Dynamics and Control of Advanced Structures and Machines

Stochastic free and forced vibrations of layered beams are analyzed that result from a single bounded random stiffness parameter whose probability density function is considered to be zero outside of a given interval, i.e., it is a member of a fuzzy set with bounded uncertainty. The relevant properties of natural vibrations of an ensemble of sandwich beams with three perfectly bonded layers under hard hinged support conditions are worked out in detail when a bounded random shear stiffness of the core material is assigned by employing interval mathematics. The main structure of a compound single-span railway bridge, effectively modeled as a two-layer beam, is subjected to a single moving load as well as to a series of repetitive moving loads traveling with constant speed. It serves as a complex example for the resulting forced random vibrations and resonances under the severe condition of an elastic interface slip of bounded random stiffness. In both cases exact homogenization yields a stochastic sixth-order partial differential equation of motion of the layered beam. Light modal damping is considered. The analysis of the illustrative problems is based on the interval representation with a triangular membership function of the stiffness modulus assigned. A short comment provides information on the limits of such triangular membership functions. Membership functions in the form of envelopes of the random natural frequencies, the dynamic magnification factors, and the phase angles in free vibrations are determined. Both, fuzzy peak deflection and acceleration are derived for the forced single-span compound railway bridge subjected to the moving loads. Approximating superposition of modal maxima is considered by standard routines of reliability analysis.

For a train car moving over a multi-span continuous beam of identical span length L at constant speed v, it may encounter repetitive excitations transmitted from the sustaining beam of frequency v∕L excited by the previous passing cars. If the exciting frequency v∕L coincides with the vehicle frequency f _c , namely v∕L = f _c , resonance will be developed on the running car. In such a case, when the train car travels over more and more spans of the beam, the response of the car will be accumulated and becomes larger and larger, up to the limit imposed by inherent damping. Using the rigid-vehicle/bridge interaction finite element developed previously by the authors, each train car is modeled as a two-axle vehicle and each span of the continuous beam is simulated as a number of beam elements. Then the resonant response of the train cars running over the multi-span continuous beam is analyzed. The numerical examples indicate that for a high speed train composed of a series of cars traveling over a multi-span continuous beam, the train-induced resonance on the bridge takes place at a rather high speed, but the bridge-induced resonance on the train cars takes place at a much lower speed.

Stability of a circular ring, pre-stressed by a temperature-like intrinsic deformation, is studied using the equations of the nonlinear theory of rods. The temperature gradient in the radial direction results in a bending moment. The critical state depends on the ratio of the bending stiffness coefficients. In the supercritical range, the ring begins to turn inside out as its cross-sections rotate about the axis. The analytical solutions are successfully compared against results of finite element simulations for a shell model of the ring.

In our study, the uniaxial tensile response of lattice panel with missing cell region was investigated using nonlinear FE analysis. In particular, the effects of missing cell size and shape on the initial stiffness E ^∗ and the plastic collapse strength σ _pl ^∗ were discussed. The initial stiffness is mainly affected by the ratio of missing cell height h∕h ₀ as well as the missing cell width w∕w ₀, and independent of the unit-cell shape. On the other hand, the plastic collapse strength is mainly dominated by the missing cell width w∕w ₀ only, which implies that the strength is affected strongly by the tensile strength at the front of the missing cell region.

Structural control technologies are applied to reinforce the building to resist the external forces. Especially, passive control method is widely accepted by earthquake research community; therefore, many researchers are developing semi-active structural control systems. There are two types of semi-active hydraulic dampers—Displacement Dependent Semi-Active Hydraulic Damper (DSHD) and Accumulated Semi-Active Hydraulic Damper (ASHD) have been proposed by Shih et al. In this study, oil circuit and element hysteretic behavior of DSHD and ASHD are discussed. Then, a ten floor shear frame structure installed with DSHD and ASHD with various control conditions is simulated for analyzing the control effect of the maximum story drift, maximum absolute acceleration, and maximum base shear. Test and analysis results reveal that shock absorption ratio of structural displacement of the roof of ten floor structure added with ASHD reaches to 87.9 %. Structural acceleration responses of this structure can be diminished by the synchronization of ASHD. Base shear of this structure installed with these two dampers with various control conditions is reduced 55–60 %. Seismic proof of these two semi-active hydraulic dampers can be demonstrated by this study.

In the present contribution, the possibility of controlling dynamic stresses in force-loaded bodies by means of actuating eigenstrain fields is addressed. The action of eigenstrains, such as thermal or piezoelectric actuating strains, is subsequently gathered under the notion of actuating stresses. Our study is performed in the framework of the theory of small incremental dynamic deformations superimposed upon a state of possibly large static pre-deformation of a hyperelastic body. Particularly, we present a solution for the general problem of producing certain incremental stress trajectories by means of specifically tailored actuation stresses that are superimposed onto the force-loaded body. This we shortly call the stress tracking problem. The problem of suppressing incremental stresses is contained as a special case. Subsequently, particular emphasis is given to the systematic derivation of necessary and sufficient conditions that must be satisfied in order to solve the stress tracking problem. Necessary conditions are presented that must be satisfied by the intermediate configuration and by the desired incremental stress field that shall be tracked, and sufficient conditions are derived that must be satisfied by the incremental actuating stresses. As an illustrative example, our three-dimensional formulation is eventually applied to the one-dimensional dynamic case of a straight homogeneous rod with a support excitation at one end and a single point-mass at the other end.

