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  • 1
    Electronic Resource
    Electronic Resource
    Thermal study of date kernels via TG and DTA (1989)
    Springer
    Journal of thermal analysis and calorimetry 35 (1989), S. 2243-2254 
    Details
    ISSN: 1572-8943
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Ägyptische Dattelkerne wurden thermisch untersucht, um die Möglickkeit einer Verwendung als Quellen für wertvolle Verbindungen zu ergründen. Außerdem wurden technische Daten ermittelt, die zur Festlegung der Optimumtemperatur für die Gestaltung und den Betrieb der Geräte zur pyrolytischen Behandlung von Dattelkernen benötigt werden. Es wurden zwei Versuchsreihen durchgeführt, bei denen einerseits Thermogravimetrie (TG) und andererseits Differentialthermoanalyse (DTA) Anwendung fand. Die TG Ergebnisse eröffnen eine rein kinetisch kontrollierte Reaktion erster Ordnung. Die Aktivierungsenergie und die Arrheniuskonstante betrugen 8,17 kJ/mol bzw. 0,0115 min−1. DTA Resultate gaben Auskunft über den Charakter und Reaktionsprodukte der Reaktionen bei der Pyrolyse.
    Abstract: Резюме С целью оценки продук тов, как возможных источников полуения различных соединений, проведен термический анализ е гипетских финиковых косточек. П риведены также технические данные, н еобходимые для опред еления оптимальной темпера туры созданной пиролитической уста новки для обработки ф иниковых косточек. Проведено д ве различные серии экспериментов, включ ающих ТГ и ДТА. Результ аты ТГ показали чисто кинет ические контролируемую реак цию первого порядка. Э нергия активации и аррениус овская константа равнялись, соответст венно, 8,17 кдж-моль−1 и 0,0115 ми н−1. Результаты ДТА показ али характер реакций, про текающих в процессе п иролиза и соответствующие про дукты реакций.
    Notes: Abstract Thermal analyses was performed on Egyptian date kernels to assess the value of the products as possible sources of valuable compounds. It also furnished technical data necessary for determination of the optimum degree of temperature for the design and operation of units for the pyrolytic processing of date kernels. Two different sets of experiments were carried out, involving thermogravimetry (TG) and differential thermal analysis (DTA). The TG results revealed a purely kinetically controlled, first-order reaction. The activation energy and the Arrhenius constant were 8.17 kJ/mol and 0.0115 min−1, respectively. The DTA results indicated the nature of the reactions involved in the pyrolysis and the corresponding products.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01911888
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  • 2
    Electronic Resource
    Electronic Resource
    Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems (1999)
    Springer
    Nonlinear dynamics 20 (1999), S. 267-282 
    Details
    ISSN: 1573-269X
    Keywords: dynamics of multibody systems ; absolute nodal coordinate formulation ; Cholesky decomposition ; Cholesky coordinates ; velocity transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous publication, procedures that can be used with the absolute nodal coordinate formulation to solve the dynamic problems of flexible multibody systems were proposed. One of these procedures is based on the Cholesky decomposition. By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition is used to obtain a constant velocity transformation matrix. This velocity transformation is used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. The inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motion. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. Numerical examples are presented in order to demonstrate the use of Cholesky coordinates in the simulation of the large deformations in flexible multibody applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008323106689
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  • 3
    Electronic Resource
    Electronic Resource
    On the numerical solution of tracked vehicle dynamic equations (1994)
    Springer
    Nonlinear dynamics 6 (1994), S. 391-417 
    Details
    ISSN: 1573-269X
    Keywords: Tracked vehicles ; recursive methods ; augmented formulation ; multibody dynamics ; Lagrangian dynamics ; singular configurations ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045885
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  • 4
    Electronic Resource
    Electronic Resource
    An eight noded composite plate element for the dynamic analysis of spatial mechanism systems (1994)
    Springer
    Nonlinear dynamics 5 (1994), S. 459-476 
    Details
    ISSN: 1573-269X
    Keywords: Composite plates ; nonlinear vibration ; finite element method ; multibody dynamics ; stress analysis ; and numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The development of a shear-deformable laminated plate element, based on the Mindlin plate theory, for use in large reference displacement analysis is presented. The element is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotrophic material property sets. Coordinate mapping is utilized so that non-rectangular elements may be modeled. The Gauss quadrature method of numerical integration is utilized to evaluate volume integrals. A comparative study is done on the use of full Gauss quadrature, reduced Gauss quadrature, mixed Gauss quadrature, and closed form integration techniques for the element. Dynamic analysis is performed on the RSSR (Revolute-Spherical-Spherical-Revolute) mechanism, with the coupler modeled as a flexible plate. The results indicate the differences in the dynamic response of the transverse shear deformable eight-noded element as compared to a four-noded plate element. Dynamically induced stresses are examined, with the results indicating that the primary deformation mode of the eight-noded Mindlin plate model being bending.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00052454
