Applied Mechanics and Materials Vol. 706

Abstract: This Special Issue presents a selection of papers initially presented at the 11th International Conference on Vibration Problems (ICOVP-2013), held from 9 to 12 September 2013 in Lisbon, Portugal. The main topics of this Special Issue are linear and, mainly, nonlinear dynamics, chaos and control of systems and structures and their applications in different field of science and engineering. According to the goal of the Special Issue, the selected contributions are divided into three major parts: “Vibration Problems in Vertical Transportation Systems”, “Nonlinear Dynamics, Chaos and Control of Elastic Structures” and “New Strategies and Challenges for Aerospace and Ocean Structures Dynamics and Control”.

Abstract: The paper deals with nonlinear vibrations in discrete-continuous mechanical systems consisting of rigid bodies connected by shafts torsionally deformed with local nonlinearities having hard or soft characteristics. The systems are loaded by an external moment harmonically changing in time. In the study the wave approach is used. Numerical results are presented for three-mass systems. In the study of regular vibrations in the case of a hard characteristic amplitude jumps are observed while in the case of a soft characteristic an escape phenomenon is observed. Irregular vibrations, including chaotic motions, are found for selected parameters of the systems.

Abstract: The design of the satellite Attitude Control System (ACS) becomes more complex when the satellite structure has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel, since the ACS performance and robustness will depend if the dynamics interaction effects between these components are considered in the satellite controller design. A crucial interaction can occur between the fuel slosh motion and the satellite rigid motion during translational and/or rotational maneuver since these interactions can change the satellite center of mass position damaging the ACS pointing accuracy. Although, a well-designed controller can suppress such disturbances quickly, the controller error pointing may be limited by the minimum time necessary to suppress such disturbances affecting thus the satellite attitude acquisition. It is known that one way to minimize such problems is to design controllers with a bandwidth below the lowest slosh and/orvibration mode which can result in slow maneuvers inconsistent with the space mission requirements. As a result, the design of the satellite controller needs to explore the limits between the conflicting requirements of performance and robustness. This paper investigates the effects of the interaction between the liquid motion (slosh) and the flexible satellite dynamics in order to predict what the damage to the controller performance and robustness is. The fuel slosh dynamics is modeled using its pendulum analogs mechanical system which parameters are identified using the Kalman filter technique. This information is used to designs and to compare the satellite attitude control system by the Linear Quadratic Regulator (LQR) and the Linear Quadratic Gaussian (LQG methods. Besides, one investigates the effects of the rod length estimation in the plant of the system stability. This investigation has shown that the poles of the plant to walk to and from the imaginary axis, leaving in the end the plant more stable.

Abstract: In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

Abstract: In the area of mechanics and electronics, the behaviors of mechanical systems under periodic loadings have been examined by many researchers. Vertical conveyors are effective examples observing various kinds of parameters of this problem. In this study, the nonlinear analysis of unbalanced mass of vertical conveyor with non-ideal DC motor has been analyzed. The results of numerical simulation are plotted and Lyapunov exponents are calculated.

Abstract: With the crank-and-rod exciters, the vibrational conveyers have a trough supported on elastic stands which are rigidly fastened to the trough and a supporting frame. The trough is oscillated by a common crank drive. This vibration causes the load to move forward and upward. The movement is strictly related to vibrational parameters. In this study is the transitional behavior across resonance, during the starting of a single degree of freedom vibratory system excited by non-ideal DC motor. The mechanical system depends on the motion of the DC motor. The working rang of vibrational conveyers with cubic nonlinear spring and non-ideal vibration exciter has been analyzed analytically for primary resonance by the Method of Multiple Scales. Lyapunov exponents are numerically calculated and the results of numerical simulation are ploted.

Abstract: The great use of circular cylindrical shells for conveying fluid in modern industrial applications has made of them an important research area in applied mechanics. Many researchers have studied this problem, however just a reduced number of these works have as object the analysis of orthotropic shells. Although most investigations deal with the analysis of elastic isotropic shells in contact with internal and external quiescent or flowing fluid, several modern and natural materials display orthotropic properties and also stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of internal flowing fluid on the dynamic instability and non-linear vibrations of a simply supported orthotropic circular cylindrical shell subjected to axial and lateral time-dependent loads is studied. To model the shell, the Donnell’s non-linear shallow shell theory without considering the effect of shear deformations is used. A model with eight degrees of freedom is used to describe the lateral displacements of the shell. The fluid is assumed to be incompressible and non-viscous and the flow to be isentropic and irrotational. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. The obtained results show that the presence of the internal fluid and material properties have a great influence on the vibration characteristics of the shell.

Abstract: The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Abstract: Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

Abstract: The mathematical modelling of rotating nonlinear flexible beam-like wing with rectangular cross section is investigated here. The structure is mathematically modeled considering linear curvature and clamped-free boundary conditions. The flexible wing has an angle of attack which is considered constant. Nonlinearities resulting from the coupling between the angular velocity of the rotating axis and the transversal vibration of the beam are considered. A drag force and a lift force acting along the beam length are also included in the mathematical model. The drag force is modelled as a turbulent drag effect. The lift force is modeled as a generalized force, using the strip theory. These forces are velocity dependent nonlinear excitations acting on the bean-like wing.