Large amplitude free flexural vibration of rings using finite element approach

Patel, B.P.; Ganapathi, M.; Makhecha, Dhaval P.; Shah, P.H.

doi:10.1016/s0020-7462(02)00037-9

Cited by 21 publications

(14 citation statements)

References 11 publications

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“…As shown in Table 2, all coefficients are positive, hence, all of the modes are softening in agreement [13,15,28]. Figure 4 shows the softening backbone surface of the lowest flexural mode (m ¼ 2) of a linearly elastic ring.…”

Section: Linearly Elastic Ringsmentioning

confidence: 71%

“…Moreover, the presence of the companion mode in the nonlinear response of rings was shown to arise when large-amplitude oscillations are excited by large external excitations. More recently, in [15,28] a numerical method based on a finite-element procedure was adopted to study nonlinear vibrations of elastic oval rings. The numerical simulations, aimed at reproducing the backbone curves of the lowest three driven modes of both oval and circular rings, showed a very good agreement with the analytical results existing in the literature [14,33], and confirmed the softening behavior theoretically and experimentally predicted by Evensen. Nonlinear dynamics of circular cylindrical shells were also studied from different standpoints, such as equilibrium states under pressures [2,4], parametric resonances of breathing and flexural motions [5,8,16,17,21,26,30], or interactions between coupled modes in nonlinear flexural motions [19].…”

Section: Introductionmentioning

confidence: 99%

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Flexural vibrations of nonlinearly elastic circular rings

2014

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This paper treats free nonlinear flexural vibrations of circular elastic rings in the context of a geometrically exact formulation accounting for the effects of nonlinear material behavior. A direct asymptotic approach based on the method of multiple scales is used to investigate such vibrations. It is shown that the flexural motions are softening for linearly elastic rings, in agreement with previous results in the literature, while there are nonlinearly elastic rings for which the motions are hardening. There are thresholds in the nonlinear constitutive laws separating softening from hardening behaviors

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Section: Linearly Elastic Ringsmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Flexural vibrations of nonlinearly elastic circular rings

2014

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“…The above displacement variations in the circumferential direction are chosen according to the physics of the large deformation of shells of revolution i.e., participation of axisymmetric mode and higher asymmetric modes (Amabili et al, 1999;Patel et al, 2003;Tong and Pian, 1974;Ueda, 1979).…”

Section: Formulationmentioning

confidence: 99%

Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells

Patel

Nath

Shukla

2006

International Journal of Solids and Structures

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Here, the nonlinear thermo-elastic buckling/post-buckling characteristics of laminated circular conical-cylindrical/ conical-cylindrical-conical joined shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach. The nonlinear governing equations, considering geometric nonlinearity based on von KarmanÕs assumption for moderately large deformation, are solved using Newton-Raphson iteration procedure coupled with displacement control method to trace the pre-buckling/post-buckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, material properties and number of circumferential waves on the nonlinear thermo-elastic response of the different joined shell systems.

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“…They derived the nonlinear equations of motion of the ring using Hamilton's principle and linearized these equations to obtain the natural frequency of the ring. Patel et al [8] analyzed the vibration of isotropic and orthotropic circular rings. They considered the nonlinearity caused by the large deformation of the ring and used nite-element method to study the mechanical behavior of the ring.…”

Section: Introductionmentioning

confidence: 99%

Effect of size dependency on in-plane vibration of circular micro-rings

2017

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KEYWORDSMicro-ring; Modi ed couple stress theory; Resonant frequency.Abstract. In this paper, based on the modi ed couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The ndings are compared with classical beam theories. Response of the micro-ring under application of static and dynamic loads is investigated and compared with the classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modi ed couple stress are considerably more than those predicted based on the classical beam theories, while the de ection and natural frequencies of the classical and non-classical beam theories approach one another for the rings with thickness much larger than the material length scale.

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Large amplitude free flexural vibration of rings using finite element approach

Cited by 21 publications

References 11 publications

Flexural vibrations of nonlinearly elastic circular rings

Flexural vibrations of nonlinearly elastic circular rings

Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells

Effect of size dependency on in-plane vibration of circular micro-rings

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