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About this book

The volume includes 30 contributions from the 3rd International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines representing the frontiers in the mechanics of controlled machines and structures. The Workshop, held in Perm, Russia in September 2017 continued a series of international workshops, starting in with the Japan - Austria Joint Workshop on Mechanics and Model Based Control of Smart Materials and Structures, the Russia - Austria Joint Workshop on Advanced Dynamics and Model Based Control of Structures and Machines and the first two editions of the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines. The previous workshops took place in Linz, Austria in September 2008 and April 2010, in St. Petersburg, Russia in July 2012 and in Vienna, Austria in September 2015. The up-to-date contributions are authored by internationally re-known leading experts in dynamics and control representing a broad spectrum of topics in the field of Advanced Structures and Machines; both, with respect to theoretical aspects as well as applications to contemporary engineering problems.

Table of Contents

Frontmatter

Measurement System of Impact Force and Specimen Deflection Based on Electromagnetic Induction Phenomena

In this research, our measurement system based on electromagnetic induction phenomena was further improved to establish a complete system for measuring the impact force, specimen deflection, and collision velocity when a small impactor collides with a specimen. The measurement method and data analysis have been clarified to determine the impact force and specimen deflection from the measured electromotive forces induced in coils set near a specimen. The results of a rubber impact test confirmed the effectiveness of the system.
Tadaharu Adachi, Yuto Mochizuki, Yosuke Ishii

New Cracks for Hard Contact of Lithosphere Plates with the Base

It is being researched the existence of the hidden defects which are not visually watched in the coverings of nanomaterials in earthquake seismology and materials science. It is being developed the method of the research on such defects and coverings which are based on the topological approach. It is being adduced the analysis of the defects on the example the research on the stress–strain state of a block structure, consisting of a two-dimensional horizontal units of different types in contact with each other on the boundaries. The block structure is situated on the surface three-dimensional linearly deformable substrate and rigidly connected with it. The researching block structures are under the arbitrary harmonic outside effects. It is peculiar not only to the nanocoverings, surface reinforcement of the materials but the lithospheric plate structure, the research on which stress–strain state serves to get information about the seismic intensity of the areas. The obtained results are evidence of the fact that the hidden defects are practically new types of the cracks, additional to the cracks of Griffith–Irvine. That is, unlike crack Griffith–Irvine characterized by the roundness and smoothness of boundaries, this type of cracks includes breaks of boundaries and visually more accurately describes the boundaries of the cracks, for example, in the fragile materials such as glass.
Olga M. Babeshko, Olga V. Evdokimova, Vladimir A. Babeshko

Dynamics of Contour Motion of Belt Drive by Means of Nonlinear Rod Approach

The contour motion of the belt drive, i.e., the motion with the constant trajectory, is addressed. The belt is considered as a closed Cosserat line whose particles have translational and rotational degrees of freedom. The problem is considered in the framework of geometrically nonlinear formulation with no restrictions on the smallness of displacements and rotations. The spatial (Eulerian) coordinate which is the arc coordinate in the actual configuration is introduced. The belt is divided into four segments: two contact segments on the pulleys and two free spans. The friction forces are assumed to obey the Coulomb law. The study is limited to the stationary case with the constant angular velocities of the pulleys and the equations in components are derived for both contact and free spans. In the contact segment two assumptions are employed to eliminate the unknown contact pressure and friction: (1) the full contact, i.e., coincidence between the pulley and the belt and (2) the stick condition, i.e., the belt velocity is related to the pulley angular velocity. A nondimensional coordinate is introduced in the segments to obtain the boundary value problem with fixed boundaries. The boundary coordinates of the contact zones are the integration constants of the derived problem along with the other constants.
Alexander K. Belyaev, Vladimir V. Eliseev, Hans Irschik, Evgenii A. Oborin

