Matrix analysis of longitudinal and torsional vibrations in nonuniform multibranch beams
Matrix analysis of longitudinal and torsional vibrations in nonuniform multibranch beams
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Matrix analysis of longitudinal and torsional vibrations in nonuniform multibranch beams
Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.
An analysis of coupled torsion-flapping rotor blade vibrations in response to atmospheric turbulence revealed that at high rotor advance ratios anticipated for future high speed pure or convertible rotorcraft both flapping and torsional vibrations can be severe. While appropriate feedback systems can alleviate flapping, they have little effect on torsion. Dynamic stability margins have also no substantial influence on dynamic torsion loads. The only effective means found to alleviate turbulence caused torsional vibrations and loads at high advance ratio was a substantial torsional stiffness margin with respect to local static torsional divergence of the retreating blade.
Excessive vibration is one of the most prevalent technical obstacles encountered in the development of new rotorcraft. The inability to predict these vibrations is primarily due to deficiencies in analysis and simulation tools. The Langley Rotorcraft Structural Dynamics Program was instituted in 1984 to meet long term industry needs in the area of rotorcraft vibration prediction. As a part of the Langley program, this research endeavors to develop an efficient means of coupling the rotor to the airframe for preliminary design analysis of helicopter airframe vibrations. The main effort was to modify the existing computer program for modeling the dynamic and aerodynamic behavior of rotorcraft called DYSCO (DYnamic System COupler) to calculate the rotor impedance. DYSCO was recently developed for the U.S. Army and has proven to be adaptable for the inclusion of new solution methods. The solution procedure developed to use DYSCO for the calculation of rotor impedance is presented. Verification of the procedure by comparison with a known solution for a simple wind turbine model is about 75 percent completed, and initial results are encouraging. After the wind turbine impedance is confirmed, the verification effort will continue by comparison to solutions of a more sophisticated rotorcraft model. Future work includes determination of the sensitivity of the rotorcraft airframe vibrations to helicopter flight conditions and rotor modeling assumptions. When completed, this research will ascertain the feasibility and efficiency of the impedance matching method of rotor-airframe coupling for use in the analysis of airframe vibrations during the preliminary rotorcraft design process.
Theoretical analysis of free vibration of discretely stiffened cylindrical shells with arbitrary end conditions
Analysis of thermally induced structural vibrations by finite element techniques
Matrix-Holzer method for predicting free vibration modes of clustered launch vehicles in bending applied to first eight modes of Saturn I model
Human and animal heart function analyses by vibrocardiogram
Matrix-Holzer method for predicting free vibration modes of clustered launch vehicles in bending applied to first eight modes of Saturn I model
Measuring device, Randomdec, provides continuous on-line signatures representative of system free vibration curve. Selected points on curve are used in control and failure detection systems. Apparatus applied to both linear and nonlinear systems under nonstationary vibratory states.
NASTRAN program for calculating structural vibration characteristics of plate configurations
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.
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
A study has been conducted of the aeroelastic behavior of heat shield panels for the thermal protection system of the space shuttle. Questions of structural and aerodynamic modeling are considered along with the analysis of a single isotropic tile and an isotropic main substructure. Representative flutter results are presented, taking into account a rigid and a flexible metallic substructure.
A method that derives an approximate equivalent static load to a base excitation shock analysis is described. The transient analysis in the current level of NASTRAN, level 16, does not directly provide for either input acceleration forcing functions or enforced boundary displacement. In the suggested alternate analysis format, equivalent force input functions are applied to the constrained locations by using the artifice of placing a large mass, with respect to the total system mass, at the desired acceleration input points. This shortcut static analysis approach is presented to approximate the expensive and time consuming dynamics analysis approach to the base excitation shock analysis.
This paper presents a structural dynamic modeling of the Long Duration Exposure Facility (LDEF), which is a Space Shuttle payload of passive scientific experiments contained in trays mounted on a large cylindrically shaped structure. Special detailed finite element modeling, using the SPAR system of computer programs was required to obtain good agreement between analytical and test vibrations modes. Experimental trays contributed significantly to overall LDEF stiffnesses, and these contributions were realistically represented for each tray by the stiffness matrix of an equivalent orthotropic panel in the overall LDEF SPAR model. Orthotropic stiffnesses for this panel were obtained from finely detailed statically loaded tray SPAR models in which stiffness coupling was accounted for along with partial relative sliding allowed by the tray clamping attachments. Joint boundary conditions were also significant in the structural dynamic modeling of LDEF, and static data proved valuable in assessing modeling of local end fittings.
An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.
Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.