FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2076753643> ?p ?o ?g. }

• W2076753643 endingPage "24" @default.
• W2076753643 startingPage "17" @default.
• W2076753643 abstract "The object of this paper is to analyze the coupled flatwise (out of plane) edgewise (in plane) vibrations of a beam rotating about one if its ends. The hub is assumed motionless and the vibration is considered to occur about a large deflected position. That is, coning and lagging angles are allowed to be large. The equations of motion are derived by a combination of techniques. The kinetic energy of the system is expressed in terms of coordinates lying in the beam. This is done by making use of four coordinate transformations that relate the beam coordinate system to a fixed coordinate system. The inertial load distribution is obtained by application of the first two terms of Lagrange's equation. These loads are used to compute the bending moment distribution which is substituted into Euler's beam bending equation. The equations of motion are solved by assuming a solution in the form of a linear combination of orthogonal modes. These equations are multiplied by the jth mode shape and integrated over the beam length. There are four terms resulting; the mass and elastic stiffness terms form a diagonal array and the Coriolis' and centrifugal spring terms form a full array. These equations may be solved by easily available matrix techniques. The modes chosen for the solution are the normal modes of the nonrotating beam. The advantage of this choice is that each of the modes already satisfies the problem boundary conditions. Since the non‐rotating modes are a good approximation to the rotating modes the series converges rapidly and can be cut off after a few terms. Several sample problems are worked out. First, the beam is assumed rigid and free to flap. The classical formula for flapping frequency is verified with the addition that the terms due to large cone and lag angles are included. Second, the same problem is done except that instead of the flapping degree of freedom the lagging degree of freedom is analyzed. The classical formula for lagging is also verified for the zero cone angle. When the cone angle is large this degree of freedom becomes statically unstable. Third, the above problem is redone for the coupled lagging — flapping degrees of freedom. Fourth, a flexible beam is assumed with zero cone and lag angles. Mode shapes and frequencies are computed as a function of rotor speed. It is shown that as rotor speed increases the beam mode shapes and frequencies approach those of a chain. That is, the elastic stiffness becomes negligible relative to the centrifugal stiffness. The advantages of the formulation developed in this paper (in addition to allowing consideration of large coning and lagging angles) are: 1) that the terms that involve rotor speed (the centrifugal spring and the Coriolis coupling) have that parameter as a factor multiplying the whole matrix so that if frequencies and modes are required over a range of rotor speeds the centrifugal and Coriolis' terms need only be calculated once; 2) at large rotor speeds the Myklestad analysis has difficulty converging but in this procedure, because the non‐rotating modes already satisfy the boundary conditions, there is no difficulty in convergence." @default.
• W2076753643 created "2016-06-24" @default.
• W2076753643 creator A5052012303 @default.
• W2076753643 date "1966-10-01" @default.
• W2076753643 modified "2023-10-17" @default.
• W2076753643 title "Vibrations of a Rotating Beam" @default.
• W2076753643 cites W2051049009 @default.
• W2076753643 doi "https://doi.org/10.4050/jahs.11.17" @default.
• W2076753643 hasPublicationYear "1966" @default.
• W2076753643 type Work @default.
• W2076753643 sameAs 2076753643 @default.
• W2076753643 citedByCount "4" @default.
• W2076753643 crossrefType "journal-article" @default.
• W2076753643 hasAuthorship W2076753643A5052012303 @default.
• W2076753643 hasConcept C10138342 @default.
• W2076753643 hasConcept C105815890 @default.
• W2076753643 hasConcept C120665830 @default.
• W2076753643 hasConcept C121332964 @default.
• W2076753643 hasConcept C128172907 @default.
• W2076753643 hasConcept C134306372 @default.
• W2076753643 hasConcept C14037181 @default.
• W2076753643 hasConcept C162324750 @default.
• W2076753643 hasConcept C168834538 @default.
• W2076753643 hasConcept C17825722 @default.
• W2076753643 hasConcept C182310444 @default.
• W2076753643 hasConcept C198082294 @default.
• W2076753643 hasConcept C198394728 @default.
• W2076753643 hasConcept C24890656 @default.
• W2076753643 hasConcept C2524010 @default.
• W2076753643 hasConcept C32758168 @default.
• W2076753643 hasConcept C33923547 @default.
• W2076753643 hasConcept C74050887 @default.
• W2076753643 hasConcept C74650414 @default.
• W2076753643 hasConcept C80551277 @default.
• W2076753643 hasConceptScore W2076753643C10138342 @default.
• W2076753643 hasConceptScore W2076753643C105815890 @default.
• W2076753643 hasConceptScore W2076753643C120665830 @default.
• W2076753643 hasConceptScore W2076753643C121332964 @default.
• W2076753643 hasConceptScore W2076753643C128172907 @default.
• W2076753643 hasConceptScore W2076753643C134306372 @default.
• W2076753643 hasConceptScore W2076753643C14037181 @default.
• W2076753643 hasConceptScore W2076753643C162324750 @default.
• W2076753643 hasConceptScore W2076753643C168834538 @default.
• W2076753643 hasConceptScore W2076753643C17825722 @default.
• W2076753643 hasConceptScore W2076753643C182310444 @default.
• W2076753643 hasConceptScore W2076753643C198082294 @default.
• W2076753643 hasConceptScore W2076753643C198394728 @default.
• W2076753643 hasConceptScore W2076753643C24890656 @default.
• W2076753643 hasConceptScore W2076753643C2524010 @default.
• W2076753643 hasConceptScore W2076753643C32758168 @default.
• W2076753643 hasConceptScore W2076753643C33923547 @default.
• W2076753643 hasConceptScore W2076753643C74050887 @default.
• W2076753643 hasConceptScore W2076753643C74650414 @default.
• W2076753643 hasConceptScore W2076753643C80551277 @default.
• W2076753643 hasIssue "4" @default.
• W2076753643 hasLocation W20767536431 @default.
• W2076753643 hasOpenAccess W2076753643 @default.
• W2076753643 hasPrimaryLocation W20767536431 @default.
• W2076753643 hasRelatedWork W1604715137 @default.
• W2076753643 hasRelatedWork W2035347472 @default.
• W2076753643 hasRelatedWork W2036827061 @default.
• W2076753643 hasRelatedWork W2076753643 @default.
• W2076753643 hasRelatedWork W2137248510 @default.
• W2076753643 hasRelatedWork W2160125190 @default.
• W2076753643 hasRelatedWork W2564631833 @default.
• W2076753643 hasRelatedWork W3135352094 @default.
• W2076753643 hasRelatedWork W3171887922 @default.
• W2076753643 hasRelatedWork W4313639704 @default.
• W2076753643 hasVolume "11" @default.
• W2076753643 isParatext "false" @default.
• W2076753643 isRetracted "false" @default.
• W2076753643 magId "2076753643" @default.
• W2076753643 workType "article" @default.