ALBERT

Description:    This paper investigates the problem of sizing the width of tall free-standing columns with a given height which are intended to rock, yet shall remain stable during the maximum expected earthquake shaking. The motivation for this study is the emerging seismic design concept of allowing tall rigid structures to uplift and rock in order to limit base moments and shears. The paper first discusses the mathematical characterization of pulse-like ground motions and the dimensionless products that govern the dynamics of the rocking response of a free-standing block and subsequently, using basic principles of dynamics, derives a closed-form expression that offers the minimum design slenderness that is sufficient for a free-standing column with a given size to survive a pulse-like motion with known acceleration amplitude and duration. Content Type Journal Article Category Special Issue Pages 1-15 DOI 10.1007/s00419-012-0681-x Authors Nicos Makris, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Michalis F. Vassiliou, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 〈  α  ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated graphically. Content Type Journal Article Pages 1-18 DOI 10.1007/s00419-011-0560-x Authors Yuriy Povstenko, Institute of Mathematics and Computer Science, Jan Długosz University in Czȩstochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking into account the thermal effects, the nonlinear equations of motion and internal/external boundary conditions are derived through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations with coupling terms. These are solved using the direct multiple-scale method, leading to closed-form solutions for the mode functions, nonlinear natural frequencies and frequency–response curves of the system. The influence of system parameters on the linear and nonlinear natural frequencies, mode functions, and frequency–response curves is studied through numerical parametric analysis. It is shown that the vibration characteristics depend on the mid-plane stretching, intra-span spring, point mass, and temperature change. Content Type Journal Article Pages 1-15 DOI 10.1007/s00419-011-0558-4 Authors Mergen H. Ghayesh, Department of Mechanical Engineering, McGill University, Montreal, QC H3A 2K6, Canada Siavash Kazemirad, Department of Mechanical Engineering, McGill University, Montreal, QC H3A 2K6, Canada Mohammad A. Darabi, Department of Mechanical Engineering, University of Guilan, P.O. Box 1841, Rasht, Iran Pamela Woo, Department of Mechanical Engineering, McGill University, Montreal, QC H3A 2K6, Canada Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The paper presents a method of modelling dynamics of mechanisms in which assembly errors can occur. One of the features of the method is that such errors can be included when the kinematics of the mechanism is modelled. A closed kinematic chain consisting of flexible and rigid links with one joint displaced and turned is discussed. Use of joint coordinates together with the rigid finite element method for discretisation of flexible links has allowed us to considerably decrease the size of the problem. Numerical simulations are carried out in order to analyse the influence of inaccurate assembly on the load on joints of a four-bar linkage. Content Type Journal Article Pages 1-13 DOI 10.1007/s00419-011-0556-6 Authors Krzysztof Augustynek, Department of Transport and Informatics, University of Bielsko-Biała, Bielsko-Biała, Poland Iwona Adamiec-Wójcik, Department of Transport and Informatics, University of Bielsko-Biała, Bielsko-Biała, Poland Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    Following the previous approach of Pham and Torquato (J Appl Phys 94:6591–6602, 2003 ) and Torquato (J Mech Phys Solids 45:1421–1448, 1997 ; Random heterogeneous media, Springer, Berlin, 2002 ), we derive the strong-contrast expansions for the effective elastic moduli K e , G e of d -dimensional multiphase composites. The series consists of a principal reference part and a fluctuation part (perturbation about a homogeneous reference or comparison material), which contains multi-point correlation functions that characterize the microstructure of the composite. We propose a three-point correlation approximation for the fluctuation part with an objective choice of the reference phase moduli, such that the fluctuation terms vanish. That results in the approximations for the effective elastic moduli of isotropic composites, which coincide with the well-known self-consistent and Maxwell approximations for two-phase composites having respective microstructures. Applications to some two-phase materials are given. Content Type Journal Article Pages 1-13 DOI 10.1007/s00419-011-0562-8 Authors Duc Chinh Pham, VAST, Institute of Mechanics, 264 Doi Can, Hanoi, Vietnam Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    In this paper, we present finite element (FE) process simulations of a new production method used to coat ring-shaped work pieces with functional layers. Similarly to the conventionally applied hot isostatic pressing (HIP), this new coating method is based on powder metallurgy. It is expected to overcome some important drawbacks by integrating the consolidation of the powdery layer material into the hot rolling of the substrate ring. This makes HIP dispensable. Nevertheless several difficulties arise through the process integration. E.g., the presence of the compactable layer requires a different handling of the rolling stage compared with classical ring rolling. FE simulations shall support the