wave control for the flexural vibration suppression of the FGM beam is discussed

Ryuusuke Kawamura, Hiroshi Fujita, Kenichiro Heguri, Yoshinobu Tanigawa

13. Monitoring and control of multi-storey frame structures by strain-type actuators and sensors

Abstract

In the present paper we study monitoring and control of multistorey frame structures. In particular, we consider strain-type sensors and actuators for that purpose. In the first part the concept of collocated continuously distributed strain-type sensors and actuators is introduced. Then we discuss the design of continuously distributed sensors in detail, in order to introduce the concept of strain-type sensor networks afterwards. Here, we focuss on the optimal design of such networks to approximate continuously distributed sensors. Finally, two case studies for a three-storey frame structure are presented.(1) Structural health monitoring for the detection of joints appearing at the connection of floors and sidewalls, and(2) active control of the third floor displacement by PD-controllers

Michael Krommer, Markus Zellhofer

14. Transient Piezothermoelastic Problem of a Functionally Graded Thermopiezoelectric Cylindrical Panel

Abstract

This paper is concerned with the theoretical treatment of transient piezothermoelastic problem involving a functionally graded thermopiezoelec-tric cylindrical panel due to nonuniform heat supply in the circumferential direction. The thermal, thermoelastic and piezoelectric constants of the cylindrical panel are expressed as power functions of the radial coordinate variable. We obtained the exact solution for the two-dimensional temperature change in a transient state, and piezothermoelastic response of a simply supported cylindrical panel under the state of plane strain. Some numerical results are shown in figures. Furthermore, the influence of the nonhomogeneity of the material is investigated

Yoshihiro Ootao

15. Control of an Electronic Throttle Valve for Drive-by-Wire Applications

Abstract

Electrically actuated control devices for regulating the amount of air entering gasoline engines play an essential role in drive-by-wire applications. In this paper an approach to the control of so-called electronic throttle valves is outlined. First a standard sliding-mode controller is presented. It is shown that the performance of the feedback loop can be improved significantly by incorporating time-variable boundary layers

Markus Reichhartinger, Martin Horn, Anton Hofer

16. Output Regulation of Smart Structures, Theory and Practice

Abstract

Self sensing and actuation of piezoelectric devices make it possible to give mechanical structures new features. Under the assumption of linear piezoelasticity and Kirchhoff plate theory a mathematical model is derived, which is used for the controller design such that harmonic disturbance with either known or unknown disturbance frequency are asymptotically eliminated. Both simulations and laboratory experiments show the performance of the proposed approach

Thomas Rittenschober, Kurt Schlacher

17. Analysis of Weld Induced Plasticity by BFM

Abstract

A method of analysis for the occurrence of localized thermoplastic strain, in a material under plane strain constraint, is studied based on the Body Force Method(BFM). BFM is an indirect boundary type method for elastic stress analysis based on the principle of superposition. Any inelastic strain can be expressed by the embedded force doublets in BFM. That is, in the analysis, a continuously embedded force doublets into the elastic body are used to express the presence of plastic strain. A simplified model of welding-induced plasticity is treated as a numerical example of the present method

Akihide Saimoto

18. Evaluation of Internal Friction of Viscoelastic Composites with Meso-Scale Structures for Vibration Damping of Mechanical Structures

Abstract

Viscoelastic analysis of polymer composites is focused to understand effect of meso-scale structure of composite on the internal friction for application of vibration damping in precision instruments. In this paper, the meso-scale structure of the composite is supposed to be periodically clustered hexagonal array of fibers. Internal damping of the composite is evaluated by energy dissipation in cyclic response. Interaction of fibers and viscoelasticity of the matrix cause the energy dissipation in the composite. To evaluate the damping capacity of the composite in details, a homogenization theory with multi-scale asymptotic expansion is used to analyze meso- and macro-scale behavior of the composite

Yotsugi Shibuya

19. An Identification Method of the Time Dependence of the Impact Force by Using Acoustic Response and FEM Analysis

Abstract

The radiated sound from the impacted body must have the information with respect to the impact force. We have proposed the method in order to identify the impact force by analyzing the radiated sound from the impacted body. Normally the impact position is unknown and important to measure the impact position. Therefore, in this study, we propose the method to identify the impact position and force by using the radiated sound from the impact body. In the present method, the relationship between the impacted force and sound pressure is obtained by FEM simulation. In order to identify the impact position, the sound pressure, which is measured at the other position, is used. The efficiency of the present method is confirmed by using the many experiments of the plate as the impacted body

Tomoaki Tsuji, Takafumi Kurimoto, Toshikazu Shibuya

20. Infinite Row of Parallel Cracks in a Piezoelectric Material Strip under Mechanical and Transient Thermal Loadings

Abstract

In this paper, the problem of an infinite row of parallel cracks in a piezoelectric material strip is analyzed under static mechanical and transient thermal loadings. The crack faces are supposed to be completely insulated. By using the Laplace and Fourier transforms, the thermoelectromechanical problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors for both the embedded and edge cracks are computed. The results for the crack contact problem are also included

Sei Ueda

21. Elastodynamic Doppler Effects by a Moving Interface

Abstract

A unified mathematical technique for analyzing a one-dimensional Doppler effects by a moving interface is presented. Exact and closed form expressions for stress waves are obtained. The solution for the stress has no restriction not only for the motion of the interface, but also for the wave nature, impulsive or time-harmonic. As an application example, the Doppler frequency shifts by the uniform and back and forth motions of the interface are discussed for the time-harmonic wave

Kazumi Watanabe, Naobumi Sumi

22. Compensation of flexible vibrations in a two-link robot by piezoelectric actuation

Abstract

This paper concerns the active control of flexural vibrations in a two-link robot consisting of two flexible arms with tip masses. Due to iner-tial forces of distributed and concentrated masses flexural vibrations occur. The robot is moving in a horizontal plane, such that gravity is not considered. In order to compensate the flexible vibrations, piezoelectric actuators are integrated in the arms. In the framework of linear beam theory, the solution of the shape control problem is derived, i.e. the necessary distribution of the piezoelectric actuation strains in order to completely compensate the inertial forces. Assuming that mass distribution, geometrical properties and the link angles are exactly known by appropriate measurements, the flexible vibrations can be fully suppressed. If some parameters are not known exactly, remaining vibrations may occur. Numerical simultions are performed in order to verify the solution of shape control and to study the sensitivity to uncertainties of the parameters

C. Zehetner, J. Gerstmayr

23. The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

Abstract

Vibrations may shorten the lifetime of structures and machines, cause discomfort in many cases(noise radiation) and are totally unwanted in precision engineering. The latter requires also static shape control. The method of unique decomposition of eigenstrains into two constituents, namely in impotent eigenstrains, that do not cause stress and in the complementary nilpotent eigenstrains that do not induce any deformation in the linear elas tic solid is considered in detail. These two complete classes of eigenstrains render optimal solutions by keeping shape and stress-control problems well separated. Assuming a common time function of the dynamic load, a novel approach is addressed to annihilate the forced vibrations. This optimal benchmark solution may serve the purpose in practical application to select prop erly shaped actuator patches and the control current

Franz Ziegler