Andrei Craifaleanu

The paper studies the vibration transmitted by a mechanical oscillating system to its fixing device. The influence of the mechanical characteristics (inertial and elastic) of the device on the quantities specific to the free and forced vibration, respectively, of the principal system, is analyzed. In this context, the paper investigates the possibility to correlate the vibrations of the mechanical system with the vibrations measured on the fixing device. The conclusions of this study can be used for the calibration of vibration measuring stands. In the final part, a practical application is presented, aimed to compare the theoretical results with the data obtained by measurements performed on an experimental model built by the authors.

In this work it is presented a numerical model based on finite elements, for wave packet propagation, made of a symmetrical (S0) and an antisymmetrical wave (A0) in a steel plate. The method provides the solution by direct time-marching integration of the hyperbolic differential equations. The new elements shown are the model of wave generation by a piezoelectric patch directly applied on the plate, wave fronts identification for the two generated modes and indications on the best placement for the receiving transducer. The amplitudes and time of flight of the two modes are determined as well as interactions between incident and reflected waves and comparisons with theoretical values are made. An experimental setup based on this model is under way.

ABSTRACT The paper presents a software package dedicated to the study of some classical mechanisms with bodies in relative motion, used in numerous real mechanical systems. The package is intended for the development of a virtual laboratory used in modern teaching of technical mechanics in engineering faculties. The programs represent animatedly the mechanisms, as well as the trajectories, the velocities and the accelerations of the significant points. For the bodies with relative motion, the kinematic quantities (velocities and accelerations) specific to the absolute, relative and transport motion, respectively, are shown. The programs represent, also animatedly, the plane of velocities and the plane of accelerations, which are two diagrams used for the grapho-analytical study of mechanisms. The coordinates of the significant points, as well as the components of the velocities and accelerations are computed and displayed in real time. The students are encouraged to choose and input various values of the geometrical and kinematical parameters, in order to study their impact over the running of the mechanisms. The motions of the mechanisms can be paused and continued, in order to study the instantaneous images and values of the geometrical and kinematical parameters. The applications in the software package were successfully used at the University “Politehnica” of Bucharest, during the practical sessions for the course “Mechanics”.

... WEIGHT FUNCTIONS METHOD IN STABILITY STUDY OF THE RIGID BODY Ion STROE, AndreiCRAIFALEANU University “Politehnica” of Bucharest, Department of Mechanics, email: ion.stroe@gmail.com ... Page 3. Ion STROE , Andrei CRAIFALEANU 118 0 = W (13) ...

The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered for three cases: placed on the surface of the Earth, so it is fixed; located on Earth, but in rotation with respect to it and in the final case, located on a space station, moving around the Earth. For all the analyzed cases the motion equations are determined using the Lagrangian formalism.

The principle of virtual work is used to study the motion of a system under the action of external and internal forces. General kinematics problem of systems of rigid bodies with constraints are presented in first part of the paper. If an internal joint force has to be found, a virtual displacement is considered in the system. Based on the principle of virtual work, the elaborated method solves the problem of calculus of input forces and joint forces of a compass robot arm, sketched as a serial chain.

ABSTRACT The principle of virtual work can be used in order to study the motion of a system under the action of external forces, or to find reactions, as well as various other internal forces. For the calculus of the internal forces, a new method based on Lagrange equations ...

ABSTRACT The motion of the rigid body with a fixed point represents an important problem of classical mechanics. This type of motion is found in gyroscopic apparatuses, utilized in air and space navigation. The general motion of the rigid body can be represented as the superposition of a translation and of a motion with a fixed point. Two of the general theorems of dynamics - the theorem of the angular moment and the theorem of the kinetic energy and work - can be applied for the relative motion of an arbitrary system with respect to its center of mass. If the system is a rigid body, this is also a motion with a fixed point. The motion of a rigid body with a fixed point is complex and its analytical study can be performed only in a few particular cases. In the general case, the use of numerical methods is indispensable. This type of motion involves also stability aspects. The understanding of the motion with a fixed point is facilitated by the availability of virtual animated models. The objective of the paper is the presentation of an interactive computer program, including real-time numerical integration and animated representations of the motion, developed by the authors and used as a teaching tool in practical sessions of the course “Dynamics” in engineering faculties.

The paper proposes a method for the reduction of an arbitrary-shape plane plate to a symmetrical discrete system of material points, with the same center of mass and the same tensor of inertia. It is shown, first, that an elliptical plate can be reduced to a symmetrical system of five material points, with a spatial distribution directly related to the shape of the plate. The results are subsequently generalized for plane plates of arbitrary shape. By using the reduction procedure, various mechanical quantities can be calculated more simply, as compared to the traditional methods. The proposed method finds application in the dynamic, vibration and structural analysis of complex mechanical systems that include rigid plane plates, such as industrial robots.

A novel method of teaching mechanics to students in computer science and automation faculties is presented, based on the interactive development of simple thematic software applications. By using the theoretical background taught at the course, students are guided to write, during practical sessions in the IT laboratory, their own software solutions to simple statics, kinematics and dynamics problems, including, in some cases, animated graphical representations and interactivity. This encourages students to use their programming skills and provides a “hands-on” way of understanding mechanical phenomena. The favorable responses of the students and the learning effectiveness observed have encouraged the authors to extend the application of the method and to gradually improve it, by promoting the use of more advanced programming technologies. The paper presents the structure and the themes of the practical sessions, including problem formulation, input data and requirements. Some illus...

The paper presents an original generalization of the Lagrange equations of the second kind, for motions with respect to reference frames in arbitrary motions. The traditional form of the equations is modified by adding certain supplementary terms. Calculation methods are presented for these terms and some conclusions useful in practical applications are drawn. For validation, the new formalism is illustrated on the application of the Foucault pendulum. The results are in full agreement with those obtained by traditional methods. The formalism can be used to determine the motions of various mechanical systems, with respect to large size movable bodies (such as planets or orbital stations), that are not influenced by the relative motion of the studied parts.

The proper operation and reliability of numerous mechanical devices depends on reducing the vibrations of embedded components, modeled as multi-degree-of-freedom dynamic systems. This can be achieved by using various types of absorbers. The design of such devices is conditioned by the understanding of the variation of their technical characteristics with the constructive parameters. The present paper is dedicated to a special type of dampers, based on the use of the magnetic phenomenon. However, available empirical formulae for the damping characteristics of magnetic dampers do not reveal all significant dependencies. Based on theoretical, numerical and experimental methods, the paper brings a number of contributions concerning the relation between the damping characteristics of a magnetic damper and some of its constructive parameters. Variation curves, useful both for theoretical studies and practical applications, are plotted.

The paper analyses a two-degree-of-freedom dynamic system, by taking into account its non-linearity. The case of the internal resonance is studied and, by local analysis, Hopf bifurcations are emphasized. Periodic motion domains, as well as domains of possible evolution ...