Stability of columns subjected to earthquake support motion

1974 ◽  
Vol 3 (4) ◽  
pp. 347-352 ◽  
Author(s):  
Naser Mostaghel
Keyword(s):  
Support Motion

Optimal Control of Nonlinear Parametrically Excited Beam Vibrations by Spatially Distributed Sensors and Actors

1997 ◽  
Author(s):  
Andreas Kugi ◽  
Kurt Schlacher ◽  
Hans Irschik
Keyword(s):  
Axial Strain ◽  
Equations Of Motion ◽  
Nonlinear Formulation ◽  
Control Laws ◽  
Distributed Sensors ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Piezoelectric Layers ◽  
Spatially Distributed ◽  
Support Motion

Abstract This contribution is focused on a straight composite beam with multiple piezoelectric layers under the action of an axial support motion. In the sense of v. Karman a nonlinear formulation for the axial strain is used and the equations of motion are derived by means of the Hamilton formalism. This system turns out to be a special class of infinite dimensional systems, the so called Hamilton AI-systems with external inputs. In order to suppress the excited vibrations two infinite control laws are proposed. The first one is an infinite PD-feedback law and the second one is based on the nonlinear H∞-design, where an exact solution of the corresponding Hamilton Jacobi Isaacs equation is presented. The necessary quantities for the control laws can be measured by appropriate space-wise shaped sensors and the asymptotic stability of the equilibrium point can be proved.

Transient Response of a Shear Beam to Correlated Random Boundary Excitation

1977 ◽  
Vol 44 (3) ◽  
pp. 487-491 ◽  
Author(s):  
S. F. Masri ◽  
F. Udwadia
Keyword(s):  
Time Delays ◽  
Spectral Characteristics ◽  
Mean Square Displacement ◽  
Dimensionless Time ◽  
Mean Square ◽  
Random Boundary ◽  
Mean Square Response ◽  
Shear Beam ◽  
The Mean ◽  
Support Motion

The transient mean-square displacement, slope, and relative motion of a viscously damped shear beam subjected to correlated random boundary excitation is presented. The effects of various system parameters including the spectral characteristics of the excitation, the delay time between the beam support motion, and the beam damping have been investigated. Marked amplifications in the mean-square response are shown to occur for certain dimensionless time delays.

Stability and Stationary Response of a Skew Jeffcott Rotor With Geometric Uncertainty

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Nicolas Driot ◽  
Alain Berlioz ◽  
Claude-Henri Lamarque
Keyword(s):  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Forced Response ◽  
Stochastic Methods ◽  
Steady State Response ◽  
State Response ◽  
Internal Excitation ◽  
Geometric Uncertainty ◽  
Jeffcott Rotor ◽  
Support Motion

The aim of this work is to apply stochastic methods to investigate uncertain parameters of rotating machines with constant speed of rotation subjected to a support motion. As the geometry of the skew disk is not well defined, randomness is introduced and affects the amplitude of the internal excitation in the time-variant equations of motion. This causes uncertainty in dynamical behavior, leading us to investigate its robustness. Stability under uncertainty is first studied by introducing a transformation of coordinates (feasible in this case) to make the problem simpler. Then, at a point far from the unstable area, the random forced steady state response is computed from the original equations of motion. An analytical method provides the probability of instability, whereas Taguchi’s method is used to provide statistical moments of the forced response.

Autoparametric Vibration of Coupled Beams Under Random Support Motion

1986 ◽  
Vol 108 (4) ◽  
pp. 421-426 ◽  
Author(s):  
R. A. Ibrahim ◽  
H. Heo
Keyword(s):  
Resonance Condition ◽  
Wide Band ◽  
Random Excitation ◽  
State Response ◽  
Coupled Beams ◽  
The Moment ◽  
Non Gaussian ◽  
Two Degree Of Freedom ◽  
Support Motion ◽  
Gaussian Closure

The dynamic response of a two degree-of-freedom system with autoparametric coupling to a wide band random excitation is investigated. The analytical modeling includes quadratic nonlinearity, and a general first-order differential equation of the moments of any order is derived. It is found that the moment equations form an infinite hierarchy set which is closed via two different closure methods. These are the Gaussian closure and the non-Gaussian closure schemes. The Gaussian closure solution shows that the system does not reach a stationary response while the non-Gaussian closure solution gives a complete stationary steady-state response. In both cases, the response is obtained in the neighborhood of the autoparametric internal resonance condition for various system parameters.

Mode Localization in Coupled Circular Plates

1994 ◽  
Vol 116 (3) ◽  
pp. 286-294 ◽  
Author(s):  
C. O. Orgun ◽  
B. H. Tongue
Keyword(s):  
Periodic Structures ◽  
Qualitative Change ◽  
Disk Drive ◽  
Circular Plates ◽  
Mode Localization ◽  
Infinite Dimensional ◽  
Write Heads ◽  
The Individual ◽  
Support Motion ◽  
Computer Disk

When analyzing structures that are comprised of many similar pieces (periodic structures), it is common practice to assume perfect periodicity. Such an assumption will lead to the existence of eigenmodes that are global in character, i.e., the structural deflections will occur throughout the system. However, research in structural mechanics has shown that, when only weak coupling is present between the individual pieces of the system, small amounts of disorder can produce a qualitative change in the character of the eigenmodes. A typical eigenmode of such a system will support motion only over a limited extend of the structure. Often only one or two of the smaller pieces that make up the structure show any motion, the rest remain quiescent. This phenomenon is known as “mode localization”, since the modes become localized at particular locations on the overall structure. This paper will examine the behavior of several circular plates that are coupled together through springs, a system that models a multiple disk computer disk drive. These drives typically consist of several disks mounted on a single spindle, coupled by read/write heads, which act as weak springs, thus leading one to suspect the possibility of localization. Since such an effect would impact accurate read/write operations at small fly heights, the problem deserves attention. Although computer disk drives contain space fixed read/write heads, this paper will consider springs that are fixed to the plates in order to understand the effect of localization on a set of infinite dimensional structures (the circular plates). Later work will extend the model to the case of space fixed springs and the wave behavior and destabilizing effects that such a configuration will induce.

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