Vibration Analysis of Non-Classically Damped Linear Systems

2004 ◽  
Vol 126 (3) ◽  
pp. 456-458 ◽  
Author(s):  
Z. S. Liu, ◽  
D. T. Song, and ◽  
C. Huang ◽  
D. J. Wang ◽  
S. H. Chen
Keyword(s):  
Linear Systems ◽  
Physical Meaning ◽  
Vibration Analysis ◽  
Original System ◽  
New Method ◽  
Order System ◽  
Damping Term ◽  
Clear Physical Meaning ◽  
Damped System

This Technical Brief presents a new method for vibration analysis of a non-classically damped system. The basic idea is to introduce a transformation, which bears clear physical meaning, so that the original non-classical damped system is transformed into a new 2nd-order system that does not have the damping term. The transformed system not only provides an alternative of calculating response, but also reveals more clearly vibration behaviors of the original system.

A NEW METHOD FOR IN-PLANE VIBRATION ANALYSIS OF CIRCULAR RINGS WITH WIDELY DISTRIBUTED DEVIATION

2002 ◽  
Vol 254 (4) ◽  
pp. 787-800 ◽  
Author(s):  
Y.J. YOON ◽  
J.M. LEE ◽  
S.W. YOO ◽  
H.G. CHOI
Keyword(s):  
Vibration Analysis ◽  
New Method ◽  
Plane Vibration ◽  
Circular Rings

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

2021 ◽  
Author(s):  
Jin Zhu ◽  
Kai Xia ◽  
Geir E Dullerud
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Hidden Markov ◽  
Transition Probability ◽  
Original System ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Weighting Matrix ◽  
Markov Jump Linear Systems

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

scholarly journals Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 289
Author(s):  
Daniel Cao Labora ◽  
José António Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Thin Plate ◽  
Newtonian Fluid ◽  
Physical Meaning ◽  
Source Term ◽  
Vertical Motion ◽  
Bounded Solutions ◽  
Clear Physical Meaning ◽  
Fractional Differential

This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. From this model, we can derive an FDE for the particular case of lacking the spring. Here, we find conditions for the source term ensuring that the solutions to the equation of the motion are bounded, which has a clear physical meaning.

Reduction-by-Projection Method for Linear Programming Problems

2014 ◽  
Vol 672-674 ◽  
pp. 1968-1971
Author(s):  
Xue Tong ◽  
Jun Qiang Wei
Keyword(s):  
Linear Programming ◽  
Linear Systems ◽  
Integer Linear Programming ◽  
Projection Method ◽  
Simplex Method ◽  
New Method ◽  
Linear Programming Problems

This paper defines the projection of algebic systems, and studies the projecting algorithm for linear systems. As its application, a new method is given to solve linear programming problems, which is called reduction-by-projection method. For many problems, especially when the problems have many constraint conditions in comparison with the number of their variables, the method needs less computation than simplex method and others. The great advantage of the method is shown when solving the integer linear programming problems.

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