Abstract: This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.
Abstract: This paper presents a 4-DOF nonlinear model of a
cracked de Laval rotor-stator system derived based on Energy
Principles. The model has been used to simulate coupled torsionallateral
response of the faulty system with multiple parametric
excitations; rotor-stator-rub, a breathing transverse crack, eccentric
mass and an axial force. Nonlinearity of a “breathing” crack is
incorporated in the model using a simple hinge mechanism suitable
for a shallow crack. Response of the system while passing via its
critical speed with intermittent rotor-stator rub is analyzed. Effects of
eccentricity with phase and acceleration are investigated. Features of
crack, rub and eccentricity in vibration response are explored for
condition monitoring. The presence of a crack and rub are observable
in the power spectrum despite excitations by an axial force and rotor
unbalance. Obtained results are consistent with existing literature and
could be adopted into rotor condition monitoring strategies.
Abstract: For stable bipedal gait generation on the level floor,
efficient restoring of mechanical energy lost by heel collision at
the ground is necessary. Parametric excitation principle is one of
the solutions. We dealt with the robot-s total center of mass as
an inverted pendulum to consider the total dynamics of the robot.
Parametrically excited walking requires the use of continuous target
trajectory that is close to discontinuous optimal trajectory. In this
paper, we proposed the new target trajectory based on a position
in the walking direction. We surveyed relations between walking
performance and the parameters that form the target trajectory via
numerical simulations. As a result, it was found that our target
trajectory has the similar characteristics of a parametrically excited
inverted pendulum.