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Theoretical and Applied Mechanics Letters is jointly published by the Chinese Society of Theoretical and Applied Mechanics and American Institute of Physics. The Chinese Society of Theoretical and Applied Mechanics is the sole distributor of the print and electronic versions in Mainland China, and American Institute of Physics is the sole distributor of the print and electronic versions outside Mainland China.

Select this Article		Internal motion of the complex oscillators near main resonance Jan Awrejcewicz and Roman Starosta Theor. Appl. Mech. Lett. 2, 043002 (2012); http://dx.doi.org/10.1063/2.1204302 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approach allows reducing the problem to the Duffing equation with adequate initial conditions. A novel idea for an effective study of nonlinear dynamical systems consisting in a concept of the socalled limiting phase trajectories is applied. Both qualitative and quantitative complex analyses have been performed. Important nonlinear dynamical transition type phenomena are detected and discussed. In particular, nonsteady forced system vibrations are investigated analytically.

Select this Article		Modern information technologies in construction of kinetic models for reactions of metal complex catalysis Jan Awrejcewicz, Yuliya B. Lind, Irek M. Gubaidullin, and K. F. Koledina Theor. Appl. Mech. Lett. 2, 043003 (2012); http://dx.doi.org/10.1063/2.1204303 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract For detailed study of complex chemical reactions mechanisms experiment is conducted for selected private reactions. This causes a problem of kinetic parameters getting—the same set of rate constants must describe both public and private reaction stages, and also a general mechanism. In this paper, solution of this problem for a reaction of olefins hydroalumination is proposed. To optimize the computational process a methodology of parallelization is elaborated. On the base of parallel computations, a kinetic model for the reaction assigned is constructed, and on its base, the physical and chemical conclusions about reaction mechanism are done.

Select this Article		Stability case study of the ACROBOTER underactuated service robot László L. Kovács and László Bencsik Theor. Appl. Mech. Lett. 2, 043004 (2012); http://dx.doi.org/10.1063/2.1204304 (7 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract The dynamics of classical robotic systems are usually described by ordinary differential equations via selecting a minimum set of independent generalized coordinates. However, different parameterizations and the use of a nonminimum set of (dependent) generalized coordinates can be advantageous in such cases when the modeled device contains closed kinematic loops and/or it has a complex structure. On one hand, the use of dependent coordinates, like natural coordinates, leads to a different mathematical representation where the equations of motion are given in the form of differential algebraic equations. On the other hand, the control design of underactuated robots usually relies on partial feedback linearization based techniques which are exclusively developed for systems modeled by independent coordinates. In this paper, we propose a different control algorithm formulated by using dependent coordinates. The applied computed torque controller is realized via introducing actuator constraints that complement the kinematic constraints which are used to describe the dynamics of the investigated service robotic system in relatively simple and compact form. The proposed controller is applied to the computed torque control of the planar model of the ACROBOTER service robot. The stability analysis of the digitally controlled underactuated service robot is provided as a real parameter case study for selecting the optimal control gains.

Select this Article		Command functions of open loop galvanometer scanners with optimized duty cycles V. F. Duma Theor. Appl. Mech. Lett. 2, 043005 (2012); http://dx.doi.org/10.1063/2.1204305 (6 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract The paper approaches the problem of the command functions of galvanometer-based scanners (GS) that are necessary to produce the linear plus parabolic scanning function of the GS, which we have proved previously to produce the highest possible duty cycle (i.e., time efficiency) of the device. We have completed this theoretical aspect (which contradicted what has been stated previously in the literature, where it has been considered that the linear plus sinusoidal scanning function was the best) with the experimental study of the most used scanning functions of the GSs (sawtooth, sinusoidal and triangular), with applications in biomedical imaging, in particular in optical coherence tomography, demonstrating that the triangular function is always the best one to be applied, from both an optical and a mechanical point of view. In the present study the input voltage/command function which should be applied to the GS to produce the desired triangular scanning function (with controlled non-linearity for the fastest possible stop-and-turn portions) was determined analytically, in relationship with the active torque that drives the device. This command function is analyzed with regard to the specific, respectively required parameters of the GS: natural frequency and damping factor, respectively scan speed and amplitude. The modeling in an open loop control structure of the GS is finally discussed as a trade-off between using the highest possible duty cycle and minimizing the maximum peaks of the input voltage.

Select this Article		Stability analysis of the extended state observers by Popov criterion Christiav Erazo, Fabiola Angulo, and Gerard Olivar Theor. Appl. Mech. Lett. 2, 043006 (2012); http://dx.doi.org/10.1063/2.1204306 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract The analysis and design of the extended state observer (ESO) involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dynamics systems is proposed.

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July 2012

Volume 2, Issue 4, Articles (04xxxx)

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Select this Article		Editorial: Modeling and control of mechanical/ biomechanical systems Jan Awrejcewicz and Paweł Olejnik Theor. Appl. Mech. Lett. 2, 043001 (2012); http://dx.doi.org/10.1063/2.1204301 (4 pages) Full Text: Read Online (HTML) \| Download PDF
		Abstract Unavailable

Select this Article		Experimental investigation on using the piezoelectric and electromagnetic vibration absorbers in milling Marcin Hoffmann, Krzysztof Marchelek, Miroslaw Pajor, and Arkadiusz Parus Theor. Appl. Mech. Lett. 2, 043007 (2012); http://dx.doi.org/10.1063/2.1204307 (3 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract The paper presents an active control system that counteracts the development of chatter vibration. The vibration amplitude depends on the dynamic properties of the machine tool, cutting tool and work-piece. In the paper we analyze the case when the loss of machining stability is caused by the work-piece. The proposed active control system employs electromagnet or piezoelectric actuator to suppress vibration during milling. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters that for the uncontrolled system. Cutting tests are performed on JAFO FYN-50 machine with mill DIN 845 B-25 K-N HSS to demonstrate an effectiveness of the proposed systems.

