Large Amplitude Free Vibrations of a Uniform Cantilever Beam Carrying an Intermediate Lumped Mass and Rotary Inertia

Hamdan, M. A.; Dado, Mohammad

doi:10.1006/jsvi.1997.1081

Cited by 56 publications

(58 citation statements)

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“…The last term is a static-type cubic nonlinearity associated with the potential energy stored in bending. The modal constants α and β result from the discretization procedure and they have specific values for each mode as described in (Hamdan and Dado, 1997).…”

Section: Introductionmentioning

confidence: 99%

“…The Structural engineering theory is based upon physical laws and empirical knowledge of the structural performance of different landscapes and materials. Many engineering structures can be modelled as a slender, flexible cantilever beam carrying a lumped mass with rotary inertia at an intermediate point along its span; hence they experience large-amplitude vibration (Wu, 2003;Herisanu and Marinca, 2010;Cveticanin and Kovacic, 2007;Hamdan and Shabaneh, 1997;Hamdan and Dado, 1997). …”

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confidence: 99%

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Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

Nikkar

2014

Lat. Am. j. solids struct.

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In this paper, a mathematical model of large amplitude vibration of a uniform cantilever beam arising in the structural engineering is proposed. Two efficient and easy mathematical techniques called variational iteration method and He's variational approach are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. An excellent agreement of the approximate frequencies and periodic solutions with the numerical results and published results has been demonstrated. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics. The Structural engineering theory is based upon physical laws and empirical knowledge of the structural performance of different landscapes and materials. Many engineering structures can be modelled as a slender, flexible cantilever beam carrying a lumped mass with rotary inertia at an intermediate point along its span; hence they experience large-amplitude vibration (Wu, 2003;Herisanu and Marinca, 2010;Cveticanin and Kovacic, 2007;Hamdan and Shabaneh, 1997;Hamdan and Dado, 1997). Key wordsIn general, such problems are not amenable to exact treatment and approximate techniques must be resorted to. So, many new techniques have appeared in the open literature such as: variational iteration method (He, 2007a;Barari et al., 2011), homotopy perturbation method Saravi et al., 2013), homotopy analysis method (Liao, 2003;Khan et al., 2012)and some other methods Ghasempoor et al., 2102;Akbarzade and Khan, 2012;Alinia et al., 2011;Ganji, 2012;Torabi et al., 2012;

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

Nikkar

2014

Lat. Am. j. solids struct.

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“…The nonlinear inertial term, on the other hand, softens the response of the structure and reduces its natural frequency [21]. However, its contribution becomes significant at resonances higher than the first mode [20]. Potentially, additional sources of nonlinearity may appear during the experimental study of cantilever isotropic slender beams because of practical reasons such as the manner in which the beam is clamped to the surrounding material at its boundaries.…”

Section: Nonlinear Dynamics Of Undamaged and Damaged Structuresmentioning

confidence: 96%

“…Nonlinearity in the dynamic response of structures can be instigated by material properties such as nonlinear constitutive relations [14,15], nonideal boundary conditions [16,17], complex multiaxial loading [18], damping mechanisms [19], and large-deformation kinematics (geometric nonlinearity) with inertial effects [20]. Geometric nonlinearity arises from nonlinear strain-displacement relations for large deformations and produces a nonlinear stiffening effect that appears in many engineering applications [21,22].…”

Section: Nonlinear Dynamics Of Undamaged and Damaged Structuresmentioning

confidence: 99%

“…Because the beam length to width ratio is kept short (AR < 30), it can be assumed that the beam undergoes purely planar flexural vibrations as long as the tip mass and cross-section geometry are symmetric with respect to the beam's centerline [45]. The assumed first mode deflection is the exact linear mode shape generated from solving the linear problem with attached lumped mass that includes the rotary inertia effect [20,44].…”

Section: Model Developmentmentioning

confidence: 99%

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Detection of fatigue damage precursor using a nonlinear vibration approach

Habtour

Cole

Riddick

et al. 2016

Struct. Control Health Monit.

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SUMMARYA nonlinear dynamic methodology is developed for detecting and estimating fatigue damage precursor in isotropic metal structures, prior to fatigue crack initiation, based on measurement of changes in the structure nonlinear response to harmonic base excitation. As an example, a damage precursor feature was extracted for cantilever beams by quantifying the reduction in the nonlinear stiffness because of localized microscopic material softening. The nonlinear dynamic analytical model parametrically tracks changes in the nonlinear structural stiffening as a function of the structural response and the loading cycles. Experimental results are obtained by exciting the base of cantilever beams at various amplitude levels. At high response amplitudes, the beams experience three competing simultaneous nonlinear dynamic mechanisms: (i) stiffening because of high response amplitude at the fundamental mode; (ii) softening because of inertial forces; and (iii) softening because of localized microscopic material damage caused by cyclic micro-plasticity. The third mechanism-a potential precursor to fatigue crack initiation in the structure-resulted in a cumulative softening because of early accumulation of cyclic fatigue damage and is the focus of this study. The loading intensity and the number of cycles influenced the relative contribution of these dynamic mechanisms. Nanoindentation studies near the beam clamped boundary were conducted to confirm the fatigue degradation in the local mechanical properties as a function of loading cycles. The proposed detection method is simple to implement and detects the presence of damage precursors but lacks the resolution to discern spatial distributions of the damage intensity. Based on prior knowledge of the structural dynamic characteristics of the beam and using the proposed methodology, damage level and stiffness reduction can be detected and estimated based on changes in the nonlinear structural response. The nonlinear stiffness term in the equation of motion is found to be very sensitive to the proposed fatigue damage precursor, making it an effective method for monitoring structural degradation prior to crack developments. The proposed methodology provides new insights and constitutes a significant step toward the development of new inspection techniques.

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Natural Frequencies and Ope–loop Responses of an Elastic Beam Fixed on a Moving Cart and Carrying an Intermediate Lumped Mass

Park

Chung

Youm

et al. 2000

Journal of Sound and Vibration

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Large Amplitude Free Vibrations of a Uniform Cantilever Beam Carrying an Intermediate Lumped Mass and Rotary Inertia

Cited by 56 publications

References 0 publications

Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

Detection of fatigue damage precursor using a nonlinear vibration approach

Natural Frequencies and Ope–loop Responses of an Elastic Beam Fixed on a Moving Cart and Carrying an Intermediate Lumped Mass

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