In this contribution we show, mainly based on an example, how Hamiltonian counterparts for partial differential equations that allow for a variational principle can be derived in a systematic manner. The main tool will be the appropriate use of the Lagrange multiplier technique, which allows us to obtain several well-known Hamiltonian formulations by using a common principle. The Mindlin plate will be used to visualize the presented approach

This contribution outlines key developments and first results towards an innovative hardware-in-the-loop test rig for high-speed pantographs that can accurately emulate high-speed train rides. This allows for efficient pantograph testing in laboratory and thus reduces the need for expensive track tests. Efficient real-time-capable models of the relevant and complex catenary dynamics are needed, but due to the distributed-parameter dynamics and weak damping, special care in the model formulation has to be taken. A novel moving coordinate formulation combined with controlled absorbing boundary layers yields an accurate and efficient catenary model. A model-based predictive test rig impedance control scheme is then used to emulate the catenary behavior on the test rig. Additionally, physical conservation laws (energy and momentum) can be considered by the controller as control goals. First experimental results demonstrate the test rig ability to emulate catenary behavior and eliminate errors in energy and momentum between the coupled systems.

We study swelling-induced bending of hydrogel bistrips comprising an elastomer strip and a gel strip by using finite element method. The constitutive laws of the elastomer and gel strips are assumed to be the neo-Hookean and Flory–Rehner models, respectively. We explore the swelling-induced bending of bistrips due to chemical potential and specifically focus on how the stiffness and thickness ratios between the elastomer and gel strips affect their swelling-equilibrium shapes. We show that there exist the specific values to maximize their bending curvatures.

The paper considers the piece-wise homogeneous bodies composed of elastic deformable elements, some of which show piezoelectric properties and can be coupled with series-connected external circuits via the electroded surfaces of piezoelements. The objective of this study is to develop effective algorithms of mathematical modeling, which will allow us to find the values of the circuit element parameters providing maximum damping of the system vibrations at the prescribed resonant frequencies. The optimal values of the parameters for the circuit elements are determined based on the natural vibration problem and equivalent circuits for elastic system incorporating piezoelectric element and external electric circuit. The efficiency of the proposed approach is demonstrated by solving particular problems.

The objective of this article is to give an overview of the methods available in literature to model the forming of woven-reinforced thermoplastic-matrix composites. Modelling approaches, namely kinematic and mechanics-based, to simulate the forming process are discussed. The experimental tests for the determination of the necessary parameters are listed and discussed. A great part of the efforts has been devoted to the shear characterization since it is the most important deformation mode. The bending behaviour is usually neglected but it is starting to be considered since it is important to simulate the shape of wrinkles.

In semiconductor manufacturing tight temperature control of chemicals is crucial for meeting clean application requirements. The use of multiple chemistries as well as various configuration options makes precise temperature control a challenging task. In this paper a generic solution for the temperature control in a single wafer manufacturing machinery for wet-chemical processing based on a model predictive control technique is presented. The developed control strategy is implemented and evaluated on a real world unit with realistic wafer cleaning recipes.

In this paper an electromechanical system with two different types of motor is considered. It is shown that during the spin-up, the system with DC motor may experience unwanted vibration—the Sommerfeld effect. This is a well-known effect when the motor of electromechanical system gets stuck near the resonance zone instead of reaching its nominal power. The absence of this effect is demonstrated in the system with synchronous motor. Nowadays, there are many works devoted to the study of this effect in various systems. Here we discuss the Sommerfeld effect from the point of view of localization of the so-called hidden oscillations.

The present study intends to evaluate heat conductance and mechanical strength at elevated temperature of a prototype of flat type receiver composed of carbon steel fin and copper tubes. Considering a compound circular plate composed of different kinds of material layers as an analytical model of the receiver, a mathematical analysis of plane axisymmetric transient heat conduction and thermal stresses for the plate is developed. Performing numerical calculation for a compound circular plate consisted of carbon steel layer and copper one, the effect of thickness of copper layer on spatial variations and time-evolutions of temperature change and thermal stresses is discussed briefly.

Multiple support excitations of elastic multi-span beams are studied. Based on the common set of equations of motion an efficient formulation is developed in order to reduce the degrees of freedom. The resulting equations are formally identical to those that are valid for structures under uniform support excitations. Applying classical modal analysis results in a set of uncoupled differential equations with time-dependent participation factor. A numerical example is given for a two-span railway bridge.

Some models of a sliding contact of the surfaces with periodic microgeometry over a viscoelastic body are presented. The various gap conditions, such as complete contact, boundary friction, and the contact of dry surfaces with adhesive interaction, are considered. Based on the analytical or semi-analytical solutions of the periodic contact problems, the effects of the microgeometry parameters on the contact pressure distribution and the mechanical component of the friction force are analyzed for various gap and load/velocity conditions.