Select this Article		Adaptive control of anti-aircraft missile launcher mounted on a mobile base Izabela Krzysztofik and Zbigniew Koruba Theor. Appl. Mech. Lett. 2, 043008 (2012); http://dx.doi.org/10.1063/2.1204308 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract This paper presents the problem of control of anti-aircraft missile launcher mounted on a moving carrier-vehicle. Direct excitations on the vehicle from the road cause adverse vibrations of the launcher. In order to increase the precision of the guiding system in the conditions of self-propelled movement of the setup on a bumpy road, the adaptive control algorithm was proposed. Some research results of computer simulation are presented in a graphical form.

Select this Article		Energy harvesting by two magnetopiezoelastic oscillators with mistuning Grzegorz Litak, Michael I. Friswell, Cedrick A. Kitio Kwuimy, Sondipon Adhikari, and Marek Borowiec Theor. Appl. Mech. Lett. 2, 043009 (2012); http://dx.doi.org/10.1063/2.1204309 (5 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract We examine an energy harvesting system of two magnetopiezoelastic oscillators coupled by electric circuit and driven by harmonic excitation. We focus on the effects of synchronization and escape from a single potential well. In the system with relative mistuning in the stiffness of the harvesting oscillators, we show the dependence of the voltage output for different excitation frequencies.

Select this Article		Optimal control of quadratic functionals for affine nonlinear systems M. Popescu and A. Dumitrache Theor. Appl. Mech. Lett. 2, 043010 (2012); http://dx.doi.org/10.1063/2.1204310 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract In this paper we analyze the optimal control problem for a class of affine nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.

Select this Article		Parametric vibrations in offset printing units Yuriy Pyryev and Juliusz Krzyzkowski Theor. Appl. Mech. Lett. 2, 043011 (2012); http://dx.doi.org/10.1063/2.1204311 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract Vibrations of offset printing presses are serious problem, which cause many difficulties while printing and impair quality of the prints. The biggest problem lies in construction of printing unit. It mainly consists of three cylinders, but two of them are in a direct contact generate undesired vibrations. Construction of the cylinders makes that stiffness of the unit varies periodically while printing. In this paper model of offset printing unit is presented. The model is described by the system of two parametric differential equations. Computer simulations of the behaviour of the printing unit have been performed. Conditions in which parametric resonance appears are also appointed here.

Select this Article		Middle ear reconstruction estimated by recurrence plot technique Rafal Rusinek, Jerzy Warminski, Marek Zadrozniak, and Marcin Szymanski Theor. Appl. Mech. Lett. 2, 043012 (2012); http://dx.doi.org/10.1063/2.1204312 (5 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract Middle ear surgery techniques have enabled to improve hearing destroyed by a disease. Despite huge improvement in instrumentation and techniques the results of hearing improvement surgery are still difficult to predict. This paper presents the results of vibrations measurements in a human middle ear obtained at the Medical University of Lublin. Vibrations of the stapes in the case of the intact ossicular chain, after cement incus rebuilding and incus interpositions are compared each other. In this aim a new approach of ossicles vibrations observation is introduced in order to complete information obtained from classical approach which bases on the transfer function. Measurements of ossicular chain vibrations are performed on fresh human temporal bone specimen using the laser doppler vibrometer. Next, after classical research, the extended analysis with the recurrence plots technique is performed.

Select this Article		Pseudoelastic effect in autoparametric non-ideal vibrating system with SMA spring Danuta Sado, Marek Pietrzakowski, and Krzysztof Gajos Theor. Appl. Mech. Lett. 2, 043013 (2012); http://dx.doi.org/10.1063/2.1204313 (6 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connected by shape memory alloy (SMA) spring. Shape memory alloys have ability to change their material properties with temperature. A polynomial constitutive model is assumed to describe the behavior of the SMA spring. The non-ideal source of power adds one degree of freedom, so the system has four degrees of freedom. The equations of motion have been solved numerically and pseudoelastic effects associated with the martensitic phase transformation are studied. It is shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system's various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities, Poincarè maps and exponents of Lyapunov may be used.

Select this Article		Dynamics of vehicles with high gravity centre Szymon Tengler and Andrzei Harlecki Theor. Appl. Mech. Lett. 2, 043014 (2012); http://dx.doi.org/10.1063/2.1204314 (4 pages) Online Publication Date: July 10, 2012 Full Text: Read Online (HTML) \| Download PDF
	+ -	Show Abstract The vehicles with high gravity centre are more prone to roll over. The paper deals with a method of dynamics analysis of fire engines which is an example of these types of vehicle. Algorithms for generating the equations of motion have been formulated by homogenous transformations and Lagrange's equation. The model presented in this article consists of a system of rigid bodies connected one with another forming an open kinematic chain. Road maneuvers such as a lane change and negotiating a circular track have been presented as the main simulations when a car loses its stability. The method has been verified by comparing numerical results with results obtained by experimental measurements performed during road tests.