Effect of spacewise variations in a random load field on the response of a linear system
Effect of spacewise variations in random load field on response of linear system - statistical mechanics
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Effect of spacewise variations in random load field on response of linear system - statistical mechanics
Dynamic response of cylindrical shell to random acoustic excitation
Closed cylindrical shell response for acoustic excitation random in time and deterministic in space
The fatigue damage of a space propulsion system component is computed using probabilistic structural analysis methods. The analysis takes into account the variations in static and dynamic loads, the uncertainty in structural damping, and the scatter in material fatigue resistance. The key elements of the probabilistic approach include: (1) a numerical engine model for describing the global component interface loads consistent with engine balance, (2) models for computing the local mode boundary conditions on the component, (3) a static structural analysis model that captures the strains at a damage critical location as a function of engine performance variables, (4) a finite element model for assessment of the random amplitude stress response due to random base and pressure excitations with uncertain power and correlation length, and (5) advanced first order reliability methods for computing the probabilities associated with the fatigue damage.
Mode coupling effect on response of rigid body to random excitation analyzed, using two degree of freedom model
In this method, the gust velocities are represented as rolling gusts, yawing gusts, and side gusts. Random distributions of gust velocities across the span are taken into account in defining the rolling and yawing gusts. Complex stability derivatives are used to account for the random distribution of side gusts along the fuselage and vertical tail and the lag effects in gust penetration. A sample calculation procedure is presented for obtaining the response of the airplane in each degree of freedom.
The random vibration response of a gas bearing rotor support system has been experimentally and analytically investigated in the amplitude and frequency domains. The NASA Brayton Rotating Unit (BRU), a 36,000 rpm, 10 KWe turbogenerator had previously been subjected in the laboratory to external random vibrations, and the response data recorded on magnetic tape. This data has now been experimentally analyzed for amplitude distribution and magnetic tape. This data has now been experimentally analyzed for amplitude distribution and frequency content. The results of the power spectral density analysis indicate strong vibration responses for the major rotor-bearing system components at frequencies which correspond closely to their resonant frequencies obtained under periodic vibration testing. The results of amplitude analysis indicate an increasing shift towards non-Gaussian distributions as the input level of external vibrations is raised. Analysis of axial random vibration response of the BRU was performed by using a linear three-mass model. Power spectral densities, the root-mean-square value of the thrust bearing surface contact were calculated for specified input random excitation.
Mechanical single degree of freedom system mean square response to AM random noise, considering frequency response, input excitation spectrum, etc
On the P6M the shake behavior, i.e., the response to random excitation at subcritical speeds of lowly damped airplane modes, is as important as the actual flutter speed. The approach is to first study the problem by means of analyses and wind-tunnel tests. These predictions are compared with flight test data obtained by spectral analysis of tape recordings of the airplane vibration responses to random aerodynamic turbulence. A similar spectrum analysis approach was used in high speed wind-tunnel tests. A resonance excitation technique was developed for low speed wind-tunnel testing, and well defined V-g curves were obtained. The effect of various parameters on both shake and flutter of T-tails with and without dihedral were studied. Preliminary flight tests yielded good correlation; they also yielded interesting information concerning a low frequency transonic snaking mode, and excitation by shed vortices.
An algorithm is developed to obtain the free responses of a structure from its random responses due to some unknown or known random input or inputs, using the random-decrement technique without changing time correlation between signals. The algorithm is tested using random responses from a 'generalized payload' model and from the 'Space Shuttle' model. The resulting free responses are then used to identify the modal characteristics of the two systems.
The effects of various gust alleviation methods on the random blade response in flapping were studied analytically, assuming a rigid rotor support. The analytical model assumes rigid flapping blades with elastic root restraints. Linearized equations which are approximately valid at low lift conditions were used. Because of the interblade coupling from the feedback devices, the method of multiblade generalized coordinates was most convenient and was extended to include coning, differential coning, and warping of the rotor. The numerical examples cover the dynamic stability characteristics as affected by feedback gains of three- to six-bladed rotors. The number of blades had large effects on stability limits and modal time functions at these limits. The random flapping response of the blades to atmospheric turbulence was determined at 1.6 rotor advance ratio using feedback gains below the stability limit. The most effective reduction of the flapping response per unit gain was achieved with a rotor coning angle feedback.
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We report a new method for the noninvasive characterization of the frequency response of the autonomic nervous system (ANS) in mediating fluctuations in heart rate (HR). The approach entails computation of the transfer function magnitude and phase between instantaneous lung volume and HR. Broad band fluctuations in lung volume were initiated when subjects breathed on cue to a sequence of beeps spaced randomly in time. We studied 10 subjects in both supine and standing positions. The transfer function, averaged among all the subjects, showed systematic differences between the two postures, reflecting the differing frequency responses of the sympathetic and parasympathetic divisions of the ANS.
The response of an infinite Bernoulli-Euler plate placed on the surface of a randomly vibrating viscoelastic half-space is calculated, allowing for the presence of shear stresses between the plate and the half-space. The shear stresses arise from the condition that the relative motion between the plate and the half-space vanishes at the interface. The three components of displacement of the free surface of the half-space before the plate is added are assumed to be stationary homogeneous random functions of position and time. From the wavenumber-frequency spectra of these displacements the frequency spectra of the three components of displacement of the plate half-space interface are calculated. As an example, the frequency spectrum of the vertical interface displacement is calculated for two assumed forms of the wavenumber spectra of the free-surface displacements.
This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.
This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.
A comparison with NASA conducted simulator studies has shown that the approximate digital method for computing rotor blade flapping responses to random inputs, tentatively suggested in Phase I Report, gives with increasing rotor advance ratio the wrong trend. Consequently, three alternative methods of solution have been considered and are described: (1) an approximate method based on the functional relation between input and output double frequency spectra, (2) a numerical method based on the system responses to deterministic inputs and (3) a perturbation approach. Among these the perturbation method requires the least amount of computation and has been developed in two forms - the first form to obtain the response correlation function and the second for the time averaged spectra of flapping oscillations.