On the Method of Low-Frequency Monitoring of the Initial Stress State of a Body

A method for low-frequency control of the stress state of structures is proposed, based on an analysis of the parameters of the surface wave field created by the impact. To process the recorded signal, a special method is used, based on the use of optimal orthogonal decompositions of the signal in the base, adaptively tuned to the training sample. A series of computational experiments on simulation of dynamic processes in a prestressed medium was carried out. Studies have shown a high degree of informativeness of the method to various types of initial stress state in the medium and also a high sensitivity to a change in the value of the initial deformation.
T. I. Belyankova, O. V. Bocharova, A. V. Sedov, V. V. Kalinchuk

Mesomechanical Response of a Soft Magnetic Elastomer to AC Magnetization

The behavior of a pair of magnetizable spherical particles embedded in a viscoelastic elastomer is studied for the case, where an AC magnetic field is applied along the center-to-center line of the particles. This system is considered as a small-scale (mesoscopic) structure element of a magnetorheological elastomer. Under a quasistatic cycle of the field, the system in question is prone to hysteretic behavior. Namely, the particles initially positioned well apart, at some finite field strength, fall onto one another (cluster) and reside in this state until the field decreases well below the value at which the cluster has been formed. Under dynamic cycling of the field, the viscous friction interferes with the particle displacement process and impedes the occurrence of the magnetodeformational hysteresis of the element. Starting from small-amplitude overdamped oscillations and enhancing the role of magnetic forces over viscous ones, we show how the anharmonicity of the system grows while it approaches the transition threshold, above which the dynamics of the element includes the cluster state. The dynamic hysteresis of magnetization that accompanies the mechanical oscillations of the particles is presented as well.
A. M. Biller, O. V. Stolbov, Yu. L. Raikher

Two-Dimensional Motions of a Robot Under the Influence of Movable Internal Masses

Two-dimensional planar motions of a rigid body carrying movable internal masses are considered. The body can move along a horizontal plane in the presence of dry friction forces obeying Coulomb’s law. The motion of the body is controlled by means of internal masses that can perform prescribed movements relative to the body. Two configurations of internal movable masses are considered. For each of them, relative motions of these masses are proposed that ensure the transfer of the system from any given initial state to any prescribed terminal state in the plane. Thus, the controllability of the system by means of internal masses is proven.
F. L. Chernousko

Splitting of Strain Solitons upon Their Interaction in the Auxetic Rod

The problem of longitudinal wave propagation in a rod made from an auxetic material is considered. It is shown that a negative Poisson’s ratio leads to a qualitatively different (anomalous) dispersion behavior of linear waves. Accounting for geometric and physical elastic nonlinearities leads to the possibility of generating in a rod of stationary strain waves of a substantially non-sinusoidal profile—solitons and their periodic analogues. By means of numerical simulation it is shown that qualitatively different scenarios of interaction of solitons depend on the relative collision velocity.
Vladimir I. Erofeev, Vladimir V. Kazhaev, Igor S. Pavlov

Analysis of Acoustic Second-Harmonic Generation in a Multilayered Structure with Nonlinear Interfaces

The one-dimensional longitudinal wave propagation in a multilayered structure consisting of alternating layers and nonlinear spring-type interlayer interfaces is analyzed theoretically to investigate the acoustic second-harmonic generation due to the interfacial nonlinearity. Assuming that the nonlinearity is sufficiently weak, the second-harmonic components contained in the reflected and transmitted waves when a monochromatic longitudinal wave impinges perpendicularly on the structure are derived using a perturbation approach and the transfer-matrix method. Some numerical results of frequency dependence of second-harmonic amplitudes are shown and discussed with the aid of the band structure of layered structures.
Yosuke Ishii, Tadaharu Adachi

Experimental and Analytical Examination in Solid Sensible Cylindrical Heat Storage Block Consisted of Ferronickel Slag