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  • 5
    Electronic Resource
    Electronic Resource
    Control structure interaction in the nonlinear analysis of flexible mechanical systems (1993)
    Springer
    Nonlinear dynamics 4 (1993), S. 183-206 
    Details
    ISSN: 1573-269X
    Keywords: Nonlinear dynamics ; control structure interaction ; multibody dynamics ; finite element method ; Lagrangian dynamics ; inverse dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The effect of the control structure interaction on the feedforward control law as well as the dynamics of flexible mechanical systems is examined in this investigation. An inverse dynamics procedure is developed for the analysis of the dynamic motion of interconnected rigid and flexible bodies. This method is used to examine the effect of the elastic deformation on the driving forces in flexible mechanical systems. The driving forces are expressed in terms of the specified motion trajectories and the deformations of the elastic members. The system equations of motion are formulated using Lagrange's equation. A finite element discretization of the flexible bodies is used to define the deformation degrees of freedom. The algebraic constraint equations that describe the motion trajectories and joint constraints between adjacent bodies are adjoined to the system differential equations of motion using the vector of Lagrange multipliers. A unique displacement field is then identified by imposing an appropriate set of reference conditions. The effect of the nonlinear centrifugal and Coriolis forces that depend on the body displacements and velocities are taken into consideration. A direct numerical integration method coupled with a Newton-Raphson algorithm is used to solve the resulting nonlinear differential and algebraic equations of motion. The formulation obtained for the flexible mechanical system is compared with the rigid body dynamic formulation. The effect of the sampling time, number of vibration modes, the viscous damping, and the selection of the constrained modes are examined. The results presented in this numerical study demonstrate that the use of the driving forees obtained using the rigid body analysis can lead to a significant error when these forces are used as the feedforward control law for the flexible mechanical system. The analysis presented in this investigation differs significantly from previously published work in many ways. It includes the effect of the structural flexibility on the centrifugal and Coriolis forces, it accounts for all inertia nonlinearities resulting from the coupling between the rigid body and elastic displacements, it uses a precise definition of the equipollent systems of forces in flexible body dynamics, it demonstrates the use of general purpose multibody computer codes in the feedforward control of flexible mechanical systems, and it demonstrates numerically the effect of the selected set of constrained modes on the feedforward control law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045253
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  • 6
    Electronic Resource
    Electronic Resource
    Effect of the order of the finite element and selection of the constrained modes in deformable body dynamics (1992)
    Springer
    Nonlinear dynamics 3 (1992), S. 57-80 
    Details
    ISSN: 1573-269X
    Keywords: Dynamics ; finite element method ; triangular elements ; multibody dynamics ; component mode synthesis ; nonlinear vibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Finite elements with different orders can be used in the analysis of constrained deformable bodies that undergo large rigid body displacements. The constrained mode shapes resulting from the use of finite elements with different orders differ in the way the stiffness of the body bending and extension are defined. The constrained modes also depend on the selection of the boundary conditions. Using the same type of finite element, different sets of boundary conditions lead to different sets of constrained modes. In this investigation, the effect of the order of the element as well as the selection of the constrained mode shapes is examined numerically. To this end, the constant strain three node triangular element and the quadratic six node triangular element are used. The results obtained using the three node triangular element are compared with the higher order six node triangular element. The equations of motion for the three and six node triangular elements are formulated from assumed linear and quadratic displacement fields, respectively. Both assumed displacement fields can describe large rigid body translational and rotational displacements. Consequently, the dynamic formulation presented in this investigation can also be used in the large deformation analysis. Using the finite element displacement field, the mass, stiffness, and inertia invariants of the three and six-node triangular elements are formulated. Standard finite element assembly techniques are used to formulate the differential equations of motion for mechanical systems consisting of interconnected deformable bodies. Using a multibody four bar mechanism, numerical results of the different elements and their respective performance are presented. These results indicate that the three node triangular element does not perform well in bending modes of deformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045471
