Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Analysis of the Equations of Linear Controlled Structures

1995 ◽  
Author(s):  
F. Ma ◽  
W. C. Lee
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
First Order ◽  
Physical Insight ◽  
Controlled Structure ◽  
Space Approach

Abstract The coefficients of the equation of a linear controlled structure are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to structures with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Generalization of Classical Modal Analysis

1996 ◽  
Author(s):  
F. Ma ◽  
W. C. Lee
Keyword(s):  
Modal Analysis ◽  
State Space ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

Abstract The coefficients of a linear nonconservative structure are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to structures with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Analysis of Linear Nonconservative Vibrations

1994 ◽  
Author(s):  
Fai Ma
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Numerical Techniques ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
Physical Insight ◽  
Space Approach

Abstract The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to linear nonconservative systems. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the extended modal analysis can offer substantial reduction in computational effort and ample physical insight. Many numerical techniques, for example the collocation method, involve discretized equations resembling those of linear nonconservative vibrations. These numerical techniques can be greatly streamlined if the method of equivalence transformations is incorporated.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

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