Using ferronickel slag as heat storage medium, low cost solid sensible heat storage system for concentrating solar thermal power generation plant has been considered. Effects of ferronickel slag mix on amount of heat storage of mortar block specimen using ferronickel slag as a fine aggregate are evaluated. It has been shown that amount of heat storage increases as volume fraction of ferronickel slag increases in heat storage test. On the other hand, it has been shown that variation of amount of heat storage with volume fraction of ferronickel slag differs between numerical results in steady state and those in unsteady state in numerical calculations based on theoretical analysis. The reason is explained by variations of specific heat capacity and thermal conductivity in the block with volume fraction of ferronickel slag. Variation of amount of heat storage in the block in unsteady state with volume fraction of ferronickel slag has been clarified.
Ryuusuke Kawamura, Kozo Onoue, Yoshinori Nagase, Shigeki Tomomatsu

A Complete Direct Approach to Modeling of Dielectric Elastomer Plates as Material Surfaces

In this paper we present a complete direct approach to modeling nonlinear plates, which are made of incompressible dielectric elastomer layers. In particular, the layers are assumed to exhibit a neo-Hookean elastic behavior and the effect of electrostatic forces is incorporated by a purely electrical contribution to the Helmholtz free energy. In our previous work on this subject, two-dimensional constitutive relations for the plate were derived by numerical integration of the three-dimensional augmented free energy through the plate thickness imposing a plane stress assumption and an a-priori assumption concerning the distribution of the strain through the thickness of the plate. In contrast, we directly postulate the form of the two-dimensional augmented free energy for the structural plate problem in this paper. Results computed within the framework of this novel approach are compared to results from our previous work, which are well tested against existing solutions in the literature. A very good agreement is found.
Michael Krommer, Elisabeth Staudigl

Harmonic Balance Method and Stability of Discontinuous Systems

The development of the theory of discontinuous dynamical systems and differential inclusions was not only due to research in the field of abstract mathematics but also a result of studies of particular problems in mechanics. One of the first methods, used for the analysis of dynamics in discontinuous mechanical systems, was the harmonic balance method developed in the thirties of the twentieth century. In our work, the results of analysis obtained by the method of harmonic balance, which is an approximate method, are compared with the results obtained by rigorous mathematical methods and numerical simulation.
E. V. Kudryashova, N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, R. N. Mokaev

Optimization of the Dissipative Properties of Electroelastic Bodies with Electric Circuits Through the Analysis of Natural Vibrations

This paper presents a formulation and equations for the problem of natural vibrations of electroelastic bodies with external electric circuits that contain resistive, capacitive, and inductive elements. As one of its applications, the results of the solution of this problem are suggested for determining external electric circuit parameters that ensure optimal damping of one or several vibration modes. In order to illustrate the proposed approach, there are presented results of definition of optimal parameters of external series RL-circuit, shunting piezoelectric element attached to the surface of thin-walled shell in the form of half-cylinder and providing the best variants of damping for one or two vibration modes.
V. P. Matveenko, N. A. Yurlova, N. V. Sevodina, D. A. Oshmarin, M. A. Yurlov

Multiscale Dynamics of Damage-Failure Transitions and Structures Control Under Intensive Loading