design of this new process in order to investigate critical process parameters. For this purpose, new finite element modules have to be developed. A crucial point is the adequate modelling of the layer material. In this regard, we present a rate-dependent finite strain material model that describes the consolidation of the layer material in a thermodynamically consistent way. Moreover, FE process simulations of the new production method are presented and compared with experimental results. Content Type Journal Article Pages 1-17 DOI 10.1007/s00419-011-0553-9 Authors J. Frischkorn, RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Straße 1, Aachen, Germany S. Reese, RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Straße 1, Aachen, Germany Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    In this study, we checked experimentally whether anterior–posterior accelerations of the head during quiet human stance are usually below or above known thresholds of the otolith sensor. Thereto, we measured head kinematics with high spatial resolution. Furthermore, we used both these experimental data and computer simulations of two double inverted pendulum (DIP) models in order to verify the validity of DIP models in general. The results are clear cut. First, not only are acceleration thresholds regularly exceeded about once a second but also are velocity thresholds exceeded, albeit probably less frequently. Second, COM and head movement predicted by interwoven DIP model dynamics can not reproduce the mean measured amplitudes at once. Thus, neither the formerly promoted single inverted pendulum nor any DIP model can causally explain the dynamics of quiet human stance. Instead, we suggest to factor in at least three mechanical degrees of freedom. Due to a couple of reasons discussed, the triple inverted pendulum (TIP) model seems to be a promising abstraction implying potential to better understand the dynamics of quiet human stance. Content Type Journal Article Pages 1-12 DOI 10.1007/s00419-011-0559-3 Authors Michael Günther, Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Friedrich-Schiller-Universität Jena, Seidelstrasse 20, 07749 Jena, Germany Otto Müller, Dekanat der Medizinschen Fakultät, Eberhard-Karls-Universität Tübingen, 72076 Tübingen, Germany Reinhard Blickhan, Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Friedrich-Schiller-Universität Jena, Seidelstrasse 20, 07749 Jena, Germany Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    Nearly every cargo that is transported by ship is boxed in standardized containers. The land to ship and ship to land handling of containers is performed by container cranes. These cranes dominate the throughput of the containers in ports. The operators need to be well-trained and skilled because of the requirements of the task to load or unload the ships. During container handling, the crane-load system can be compared to a pendulum of rope length L and deflection f . It is referred to as an underactuated system. Whenever the fixed point of the pendulum is displaced, the load starts oscillating. In the nonlinear dynamics literature, one finds the field of resonant coupling to transfer energy from actuated controllable modes to underactuated uncontrollable modes. This work presents a novel normal form approach in order to identify the mode coupling. The proposed method decomposes a nonlinear control system into controllable and uncontrollable subsystem. Only the normal form terms in the controllable subsystem are utilized to design a general controller. Simulation results are given to highlight the load oscillation suppression. Content Type Journal Article Pages 1-19 DOI 10.1007/s00419-011-0557-5 Authors Christian Rapp, Institute for Mechanics and Ocean Engineering, Hamburg University of Technology, Eissendorfer Straße 42, 21073 Hamburg, Germany Edwin Kreuzer, Institute for Mechanics and Ocean Engineering, Hamburg University of Technology, Eissendorfer Straße 42, 21073 Hamburg, Germany N. Sri Namachchivaya, Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Laboratory, 104 South Wright Street, Urbana, IL 61801, USA Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition. Content Type Journal Article Pages 1-12 DOI 10.1007/s00419-011-0522-3 Authors A. Loghman, Department of Mechanical Engineering, Faculty of Engineering, University of Kashan, Kashan, I.R. Iran A. Ghorbanpour Arani, Department of Mechanical Engineering, Faculty of Engineering, University of Kashan, Kashan, I.R. Iran A. R. Shajari, Department of Mechanical Engineering, Faculty of Engineering, University of Kashan, Kashan, I.R. Iran S. Amir, Department of Mechanical Engineering, Faculty of Engineering, University of Kashan, Kashan, I.R. Iran Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    This paper presents results of experimental and numerical analyses of in-plane waves propagating in a 5 mm-thick steel plate in the frequency range of 120–300 kHz. For such a thickness/frequency ratio, extensional waves reveal dispersive character. To model in-plane wave propagation taking into account the thickness-stretch effect, a novel 2D spectral element, based on the Kane–Mindlin theory, was formulated. An application of in-plane waves to damage detection is also discussed. Experimental investigations employing a laser vibrometer demonstrated that the position and length of a defect can precisely be identified by analysing reflected and diffracted waves. Content Type Journal Article Pages 1-12 DOI 10.1007/s00419-011-0524-1 Authors Magdalena Rucka, Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533