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  • 7
    Electronic Resource
    Electronic Resource
    Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1941-1966 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620351003
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  • 8
    Electronic Resource
    Electronic Resource
    Effect of the coupling between stretching and bending in the large displacement analysis of plates (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1233-1262 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The effect of the rotary inertia on the non-linear dynamics of plates that undergo a large reference displacement is examined in this paper. An assumed displacement field that accounts for the coupling between the stretching and bending of the plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate. Furthermore, the coupling between the stretching and bending of the plate as the result of finite rotation is also considered in this investigation. Based on the assumed displacement field that accounts for the effect of the rotary inertia, a non-linear finite element formulation is developed for the large displacement analysis of plates. The element equations of motion are expressed in terms of a set of element invariants that depend on the assumed displacement field as well as the rotary inertia. The use of the formulation presented in this paper is demonstrated using numerical examples.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300703
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  • 9
    Electronic Resource
    Electronic Resource
    Constrained motion of deformable bodies (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1813-1831 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, issues related to the dynamic modelling of constrained deformable bodies that undergo large rigid body displacements are discussed. Particular attention is focused on finite element formulations. It is shown that the use of nodal co-ordinates and shape functions to describe the finite rotation of some of the commonly used finite elements leads to a linearization of the kinematics and dynamic relationships. The structure of the non-linear dynamic equations that govern the motion of deformable bodies that undergo large displacements is examined. Comments on the finite element formulation of the invariants of motion, the definition of the generalized forces and moments in flexible body dynamics and the computational strategy used for the automatic generation of the equations of motion are made. The computer formulation of the joint constraints between deformable bodies as well as the numerical algorithms currently used in many of the general purpose computer programs that are based on the augmented formulation are discussed. A decoupled joint-elastic acceleration recursive formulation is also presented. This formulation leads to a small system of acceleration equations whose dimensions are independent of the number of the elastic degrees of freedom of the system. In this paper, the coupling between the displacements of the deformable bodies is classified as kinematic, inertia and elastic. In view of this classification, comments on the validity of using the updated finite element Lagrangian formulation and the 4 × 4 transformation matrix in the dynamic analysis of flexible multibody systems are made. The coupling between the finite rotation and the wave motion in constrained deformable bodies is also discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320817
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  • 10
    Electronic Resource
    Electronic Resource
    Large reference displacement analysis of composite plates. Part II: Computer implementation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 17-42 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This investigation concerns itself with the computer implementation of the dynamic formulation of thin laminated composite plates consisting of layers of orthotropic laminae that undergo large arbitrary rigid body displacements and small elastic deformations. A finite element preprocessor computer program is developed to automatically generate the invariants of the laminae, which may have arbitrary orientations. The laminae invariants are then used to obtain the invariants of the elements and the composite laminated plate. The consistent and lumped mass formulations of the invariants of motion of composite plates are compared and it is concluded that the two methods are comparable, if a fine enough finite element mesh is used. The structure of the dynamic equations of motion, based on the formulation presented in Part I of this paper, is examined. Non-linear centrifugal and Coriolis forces arising as the result of the finite rotations of the laminae are defined, and the solution schemes of the resulting non-linear differential equations of motion are discussed. Numerical examples illustrating the differences between homogeneous isotropic and laminated composite plates are presented. An RSSR (Revolute-Spherical-Spherical-Revolute) mechanism is used in the numerical examples, with the coupler modelled as a laminated plate flexible body. It is found that the inertia of the plate contributed greatly to the transverse deformation. The effects of laminae orientation is also investigated.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360103
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