Nonstationary Response of Linear Time-Varying Dynamical Systems to Random Excitation

1973 ◽  
Vol 40 (2) ◽  
pp. 422-428 ◽  
Author(s):  
F. Y. M. Wan
Keyword(s):  
Rotor Blade ◽  
Linear Time ◽  
Expansion Method ◽  
Random Excitation ◽  
Variable Coefficients ◽  
Perturbation Series ◽  
Rotating Speed ◽  
Nonstationary Response ◽  
New Information ◽  
Mean Square Response

A direct time-domain method is used to analyze the titled problem. Special attention is paid to a system characterized by a general second-order equation with variable coefficients. The equation of flapping motion of a rigid rotor blade advancing in atmospheric turbulence belongs to this class. Steady-state mean-square response to ideal white noise and to exponentially correlated excitation is obtained by a perturbation series solution in a stiffness parameter. An upperbound of the same is derived. Explicit solution for the correlation matrix is obtained by the two-variable expansion method. Specialized to the rotor blade problem, the results have led to some new information concerning the blade behavior in a certain range of rotating speed. They have also served as useful check cases for computer programs developed for more general problems. Higher-order equations and their applications are also discussed.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Response of Rotor Blades to Random Loads under Forward Flight Conditions

1973 ◽  
Vol 24 (4) ◽  
pp. 252-260 ◽  
Author(s):  
C Lakshmikantham ◽  
K S Aravamudan
Keyword(s):  
Rotor Blade ◽  
Random Excitation ◽  
Rotor Blades ◽  
Linear Dynamical System ◽  
Forward Flight ◽  
Filtering Theory ◽  
Random Loads ◽  
Helicopter Rotor Blade ◽  
System Equations ◽  
Blade Model

SummaryThis paper contains results for the response of a helicopter rotor blade under stationary random excitation when the helicopter is in forward flight. The blade model takes into account the bending and torsional modes as well as the root-rigidity conditions. The resulting linear dynamical system equations with periodic coefficients are treated within the framework of the filtering theory to yield matrix ordinary differential equations for the required response-statistics themselves.

Nonlinear and Time-Varying Dynamical Models of Human Operators in Manual Control Systems

1966 ◽  
Vol 8 (2) ◽  
pp. 97-120 ◽  
Author(s):  
Walter W. Wierwille ◽  
Gilbert A. Gagne
Keyword(s):  
Control System ◽  
Linear Time ◽  
Human Operator ◽  
Manual Control ◽  
Time Variability ◽  
Time Varying ◽  
Deterministic Theory ◽  
Manual Control System ◽  
New Information ◽  
Human Operators

This paper describes the application of a deterministic theory for characterizing or modeling the dynamics of a human operator in a manual control system. Linear time-varying, nonlinear time-varying, and non-linear constant-coefficient models are obtained by applying the theory to tracking data taken for one- and two-axis tasks with various displays. The accuracy and fidelity of these advanced models are explored in detail. Also, new information about time variability and nonlinearity of the human operator, obtained by studying the models and the manual control system signals, is presented.

Mean-Square Response of Thermoviscoelastic Medium to Nonstationary Random Excitation

1976 ◽  
Vol 43 (1) ◽  
pp. 150-158 ◽  
Author(s):  
W. Mosberg ◽  
M. Yildiz
Keyword(s):  
Random Excitation ◽  
Irreversible Thermodynamics ◽  
Envelope Function ◽  
Statistical Characteristics ◽  
Mean Square ◽  
Statistical Property ◽  
Step Functions ◽  
Mean Square Response ◽  
The Mean ◽  
Thermoviscoelastic Medium

The mean-square wave response of a lightly damped thermoviscoelastic medium to a special type of nonstationary random excitation is determined. The excitation function on the thermoviscoelastic medium is taken in the form of a product of a well-defined, slowly varying envelope function, and a part which prescribes the statistical characteristics of the excitation. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. By taking into consideration the slow variation envelope function and the wave characteristics of the lightly damped thermoviscoelastic medium, the mean-square response (as a function of temperature, excitation, and damping parameters with the aid of reversible and irreversible thermodynamics) is evaluated.

scholarly journals Modeling of vibration for functionally graded beams

2016 ◽  
Vol 14 (1) ◽  
pp. 661-672 ◽  
Author(s):  
Gülsemay Yiğit ◽  
Ali Şahin ◽  
Mustafa Bayram
Keyword(s):  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Bernoulli Beam ◽  
Adomian Decomposition ◽  
Graded Material ◽  
Euler Bernoulli Beam

AbstractIn this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

Mean-Square Response of Simple Mechanical Systems to Nonstationary Random Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 221-227 ◽  
Author(s):  
R. L. Barnoski ◽  
J. R. Maurer
Keyword(s):  
White Noise ◽  
Random Noise ◽  
Random Excitation ◽  
Correlated Noise ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Step Functions ◽  
Unit Step ◽  
Mean Square Response ◽  
The Mean

This paper concerns the mean-square response of a single-degree-of-freedom system to amplitude modulated random noise. The formulation is developed in terms of the frequency-response function of the system and generalized spectra of the nonstationary random excitation. Both the unit step and rectangular step functions are used for the amplitude modulation, and both white noise and noise with an exponentially decaying harmonic correlation function are considered. The time-varying mean-square response is shown not to exceed its stationary value for white noise. For correlated noise, however, it is shown that the system mean-square response may exceed its stationary value.

Performance of Particle Dampers Under Random Excitation

1996 ◽  
Vol 118 (4) ◽  
pp. 614-621 ◽  
Author(s):  
A. Papalou ◽  
S. F. Masri
Keyword(s):  
Wide Band ◽  
Small Mass ◽  
Random Excitation ◽  
Primary System ◽  
Mass Ratio ◽  
Impact Damper ◽  
Mean Square Response ◽  
Small Model ◽  
Particle Dampers ◽  
Auxiliary Mass

An experimental and analytical study is made of the performance of particle dampers under wide-band random excitation. A small model, provided with a nonlinear auxiliary mass damper, was used to investigate the major system parameters that influence the performance of particle dampers: total auxiliary mass ratio, particle size, container dimension, and the intensity and direction of the excitation. It is shown that properly designed particle dampers, even with a relatively small mass ratio, can considerably reduce the response of lightly damped structures. An approximate analytical solution, which is based on the concept of an equivalent single unit-impact damper, is presented. It is shown that the approximate solution can provide an adequate estimate of the root-mean-square response of the randomly excited primary system when provided with a particle damper that is operating in the vicinity of its optimum range of parameters.

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