scholarly journals Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed

2020 ◽  
Author(s):  
Hector Laos
Keyword(s):  
Closed Form ◽  
Equations Of Motion ◽  
Closed Form Solutions

Active-Passive Hybrid Constrained Layer for Structural Damping Augmentation

2000 ◽  
Vol 122 (3) ◽  
pp. 254-262 ◽  
Author(s):  
Yanning Liu ◽  
K. W. Wang
Keyword(s):  
Closed Form ◽  
Viscoelastic Material ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Generic Model ◽  
Structural Damping ◽  
Active Materials ◽  
Closed Form Solutions ◽  
Fail Safe ◽  
Active Constrained Layer

A new surface-damping concept with an active-passive hybrid constraining layer (HCL) is proposed to improve the damping performance of traditional active constrained layer (ACL) systems. Instead of using a pure piezoelectric constraining layer, passive and active materials are used together to constrain the viscoelastic material layer. A generic model of the HCL treatment is presented. Nondimensional equations of motion and boundary and connecting conditions are derived. The closed-form solutions to the equations are developed and analyzed. Tabletop tests are also performed to verify the feasibility of the new damping concept. It is shown that by properly selecting a passive constraining material and assigning appropriate lengths for the active and passive constraining parts, HCL can outperform a system with a pure active PZT coversheet, both in terms of its fail-safe ability and closed-loop damping performance. [S0739-3717(00)01503-8]

On Wave Propagation in Thermoplastic Media

1966 ◽  
Vol 33 (3) ◽  
pp. 514-520 ◽  
Author(s):  
A. D. Fine ◽  
H. Kraus
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
Wave Front ◽  
Dynamic Behavior ◽  
Static Analysis ◽  
Equations Of Motion ◽  
Normal Velocity ◽  
Wave Fronts ◽  
Closed Form Solutions ◽  
Infinite Region

The dynamic behavior of a medium, according to the uncoupled thermoplastic theory, is presented and is compared to the behavior that would be obtained from an uncoupled quasi-static analysis. Since the inertia terms are retained in the equations of motion, wave fronts (or surfaces of discontinuity) are produced in the medium. The normal velocity of the wave front separating the elastic and plastic regions is determined. General closed-form solutions of the displacement (according to both the dynamic and the quasi-static approaches) are obtained; their unique forms are found for the semi-infinite region, and an illustrative numerical example is then presented.

Surface Damping Treatment With an Active-Passive Hybrid Constraining Layer

1999 ◽  
Author(s):  
Yanning Liu ◽  
K. W. Wang
Keyword(s):  
Closed Form ◽  
Viscoelastic Material ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Generic Model ◽  
Active Materials ◽  
Closed Form Solutions ◽  
Material Layer ◽  
Fail Safe ◽  
Active Constrained Layer

Abstract A new surface-damping concept with an active-passive hybrid constraining layer (HCL) is proposed to improve the damping performance of traditional active constrained layer (ACL) systems. Instead of using a piezoelectric constraining layer, passive and active materials are used together to constrain the viscoelastic material layer. A generic model of the HCL treatment is presented. Non-dimensional equations of motion and boundary and connecting conditions are derived. The closed-form solutions to the equations are developed and analyzed. It is shown that by properly selecting a passive constraining material and assigning appropriate lengths for the active and passive constraining parts, HCL can outperform a system with pure active PZT coversheet, both in terms of its fail-safe ability and closed-loop damping performance.

The Lure of the Mean Axes

2006 ◽  
Vol 74 (3) ◽  
pp. 497-504 ◽  
Author(s):  
Leonard Meirovitch ◽  
Ilhan Tuzcu
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Space Structures ◽  
Aerodynamic Forces ◽  
State Equations ◽  
Flexible Bodies ◽  
Closed Form Solutions ◽  
The Mean

A variety of aerospace structures, such as missiles, spacecraft, aircraft, and helicopters, can be modeled as unrestrained flexible bodies. The state equations of motion of such systems tend to be quite involved. Because some of these formulations were carried out decades ago when computers were inadequate, the emphasis was on analytical solutions. This, in turn, prompted some investigators to simplify the formulations beyond all reasons, a practice continuing to this date. In particular, the concept of mean axes has often been used without regard to the negative implications. The allure of the mean axes lies in the fact that in some cases they can help decouple the system inertially. Whereas in the case of some space structures this may mean complete decoupling, in the case of missiles, aircraft, and helicopters the systems remain coupled through the aerodynamic forces. In fact, in the latter case the use of mean axes only complicates matters. With the development of powerful computers and software capable of producing numerical solutions to very complex problems, such as MATLAB and MATHEMATICA, there is no compelling reason to insist on closed-form solutions, particularly when undue simplifications can lead to erroneous results.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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