High-cycle and very-high-cycle fatigue is the most important fundamental and engineering problem for a variety of applications. Series of accidents caused by the gas turbine engine failure (Cowles, Int J Fract 80:147–163, 1996; Shanyavsky, Simulation of fatigue fracture of metals. Synergetics in aviation. Monografiya, Ufa, 2007), along with high costs of service life estimation and potential costs of development of new constructions, stimulated advanced concepts of national programs for high-cycle and very-high-cycle fatigue (Bathias and Paris, Gigacycle fatigue in mechanical practice. Dekker Publisher Co., Marcel, 2005; Botvina, Fracture: kinetics, mechanisms, general laws. Nauka, Moscow, 2008; Hong et al., Metall Mater Trans A 43(8):2753–2762, 2012; Mughrabi, Int J Fatigue 28:1501–1508, 2006; Nicolas, Int J Fatigue 21:221–231, 1999; Nicholas, High cycle fatigue. A mechanics of material perspective. Elsevier, Oxford, 2006; Paris et al., Eng Fract Mech 75:299–305, 2008; Peters and Ritchie, Eng Fract Mech 67:193–207, 2000; Sakai, J Solid Mech Mater Eng 3(3):425–439, 2009; Shanyavsky, Simulation of fatigue fracture of metals. Synergetics in aviation. Monografiya, Ufa, 2007), as being based on new fundamental results of fatigue evaluation. The programs aim at developing approaches using basic research findings, modern methods of laboratory modeling, and quantitative analysis of structural changes in order to reveal fracture stages and “criticality” mechanisms in transition to macroscopic fracture. A strong interest in the gigacycle range (109 cycles) of fatigue loads is provided by the progress in the creation of new (nano- and submicrostructural) materials with a very-high-cycle fatigue life and by breakthrough tendencies in technologies requiring such life in aviation motor industry (Nicolas, Int J Fatigue 21:221–231, 1999).
O. B. Naimark

Influence of Sensors and Actuators on the Design of the Modal Control System

The efficiency of the active vibration control of flexible systems is limited by the delay in the feedback loop, which causes instability at higher frequencies. In order to design the transfer functions of the feedback control system, it is necessary to use the frequency response functions of the control object. In the case where these functions cannot be measured experimentally, they can be derived from the model of the object. We consider the object model with and without taking into account the influence of sensors and actuators on its dynamics, and the results demonstrate that if this influence is neglected in the model, the efficiency of the control system can significantly decrease. We consider modal control of bending vibrations of a metal beam using piezoelectric sensors and actuators.
V. A. Polyanskiy, A. K. Belyaev, N. A. Smirnova, A. V. Fedotov

Control of Beam Vibrations by Casimir Functions

This contribution presents a port-Hamiltonian (pH) framework for the modeling and control of a certain class of distributed-parameter systems. Since the proposed pH-formulation can be seen as a direct adoption of the calculus of variations on jet bundles, it is especially suited for mechanical systems exhibiting a variational character. Besides the pH-framework, an energy-based control scheme making heavy use of structural invariants (casimir functions) is presented on the example of a boundary-controlled Euler–Bernoulli beam.
Hubert Rams, Markus Schöberl, Kurt Schlacher

A Modular Solver for Mechanical System Dynamics Under One-Sided Contact Constraints

A modular and flexible solver for mechanical system dynamics with one-sided (inequality) contact constraints is proposed. In each time step, an active set method constructs the current set of active constraints, the α-RATTLE time integration method is employed to solve the equality-constrained subproblem, and a Newton iteration is applied to solve the implicit system of update equations. The purely geometric formulation of the constraint functions allows an efficient modeling of system couplings where the constraint forces are solved for as part of the solution. A test case showing a ball bouncing on a string illustrates the solver’s functionality.
Alexander Schirrer, Sebastian Thormann

Shock Absorption Effect of Semi-active Mass Control Mechanism for Structure

Taiwan is located in the Circum-Pacific Seismic Zone and also at the junction of the Eurasian plate and the Philippine Sea plate, initiating sensible earthquakes to threaten the structural safety. Therefore, in order to enhance the seismic proof capability of structure, a new structural control mechanism, emerged passive control and active control, is proposed in this study. This mechanism can execute the “release” and “capture” of control mass block and only produce “negative” work on structure, based on the active mass control principle without power supply. A mathematical model of control law of this proposed mechanism is derived and the parameter study for single degree of freedom is executed to compare with those of structures without control and with passive tuned mass damper to obtain the optimal design parameters. Analysis results display that amplification of steady state reaction for structure with this semi-active control is much less than those of structure with passive control under within 0.03–0.07 and around 0.6–1.6. This proposed mechanism can “capture” and “release” the active control mass based on the direction and velocity of movement of the structural displacement.
Ming-Hsiang Shih, Wen-Pei Sung

