Large amplitude free vibrations of tapered beams

Raju, Lakshmi; Raju, K. Kanaka; Rao, G. Venkateswara

doi:10.2514/3.7095

Cited by 21 publications

(14 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where subscripts t and X denote partial differentiation with respect to time and the material coordinate, respectively, and bars were omitted for convenience. Conditions (7) and (8) remain unchanged. It can be easily proved that the system of equations (10) is of the parabolic type.…”

Section: Governing Equationsmentioning

confidence: 99%

Non‐Linear Vibration of a Cantilever Beam of Variable Cross‐Section

Pielorz

Nadolski

1986

Z Angew Math Mech

View full text Add to dashboard Cite

Es werden freie Schwingungen grober Amplitude eines diinnen elastischen Balkens fester Lange mit variablem Querschnitt untersucht. Obwohl groJe Auslenkungen und Drehungen betrachtet werden, sind die Dehnungen klein. Es wird gezeigt, wie man mittels des Galerkinverfahrens Naherungslosungen erhalt, und es wird der Effekt des variablen Querschnitts untersucht. Fur den Balken mit konstantem Querschnitt werden die Ergebnisse mit denen aus der Arbeit 131 verglichen, und es wird. die exakte Losung fur den Spezialfall einer in dieser Arbeit gewonnenen gewohnlichen Differentialgleichung betrachtet. Zusatzlich wird eine einfache Methode fur statische Auslenkungen vorgeschlagen.Large amplitude free vibration of an inextensible thin elastic beam of a variable cross-section is analysed. Although large deflections and rotations are considered the strains are smdl. It is shown how approximate solutions can be obtained by using Galerkin's method, and the effect of the variation of cross-section is investigated. For the beam of constant cross-section the results are compared with those of paper [3] and the exact solution of the special case of an ordinary differential equation obtained in the paper is considered. Additionally, a simple method for static deflections of the beam is proposed. MeHHoro cesetrm. X o~a paccMaTpusamca 60nbmue oTnnonemn .EI BpaweHm, ne@opMauuu ocTamTcfi ManbiMu. I I o K~~~I B~~T c~, nan iionywTb npu6nulrce~~~1e pemeHm nocpencmoM MeToaa FanepHma, II usysae~ca B@@BKT nepeMemoro cesemm. Peaynb~a~br paccseTa B cnysae 6anm ~O C T O R H H O~O ceseHm cpasmBamcR c p e a y n b~a~a~u pa6om f3] u pacciwaqmsaews TosHoe pememe B sacTHoM cnyqae nony-Yemoro B pa6o~e O~~I~H O B~H H O~O nu@@epeHuuamHoro ypamemrr. AononmTenbHo npeAnaraeTcR npo-C T O~~ MeToa ~n r r CTaTmecKux oTnnoHeH&i. H3y' IaIOTCR CB060AHbIe ~o n e 6 a~u r r 60nbmux aMnnllTyA TOHHOa YnpJTOii 6anm IIOCTOFIIHHOfi AJIIlHbI II nepe-14, 280-282 (1976). 303-306 (1981).

show abstract

Section: Governing Equationsmentioning

confidence: 99%

Non‐Linear Vibration of a Cantilever Beam of Variable Cross‐Section

Pielorz

Nadolski

1986

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…Raju et al [9] analyzed large amplitude free vibrations of tapered beams using continuum and finite element methods. Mahmoud et al [10] applied the differential transformation method (DTM) for free vibration analysis of beams with uniform and non-uniform cross sections.…”

Section: Introductionmentioning

confidence: 99%

Large Amplitude Free Vibration Analysis of Tapered Timoshenko Beams Using Coupled Displacement Field Method

Korabathina

Saheb

2018

International Journal of Applied Mechanics and Engineering

View full text Add to dashboard Cite

Tapered beams are more efficient compared to uniform beams as they provide a better distribution of mass and strength and also meet special functional requirements in many engineering applications. In this paper, the linear and non-linear fundamental frequency parameter values of the tapered Timoshenko beams are evaluated by using the coupled displacement field (CDF) method and closed form expressions are derived in terms of frequency ratio as a function of slenderness ratio, taper ratio and maximum amplitude ratio for hinged-hinged and clamped-clamped beam boundary conditions. The effectiveness of the CDF method is brought out through the solution of the large amplitude free vibrations, in terms of fundamental frequency of tapered Timoshenko beams with axially immovable ends. The results obtained by the present CDF method are validated with the existing literature wherever possible.

show abstract

“…J " 5 The geometric nonlinearity is due to the axial force generated by stretching because of the immovability of the supports, The theory in Refs. longitudinal inertia and large deformation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of beams with variable axial restraint

Prathap

1978

AIAA Journal

View full text Add to dashboard Cite

integration schemes may be checked. It is important that the solution for depends on one (prescribed) parameter X only. Once solved, an infinite number of solutions can be generated directly by adjusting A 0 . In this sense, $ is defined by a twoparameter family of solutions. Because d/l/d/ = X^O, the solution would correspond to an initially "steady" solution with an "impulse" at t = Q + . For X = 0, of course, our formulation is just the Murman-Cole problem. Nomenclaturê(£) >A o = area at any station, reference station #(£) = nondimensional area variation I(£}Jo = moment of inertia at any station, reference station / (£) = nondimensional inertia variation E = modulus of elasticity F(t) = time function F p (t)>Fq.(t) = summed up inertial forces at a station H B -spring force K = nondimensional spring constant (= kL/EA 0 ) k = spring constant L = length of beam M = bending moment at any station m 0 =mass per unit length of.beam at reference station N = axial force at any station p(%)= distributed inertial force Q = shear force at any station q (%) = distributed inertial force V B -vertical force at movable hinge U,V = displacements of a point on neutral axis in x,y directions u,v =U/L, V/L x,y = coordinate system a =V B L 2 /EI Q y = H B L 2 /EI 0 £ =x/L; nondimensional coordinate 0,6 0 = slope at any station, at reference station X -nondimensional quantity ( = m 0 u 2 L 4 /EI 0 ) p -radius gyration at reference station co = quantity characterizing vibration

show abstract

Large amplitude free vibrations of tapered beams

Cited by 21 publications

References 12 publications

Non‐Linear Vibration of a Cantilever Beam of Variable Cross‐Section

Non‐Linear Vibration of a Cantilever Beam of Variable Cross‐Section

Large Amplitude Free Vibration Analysis of Tapered Timoshenko Beams Using Coupled Displacement Field Method

Nonlinear vibration of beams with variable axial restraint

Contact Info

Product

Resources

About