Non-linear stochastic dynamics of a cable-mass system with finite bending stiffness via an equivalent linearization technique

In high-rise buildings earthquake ground motions induce bending deformation of the host structure. Large dynamic displacements at the top of the building can be observed which in turn lead to the excitation of the cables/ropes within lift installations. In this paper, the stochastic dynamics of a cable with a spring-damper and a mass system deployed in a tall cantilever structure under earthquake excitation is considered. The non-linear system is developed to describe lateral displacements of a vertical cable with a concentrated mass attached at its lower end. The system is moving slowly in the vertical direction. The horizontal displacements of the main mass are constrained by a spring-viscous damping element. The earthquake ground motions are modelled as a filtered Gaussian white noise stochastic process. The equivalent linearization technique is then used to replace the original non-linear system with a linear one with the coefficients determined by utilising the minimization of the mean-square error between both systems. Mean values, variances and covariances of particular random state variables have been obtained by using the numerical calculation. The received results were compared with the deterministic response of the system to the harmonic process and were verified against results obtained by Monte Carlo simulation.

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Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique

Meccanica ◽

10.1007/s11012-020-01169-3 ◽

2020 ◽

Vol 55 (12) ◽

pp. 2413-2422 ◽

Cited By ~ 1

Author(s):

Hanna Weber ◽

Stefan Kaczmarczyk ◽

Radosław Iwankiewicz

Keyword(s):

Tuned Mass Damper ◽

Equivalent Linearization ◽

Base Excitation ◽

Cable System ◽

Linearization Technique ◽

Linear Dynamic ◽

Transverse Modes ◽

Mass Damper ◽

Non Linear ◽

Host Structure

AbstractNon-linear dynamic model of a cable–mass system with a transverse tuned mass damper is considered. The system is moving in a vertical host structure therefore the cable length varies slowly over time. Under the time-dependent external loads the sway of host structure with low frequencies and high amplitudes can be observed. That yields the base excitation which in turn results in the excitation of a cable system. The original model is governed by a system of non-linear partial differential equations with corresponding boundary conditions defined in a slowly time-variant space domain. To discretise the continuous model the Galerkin method is used. The assumption of the analysis is that the lateral displacements of the cable are coupled with its longitudinal elastic stretching. This brings the quadratic couplings between the longitudinal and transverse modes and cubic nonlinear terms due to the couplings between the transverse modes. To mitigate the dynamic response of the cable in the resonance region the tuned mass damper is applied. The stochastic base excitation, assumed as a narrow-band process mean-square equivalent to the harmonic process, is idealized with the aid of two linear filters: one second-order and one first-order. To determine the stochastic response the equivalent linearization technique is used. Mean values and variances of particular random state variable have been calculated numerically under various operational conditions. The stochastic results have been compared with the deterministic response to a harmonic process base excitation.

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In-Place FE Modeling of Unbonded Flexible Pipelines Capturing Pressure Stiffening and Decoupled Axial/Nonlinear Bending Stiffness

29th International Conference on Ocean, Offshore and Arctic Engineering: Volume 5, Parts A and B ◽

10.1115/omae2010-20014 ◽

2010 ◽

Author(s):

Edvin Hanken ◽

Evelyn R. Hollingsworth ◽

Lars S. Fagerland

Keyword(s):

Water Injection ◽

Bending Stiffness ◽

Axial Stiffness ◽

Fe Model ◽

Nonlinear Bending ◽

Upheaval Buckling ◽

History Effects ◽

System Integrity ◽

Non Linear ◽

Bending Behaviour

For fast track pipeline projects the need for costly installation vessels and sophisticated materials for rigid pipeline water injection systems, have made flexible pipelines a competitive alternative. They can be installed with less costly construction vessels, provide a competitive lead time and a corrosion resistant compliant material. Flexible pipelines have relative high axial stiffness and low non-linear bending stiffness which is a challenge to model correctly with FE for in-place analyses of pipelines. Whilst some FE programs can model the non-linear bending behaviour of a flexible pipeline at a given pressure, current FE tools do not include the effect of increased bending resistance as the system is pressurized. Therefore, a 3D FE model in ANSYS was developed to simulate the decoupled axial and nonlinear bending behaviour of a flexible, including the bend stiffening effect for increasing pressure. A description of the model is given in this paper. It will be demonstrated how the FE model can be used to simulate the 3D nonlinear catenary behaviour of an high pressure flexible pipeline tied into a manifold during pressurization. Due to high manifold hub loads during pressurization it is essential that such a model is capable of capturing all effects during pressurization to achieve an acceptable confidence level of the system integrity. It is also described how the FE model is used for upheaval buckling design, capturing non-linearities and load history effects that can reduce the conservatism in the design.

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Evaluation of Seismic Demand for Substandard Reinforced Concrete Structures

The Open Construction and Building Technology Journal ◽

10.2174/1874836801812010009 ◽

2018 ◽

Vol 12 (1) ◽

pp. 9-33

Author(s):

Nicholas Kyriakides ◽

Ahmad Sohaib ◽

Kypros Pilakoutas ◽

Kyriakos Neocleous ◽

Christis Chrysostomou ◽

...

Keyword(s):

Reinforced Concrete ◽

Seismic Performance ◽

Performance Prediction ◽

Brittle Failure ◽

Failure Modes ◽

Shaking Table ◽

Equivalent Linearization ◽

Diagram Method ◽

Capacity Curves ◽

Non Linear

Background: Reinforced Concrete (RC) buildings with no seismic design exhibit degrading behaviour under severe seismic loading due to non-ductile brittle failure modes. The seismic performance of such substandard structures can be predicted using existing capacity demand diagram methods through the idealization of the non-linear capacity curve of the degrading system, and its comparison with a reduced earthquake demand spectrum. Objective: Modern non-linear static methods for derivation of capacity curves incorporate idealization assumptions that are too simplistic and do not apply for sub-standard buildings. The conventional idealisation procedures cannot maintain the true strength degradation behaviour of such structures in the post-peak part, and thus may lead to significant errors in seismic performance prediction especially in the cases of brittle failure modes dominating the response. Method: In order to increase the accuracy of the prediction, an alternative idealisation procedure using equivalent elastic perfectly plastic systems is proposed herein that can be used in conjunction with any capacity demand diagram method. Results: Moreover, the performance of this improved equivalent linearization procedure in predicting the response of an RC frame is assessed herein. Conclusion: This improved idealization procedure has been proven to reduce the error in the seismic performance prediction as compared to seismic shaking table test results [1] and will be further investigated probabilistically herein.

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