Hierarchical Modeling of Damage and Fracture in a Structurally Inhomogeneous Materials Subjected to Deformation

Two computational models of deformation are presented: the first one models aluminum matrix composite with silicon carbide reinforcement; the second models complexly alloyed brass. The models account for material internal structure, as well as for rheological properties of material constituents. Material deformation on micro- and macroscale has been simulated. It is shown that damage mechanics is applicable for simulating fracture of both malleable and brittle constituents of the materials. In numerical simulations an empirically obtained model of composite matrix limiting plasticity is used, which correlates limiting plasticity with stress stiffness coefficient and Lode-Nadai stress state coefficient. On an example of the brass, a technique is developed, that allows one to derive the dependence of limiting deformation of brittle inclusions of metal alloys, on stress stiffness coefficient.
Sergey V. Smirnov, Marina V. Myasnikova, Yury V. Khalevitsky

Effect of Lattice Misfit Strain on Surface Acoustic Waves Propagation in Barium Titanate Thin Films

The finite-element approaches are used to the analysis of the properties of acoustoelectronic devices on surface acoustic waves (SAWs) made using thin-film technologies. The device consists of a barium titanate BaTiO3 film placed on a magnesium oxide substrate MgO. The barium titanate (BT) film is studied in the c-, r-, and aa-phases. The interdigital transducer (IDT) is attached to the free surface of the ferroelectric film and consists of a system parallel electrodes (pins) alternately connected to each other via common buses. The commercial software COMSOL is used for two-dimensional finite-element analysis and modeling the processes of excitation and propagation of SAW. The resonance and antiresonance frequencies are calculated for different film thicknesses and values of the lattice misfit strain. The significant influence of the film thickness and strains near the phase transitions and in r-phase on the resonant and antiresonant frequencies is discussed. In addition, a two-dimensional model of a SAW filter consisting of 40 pair pins of transmitting and receiving IDTs spaced 1.8 mm apart is considered. The frequency dependences of scattering parameters (S-parameters) have calculated and are presented.
P. E. Timoshenko, V. V. Kalinchuk, V. B. Shirokov, A. V. Pan‘kin

Control of Nanosensors Forming on Base of Aluminum Template

The results of the investigation of deposition processes of nanofilms formation on amorphous porous anodic aluminum oxide substrates, based on which it is possible to create various optic highly sensitive nanosensors, are presented in this research. The study was carried out by molecular dynamics simulation. The modified embedded atom method was used for calculation, temperature and pressure were maintained by Nose–Hoover thermostat and barostat. The different types of atoms were deposited on aluminum oxide substrates. The aims of investigation were understanding of process mechanisms of nanofilms forming and of process of filling nanopores with atoms of various substances and establishing the basic parameters governing these processes. The results of modeling the processes of precipitation of pure molecular sulfide of zinc and with the addition of additives in the form of copper atoms and manganese sulfide molecules are presented.
A. Vakhrushev, R. Valeev, A. Fedotov, A. Severyukhin

Dynamic Coupling Characteristics of Slender Suspension Footbridges with Wind-Resistant Ropes

An analytical study is presented for the slender suspension bridge with inclined wind-resistant ropes (i.e., wind-guys) susceptible to coupled flexural and torsional vibrations. Based on the linearized deflection theory of classical suspension bridges, the modal coupling mechanism of a single-span footbridge is studied analytically. The free vibration analysis is conducted to obtain the closed-form solutions of modal frequencies and modal shapes of the suspended beam with horizontal wing guys, from which the key parameters and coupling factors dominating the flexural–torsional coupled vibrations are identified. To evaluate the coupling nature of flexural–torsional vibrations for the suspended beam, the modal-based coupling contribution factor is presented in this study.
Y. B. Yang, J. D. Yau
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