The main causes of energy dissipation in sliding contact of deformable bodies are hysteresis losses and adhesive interaction of the contacting surfaces (Bowden and Tabor, The friction and lubrication of solids. Part 2. Clarendon, Oxford, 1964; Kragelsky et al., Friction and wear: calculation methods. Pergamon Press, Oxford, 1982). Their influence on friction force depends on the mechanical properties of the contacting bodies and their surface layers, conditions in the gap between surfaces, operation conditions, such as applied load, sliding velocity, temperature, and environment conditions. Besides, surface microgeometry has the significant effect on friction force, particular under conditions of dry contact and boundary lubrication. In this paper some models of a sliding contact of the surfaces with periodic microgeometry over a viscoelastic base are presented. Based on the models, the dependences of the friction force on the microgeometry parameters are analyzed for various contact conditions.

The effect of the value of preliminary plastic deformation viewed as an initial stress–strain state on the magnetic behavior of X70 pipe steels under elastic tension and compression is studied. Magnetic characteristics were measured both in a closed magnetic circuit and with the use of attached transducers along the direction of applied loading. The plastic deformation history affects the magnetic behavior of the material during subsequent elastic deformation, as plastic strain induces various residual stresses, and this necessitates taking into account the initial stress–strain state of products when developing magnetic techniques for the determination of their stress–strain parameters in operation.

The monitoring of cable-stayed bridges has a core aspect: the cables. They are a significant component of the structural skeleton and are in so large number that a one-by-one response measurement is often too ambitious. In this paper, a footbridge is studied with only 16 cables in double symmetry. Despite the evident simplification of the problem, several aspects met in the process of collecting the data are worth being reported.

Dynamical systems are considered that consist of a main rigid body and one or several movable internal bodies. The internal bodies interact with the main one by forces created and controlled by drives but do not interact with the environment. The motion of the internal bodies affects the main body, and it can move progressively under the influence of resistance forces produced by the environment. Different kinds of resistance forces are considered including Coulomb’s friction, piecewise linear and quadratic resistance. Periodic motions of the internal bodies and the corresponding translational motion of the main body are analyzed. The average speed of the system locomotion is evaluated and optimized with respect to the system parameters and control.

The ambient vibration is one of the viable output data-only structural dynamic testing options by winds and typhoons. This contribution aims to present the application of a reliable method such as the stochastic subspace identification implemented in a general-purpose software. One of the greatest infrastructures built in Hong Kong, i.e., the Ting Kau Bridge, is addressed as a case study. Results reveal that the proposed method detects both frequencies and mode shapes despite the reduced number of sensors adopted.

Impact events on soil media cause vibrations that propagate all around the impact site. These vibrations can be mitigated by the construction of suitable buried barriers. A recent proposal suggests of realizing them by meta-structures characterized by a nonlinear response. Their design requires repeated analyses of the whole system made of soil and barriers. A simplification is achieved by building the reduced order model of the linear system and incorporating the nonlinear effects as suitable external actions.

The drive belt set on two pulleys is considered as a nonlinear elastic rod deforming in plane. The modern equations of the nonlinear theory of rods are used. The static frictionless contact problem for the rod is derived. The nonlinear boundary value problems for the ordinary differential equations are solved by the finite differences method and by the shooting method by means of computer mathematics. The belt shape and the stresses are determined in the nonlinear formulation which delivers the contact reaction and the contact area. The developed method allows performing calculations for any set of geometrical and stiffness parameters.

The problem of control for group of pendulums is considered. Control goal is the synchronization of several remote pendulums over Internet. Some theoretical approach is presented. It is based on some experiments about statistic data of delays for control over Internet. Simulation results for several pendulums are presented. Experiments “in hardware” results are also presented (hardware—pendulums, constructed with Lego Mindstorms NXT, software—cloud mechatronic laboratory, http://​cmlaboratory.​com).

The paper evaluates the effect of various modelling strategies for the bridge–train interaction system on the prediction of the dynamic bridge response. Trains crossing the bridge with constant high-speed are described either by a series of moving single forces representing their static axle loads or by a planar mass-spring-damper multi-body system. The outcomes of the latter model serve as reference solution because vehicle–bridge interaction (VBI) is explicitly considered. In an application problem the vertical bridge peak response is derived based on models of different degree of sophistication. From the outcomes it can be concluded that the impact of high-speed trains on a bridge by means of single forces (representing the static train axle loads) provides accurate results if bridge damping is increased and additional dynamic distributed mass is added to the bridge to account indirectly for VBI effects.

In this research, the mechanical properties of epoxy composite filled with nano-silica particles with different crosslinking densities were experimentally studied to clarify the interaction effects between nano-particles and the network structure in matrix resins. The composite materials were prepared by adding 240-nm silica particles to the bisphenol A diglycidyl ether with a volume fraction of 0.2. The bending elastic moduli of the composites were dependent on only the volume fraction of the particles regardless of the particle size and network structures. Filling the nano-silica particles was clarified to improve the bending strength and fracture toughness of the composites with a fine network structure. However the particles acted as defects, reducing the mechanical properties of composites with rough network structures.