Dynamic Response Of Linear Systems Research Articles

Laplace-Time Domain Method for Computing Dynamic Response of Linear Systems to Arbitrary Intermittent Loadings

AbstractIn evaluating of the response of linear systems to arbitrary intermittent loadings, traditional methods have been exclusively conducted in the time domain where the time resolution must be ...

Control of fractional periodic discrete-time linear systems by parametric state feedback matrices

In this article stabilization of fractional-order periodic discrete-time linear system by a complete nonlinear parametric approach for pole assignment with respect to stability and reachability of system via state feedback is proposed. To modify the dynamic response of linear system we should change the poles of state feedback matrices. Nonlinear parametric feedback matrix makes some freedoms in conditions such as minimum norm of feedback matrix. But it makes large monodromy matrix and changing all of eigenvalues makes some problems. Reassigning a part of bad spectrums, leaving the rest of the spectrums invariant, we have lower-ordered matrix to modify the dynamic response of linear system and we can make nonlinear parametric for this new lower-ordered matrix by less expenses and better stability conditions. Numerical examples illustrate the effectiveness of the proposed approaches.

Control of Fractional Periodic Discrete-Time Linear Systems by Partial Eigenvalue Assignment of State Feedback Matrices

In this article to control of fractional-order periodic discrete-time linear system a special form of state feedback matrix is proposed to assign suitable eigenvalues to closed-loop monodromy matrix of the periodic discrete-time system. It makes large monodromy matrix and changing all of eigenvalues make some problems. By reassigning a part of bad spectrums of monodromy matrix, leaving the rest of the spectrums invariant, we have lower oredered matrix to modify the dynamic response of linear system and we can lie the poles of this systems in the unit circle by less expenses. Controlling the alternating states by other controllers such that the controllability of the resulting system is preserved. The effectiveness of our algorithm is illustrated by an example.

A modal correction method for non-stationary random vibrations of linear systems

The computational effort in determining the dynamic response of linear systems is usually reduced by adopting the well-known modal analysis along with modal truncation of higher modes. However, in the case in which the contribution of higher modes is not negligible, modal correction methods have been introduced to improve the accuracy of the dynamic response, for both deterministic and stochastic input. In the latter case the random response is usually corrected via various methods determined as rough extensions of methods originally proposed for deterministic input. Consequently the efficiency of the correction methods is not suitable, from both theoretical and computational points of view. In this paper, a new approach to cope with the non-stationary response of linear systems is presented. The proposed modal correction method provides a correction term determined as a pseudo-stationary contribution of the equation governing either first-order or second-order statistics. Owing to the fact that no truncation criteria are well established for random vibration study, the proposed modal correction method offers a suitable vehicle for determining very accurately the stochastic response of MDOF linear systems under Gaussian stationary and non stationary excitation as evidenced in the numerical applications.

DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES

We present a generalized theory for dealing with the dynamic response of linear systems to moving sources. Stochastic characteristics of the response of linear systems to moving stochastic sources are theoretically analyzed based on the time-convolution expression established in this paper. We show that the random response of a linear system under a moving stationary stochastic source becomes a non-stationary process, for which the commonly used spectral analysis is not valid. To overcome this obstacle, the follow-up spectral analysis procedure is introduced. Statistical characteristics of the dynamic response are then given in the fixed and follow-up co-ordinates. A brief physical explanation related to time-frequency domain analysis is also provided. The theory developed in the paper can be universally applied to the moving source problem for linear systems.

Dynamic response analysis in the frequency domain

AbstractAnalysis in the frequency domain using discrete Fourier transforms is an efficient means of calculating the dynamic response of linear systems. In fact, for systems with frequency dependent parameters and also in those cases where the complex frequency response functions are more easily determined, frequency domain analysis may be the only effective means of determining the dynamic response. The use of discrete transforms along with finite summation requires that the forcing function and the impulse function be converted into periodic forms. This modification may introduce unacceptable errors in the results of analysis, unless appropriate steps are taken to avoid or minimize the effect of aliasing or overlapping. For single‐degree‐of‐freedom systems, procedures that will eliminate the effect of aliasing have already been developed. However, problems related to frequency domain analysis still exist for multi‐degree‐of‐freedom systems with non‐proportional damping, in analysis through substructuring and in those cases where a continuum solution is involved. A new procedure which addresses these problems and is applicable to both single‐ and multi‐degree‐of‐freedom system as well as to analysis through substructuring is presented here.

Efficient analysis of dynamic response of linear systems

AbstractAfter reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady‐state response, a modified procedure is presented which also appears to be highly efficient for non‐classically damped systems of the type encountered in studies of soil‐structure interaction. The concepts involved are developed by reference to viscously damped single‐degree‐of‐freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.

Use of trigonometric interpolation for the analytical determination of the dynamic response of linear systems to arbitrary inputs

Commonly the loadings associated with the dynamic excitation of structural systems are expressed in the form of discrete time series. By the use of trigonometric interpolation these inputs may be transformed into continuous time functions. The dynamic response of a linear structural system when subjected to such inputs may be computed by modal analysis techniques. These methods require the solution of a set of uncoupled second-order linear ordinary differential equations with constant coefficients. The trigonometric interpolation function is a finite series of sine and cosine terms and hence it becomes a straightforward matter to solve the set of uncoupled differential equations for the displacements. Solutions obtained in this manner are also seen to be continuous functions expressed as finite series in sines and cosines. The associated velocities and accelerations may be easily obtained by differentiation of these expressions. The method is also free from the errors inherent in step-by-step integration methods, and the errors in the numerical determination of Duhamel integrals. The derivation of the coefficients of the time-series inputs and of the final evaluation of the dynamic response are both executed by a simple recursive algorithm which is fast and accurate. Since the only errors occur in the initial expression of the input a finite series of elementary functions—and these errors can be made very small—the method is a novel and attractive alternative to existing procedures. It is illustrated here by the computation of the dynamic response of a skeletal space frame when subjected to earthquake ground motions.