Non-linear theory for elastic spatial rods

Banan, M. R.; Karami, G.; Farshad, M.

doi:10.1016/0020-7683(91)90030-j

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…( 14) nor the geometrical constraint in Eq. (18). For this reason it has a certain error in Table 1.…”

Section: Let Us Investigatementioning

confidence: 99%

“…Hence, the considered i U in Eq. (18) achieved from combination of several modes of * U . In fact, the shown constraint of Figure 5 determines * U so that, the resultant vector in Eq.…”

Section: Exact Mathematical Solutionmentioning

confidence: 99%

“…Consequently, Pai and Nayfeh [7] showed that local stress and strain are required. A number of researchers focused their effort to find exact relation of deformed and un-deformed coordinates to model geometrical nonlinearities exactly [8][9][10][11][12][13][14][15][16][17][18][19]. The main problem in these researches was that the finite rotation in Euler coordinates transformation are neither independent from each other nor along a three orthogonal axis.…”

Section: Introductionmentioning

confidence: 99%

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Exact mathematical solution for nonlinear free transverse vibration of beams

Dalir

2019

Scientia Iranica

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In the present paper, an exact mathematical solution has been obtained for nonlinear free transverse vibration of beams, for the first time. The nonlinear governing partial differential equation in un-deformed coordinates system has been converted in two coupled partial differential equations in deformed coordinates system. A mathematical explanation is obtained for nonlinear mode shapes as well as natural frequencies versus geometrical and material properties of beam. It is shown that as the th mode of transverse vibration excited, the mode 2 th of in-plane vibration will be developed. The result of present work is compared with those obtained from Galerkin method and the observed agreement confirms the exact mathematical solution. It is shown that the governing equation is linear in the time domain. As a parameter, the amplitude to length ratio   Λ/l has been proposed to show when the nonlinear terms become dominant in the behavior of structure.

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“…( 14) nor the geometrical constraint in Eq. (18). For this reason it has a certain error in Table 1.…”

Section: Let Us Investigatementioning

confidence: 99%

“…Hence, the considered i U in Eq. (18) achieved from combination of several modes of * U . In fact, the shown constraint of Figure 5 determines * U so that, the resultant vector in Eq.…”

Section: Exact Mathematical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact mathematical solution for nonlinear free transverse vibration of beams

Dalir

2019

Scientia Iranica

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“…A relatively general theory of spatial rods taking into account the second-order effects arising from the axial forces have been developed by the author and his co-workers in a number of papers. On the basis of these theories, finite element models have also been developed and computer routines constructed [6][7][8][9][10]. A by-product of this theory has been its application to stability analyses of straight and curved rods.…”

Section: Review Of the Second Order Theory Of Spatial Rodsmentioning

confidence: 99%

Stability Control of Active Compressed Rods with Shape Memory Polymers

Farshad

2001

Journal of Thermoplastic Composite Materials

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In structural systems, applied compressive force fields cause second-order effects that may not only influence the buckling behavior, but also enhance the internal stress and the deformation field in the structure. Specifically, slender and thin-walled structural elements subjected to compressive force fields may experience buckling instability, which may affect their service life. In the case of imperfection-sensitive systems, loading and geometric imperfections may drastically affect the buckling response and reduce the buckling resistance. This behavior may be positively influenced by a structural adaptation to bending effects. In this connection, an attempt is made to use the potentials of the adaptive systems to influence the second-order as well as the buckling response of the slender compression elements by means of the actuator components. To this end, the stability control problem of adaptive slender rods with embedded Shape Memory Polymer (SMP) actuators is theoretically treated. The main goal of this investigation was to explore the possibility of minimizing the end deflection of a cantilever rod under eccentrically applied force via actuation of an SMP fiber. First, the stability theory of spatial rods is outlined, and the non-linear governing equations of straight rods are derived. The specific case treated is the problem of a cantilever rod with a single eccentric SMP fiber under eccentrically applied end compressive force. Numerical calculations were carried out with the help of the Runge-Kutta method. It is shown that the response of the rod can be effectively controlled by the appropriate action of the SMP actuator. Specifically, the goal of minimizing the end deflection of the eccentrically loaded cantilever rod through the action of the SMP actuator is achieved. In carrying out the computations, the second-order effects arising from the action of SMP fiber as well as the axial force were taken into consideration. Moreover, the follower action of the SMP force was considered.

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Bibliography

2004

Linear and Nonlinear Structural Mechanics

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Non-linear theory for elastic spatial rods

Cited by 5 publications

References 10 publications

Exact mathematical solution for nonlinear free transverse vibration of beams

Exact mathematical solution for nonlinear free transverse vibration of beams

Stability Control of Active Compressed Rods with Shape Memory Polymers

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