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1.
In this paper an initial-boundary value problem for a linear equation describing an axially moving string will be considered
for which the bending stiffness will be neglected. The velocity of the string is assumed to be time-varying and to be of the
same order of magnitude as the wave speed. A two time-scales perturbation method and the Laplace transform method will be
used to construct formal asymptotic approximations of the solutions. It will be shown that the linear axially moving string
model already has complicated dynamical behavior and that the truncation method can not be applied to this problem in order
to obtain approximations which are valid on long time-scales. 相似文献
2.
T. S. Amer 《Nonlinear dynamics》2008,54(3):189-198
The perturbed rotational motion of a gyrostat about a fixed point with mass distribution near to Lagrange’s case is investigated.
The gyrostat is subjected under the influence of a variable restoring moment vector, a perturbing moment vector, and a third
component of a gyrostatic moment vector. It is assumed that the angular velocity of the gyrostat is sufficiently large, its
direction is close to the axis of dynamic symmetry, and the perturbing moments are small as compared to the restoring ones.
These assumptions permit us to introduce a small parameter. Averaged systems of the equations of motion in the first and second
approximations are obtained. Also, the evolution of the precession angle up to the second approximation is determined. The
graphical representations of the nutation and precession angles are presented to describe the motion at any time. 相似文献
3.
Dr. H. P. Lee 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,65(8):564-571
Summary The dynamic behaviour of an Euler beam traversed by a moving concentrated mass, is analyzed for the general case of a mass moving with a varying speed. The equation of motion in a matrix form is formulated using the Lagrangian approach and the assumed mode method. The dimensionless form of the equation enables the numerical results to be applicable for a wide range of system parameters. The possibility of the mass separating from the beam is analyzed by examining the contact forces between the mass and the beam during the motion. 相似文献
4.
The problem of forced vibration of a hinged beam with piezoelectric layers is solved. Issues of mechanical and electric excitation
of vibration and the possibility of damping mechanically induced vibration by applying a voltage to the electrodes of the
piezolayers are studied. The effect of the physically nonlinear behavior of the passive layers on the response of the sensor
layer and entire structure and the effect of geometric nonlinearity on the behavior of the structure and sensor layer are
analyzed. The interaction of physical and geometrical nonlinearities for transient and stationary processes is studied
Translated from Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 118–136, January 2009. 相似文献