On the Heavily Damped Response in Viscously Damped Dynamic Systems

2004 ◽  
Vol 71 (1) ◽  
pp. 131-134 ◽  
Author(s):  
R. M. Bulatovic
Keyword(s):  
Linear Systems ◽  
Dynamic Systems ◽  
Degree Of Freedom ◽  
Physical Parameters ◽  
Design Constraints

Free motions of viscously damped linear systems are studied. A heavily damped multi-degree-of-freedom system is defined as one for which all its eigenvalues are real, negative, and semi-simple. Several results are obtained which state conditions for the heavy damping of the system. The conditions are given directly in terms of the coefficients of system matrices and these conditions may yield design constraints in terms of the physical parameters of the system. An example illustrates the validity and usefulness of the presented results.

Harmonic Analysis of Dynamic Systems With Nonsymmetric Nonlinearities

1979 ◽  
Vol 101 (1) ◽  
pp. 31-36 ◽  
Author(s):  
P-T. D. Spanos ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Harmonic Analysis ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Approximate Solutions ◽  
Steady State Solution ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Engineering Applications ◽  
Vehicle System

The generalized method of equivalent linearization is modified to be applicable for multi-degree-of-freedom dynamic systems with nonsymmetric nonlinearities subjected to harmonic monofrequency excitation. Readily applicable formulas are given for the construction of the equivalent linear systems related to a class of systems commonly encountered in engineering applications. As an example of its application, the proposed method is used to generate an approximate steady-state solution for a simple vehicle system. The accuracy of the approximate solutions is determined.

A Method for Identifying Parameters of Mechanical Joints

1990 ◽  
Vol 57 (2) ◽  
pp. 337-342 ◽  
Author(s):  
J. Wang ◽  
P. Sas
Keyword(s):  
Physical Parameter ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Modal Testing ◽  
Physical Parameters ◽  
Mechanical Joints ◽  
Joint Parameters

A method for identifying the physical parameters of joints in mechanical systems is presented. In the method, a multi-d.o.f. (degree-of-freedom) system is transformed into several single d.o.f. systems using selected eigenvectors. With the result from modal testing, each single d.o.f. system is used to solve for a pair of unknown physical parameters. For complicated cases where the exact eigenvector cannot be obtained, it will be proven that a particular physical parameter has a stationary value in the neighborhood of an eigenvector. Therefore, a good approximation for a joint physical parameter can be obtained by using an approximate eigenvector and the exact value for the joint parameters can be reached by carrying out this process in an iterative way.

Richardson's Iteration With Dynamic Parameters and the SIP Incomplete Factorization for the Solution of Linear Systems of Equations

1981 ◽  
Vol 21 (06) ◽  
pp. 699-708
Author(s):  
Paul E. Saylor
Keyword(s):  
Linear Systems ◽  
Field Data ◽  
Symmetric Matrix ◽  
Simple Problem ◽  
Test Problems ◽  
Physical Parameters ◽  
Incomplete Factorization ◽  
The Real ◽  
Hydrocarbon Reservoir ◽  
Linear Algebraic Equations

Abstract Reservoir simulation yields a system of linear algebraic equations, Ap=q, that may be solved by Richardson's iterative method, p(k+1)=p(k)+tkr(k), where r(k)=q-Ap(k) is the residual and t0, . . . tk are acceleration parameters. The incomplete factorization, Ka, of the strongly implicit procedure (SIP) yields an improvement of Richardson's method, p(k+1)=p(k)+tkKa−1r(k). Parameter a originates from SIP. The product of the L and U factors produced by SIP gives Ka=LU. The best values of the tk acceleration parameters may be computed dynamically by an efficient algorithm; the best value of a must be found by trial and error, which is not hard for only one value. The advantages of the method are (1) it always converges, (2) with the exception of the a parameter, parameters are computed dynamically, and (3) convergence is efficient for test problems characterized by heterogeneities and transmissibilities varying over 10 orders of magnitude. The test problems originate from field data and were suggested by industry personnel as particularly difficult. Dynamic computation of parameters is also a feature of the conjugate gradient method, but the iteration described here does not require A to be symmetric. Matrix Ka−1 A must be such that the real part of each eigenvalue is nonnegative, or the real part of each is nonpositive, but not both positive and negative. It is in this sense that the method always converges. This condition is satisfied by many simulator-generated matrices. The method also may be applied to matrices arising from the simulation of other processes, such as chemical flooding. Introduction The solution of a linear algebraic system, Ap=q, is a basic, costly step in the numerical simulation of a hydrocarbon reservoir. Many current solution methods are impractical for large linear systems arising from three-dimensional simulations or from reservoirs characterized by widely varying and discontinuous physical parameters. An iterative solution is described with these two main advantages:it is efficient for difficult problems andthe selection of iteration parameters is straightforward. The method is Richardson's method applied to a preconditioned linear system. Matrix A may be symmetric or nonsymmetric. In the simulation of multiphase flow, it is usually nonsymmetric. Convergence behavior is shown for four examples. Two of these, Examples 3 and 4, were provided by an industry laboratory (Exxon Production Research Co.), and were suggested by personnel as especially difficult to solve; SIP failed to converge and only the diagonal method1 was effective. Convergence of Richardson's method is compared with the diagonal method using data from a laboratory run. The other two examples are: Example 1, a matrix not difficult to solve, generated from field data, and Example 2, a variant of a difficult matrix described by Stone.2 The easy matrix of Example 1 is included to show the performance of Richardson's method (with preconditioning) on a simple problem.

Identification of physical parameters with memory in non-linear systems

1995 ◽  
Vol 30 (6) ◽  
pp. 841-860 ◽  
Author(s):  
Julius S. Bendat ◽  
Robert N. Coppolino ◽  
Paul A. Palo
Keyword(s):  
Linear Systems ◽  
Physical Parameters ◽  
Non Linear ◽  
Non Linear Systems ◽  
With Memory

On Degeneracy of Eigenvalues and Recursive Solution of Symmetrically Coupled Dynamic Systems

1970 ◽  
Vol 37 (4) ◽  
pp. 1180-1182
Author(s):  
Fan Y. Chen
Keyword(s):  
Dynamic Systems ◽  
Coupled System ◽  
Circulant Matrix ◽  
Mathematical Induction ◽  
Degree Of Freedom ◽  
Recursive Solution ◽  
Direct Inspection

Based on mathematical induction, we can prove that the eigenvalues of a special nth order circulant matrix are degenerate. Hence the eigenvibration problem of an n degree-of-freedom symmetrically coupled system with equal masses and equal spring stiffnesses can be solved by direct inspection of the system schematic.

Sign in / Sign up

Export Citation Format

Share Document