• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Structural Engineering and Mechanics
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• v.85 no.1
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• pp.119-133
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• 2023

Impact event is the key factor influencing the operational state of the mechanical equipment. Additionally, nonlinear factors existing in the complex mechanical equipment which are currently attracting more and more attention. Therefore, this paper proposes a novel hybrid-separate identification strategy to solve the force identification problem of the nonlinear structure under impact excitation. The 'hybrid' means that the identification strategy contains both l1-norm (sparse) and l2-norm regularization methods. The 'separate' means that the nonlinear response part only generated by nonlinear force needs to be separated from measured response. First, the state-of-the-art two-step iterative shrinkage/thresholding (TwIST) algorithm and sparse representation with the cubic B-spline function are developed to solve established normalized sparse regularization model to identify the accurate impact force and accurate peak value of the nonlinear force. Then, the identified impact force is substituted into the nonlinear response separation equation to obtain the nonlinear response part. Finally, a reduced transfer equation is established and solved by the classical Tikhonove regularization method to obtain the wave profile (variation trend) of the nonlinear force. Numerical and experimental identification results demonstrate that the novel hybrid-separate strategy can accurately and efficiently obtain the nonlinear force and impact force for the nonlinear structure.

• Steel and Composite Structures
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• v.41 no.6
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.694-699
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• 2007

The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring,nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). In NROEL, the external loads are teansformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response no EL. The objective function is defined by minimizing the maximum stress in the spring while is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.

• Korean Chemical Engineering Research
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• v.61 no.1
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• pp.89-96
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• 2023

The Wiener-type nonlinear model where a static nonlinear block follows a dynamic linear block is widely used to describe the dynamics of chemical processes. A long process excitation step is typically needed to identify this Wiener-type nonlinear model with two blocks. In order to cope with this disadvantage, an identification method for the Wiener-type nonlinear model that uses only a single-step response is proposed here. The proposed method estimates the response of the dynamic linear sub-block from the initial part of the step response, and then the static nonlinear sub-block is identified. Because the only single-step response is used to identify the Wiener-type nonlinear model, there is great benefit in time and cost for obtaining process response. The performance of the proposed identification method with the single-step response is verified through a representative Wiener-type nonlinear process, a pH titration process, and a liquid level system.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1256-1261
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• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2005.03a
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• pp.372-379
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• 2005

The earthquake resistant design concept allows the nonlinear behavior of structures under the design earthquake. Therefore the response spectrum method provided in most codes introduces the response modification factors to consider the nonlinear behavior in the design process. For bridges, the response modification factors are given according to the ductility as well as the redundancy of piers. In this study, among influence factors on the nonlinear seismic behavior, the randomness of artificial accelerograms simulated with different durations, the pier ductility represented by the inelastic behavior characteristic curve and the regularity represented by pier heights are selected. The influence of such factor on the seismic behavior is investigated by comparing response modification factors calculated with the nonlinear time step analysis.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.311-319
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• 2001

Recently, the number of seismically isolated bridges increased suddenly since the occurrence of strong earthquakes. However, because isolator lies between pier and girder, the response of the superstructure of seismically isolated bridge may be magnified and induce risk of unseating girder Consequently, the response of girder constitutes a crucial factor in designing bridge. In the case of frictional bearing, the inherent nonlinearity makes the use of former linear response spectrum unable to estimate the maximum response of the bearing, and nonlinear tlme history analysis shall be applied. In this paper, nonlinear response spectrum considering frictional element is established, and simple analysis method using such nonlinear spectrum is proposed to estimate the maximum response of the superstructure.

• Wind and Structures
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• v.5 no.5
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• pp.423-440
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• 2002

The effects of the nonlinear (quadratic) term in wind pressure have been analyzed in many papers with reference to linear structural models. The present paper addresses the problem of the response of nonlinear structures to stochastic nonlinear wind pressure. Adopting a single-degree-of-freedom structural model with polynomial nonlinearity, the solution is obtained by means of the moment equation approach in the context of It$\hat{o}$'s stochastic differential calculus. To do so, wind turbulence is idealized as the output of a linear filter excited by a Gaussian white noise. Response statistical moments are computed for both the equivalent linear system and the actual nonlinear one. In the second case, since the moment equations form an infinite hierarchy, a suitable iterative procedure is used to close it. The numerical analyses regard a Duffing oscillator, and the results compare well with Monte Carlo simulation.

• Structural Engineering and Mechanics
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• v.46 no.5
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• pp.695-711
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• 2013

It is reasonable to assume that reinforced concrete (RC) structures enter the nonlinear range of response during a severe ground motion. Numerical analysis to predict the behaviour therefore must allow for the presence of nonlinear deformations if an accurate estimate of seismic response is aimed. Among the factors contributing to inelastic deformations, the influence of the degradation of the bond slip phenomenon is important. Any rebar slip generates an additional rotation at the end regions of structural members which are not accounted for in a conventional analysis. Although these deformations could affect the seismic response of RC structures considerably, they are often neglected due to the unavailability of suitable models. In this paper, the seismic response of two types of RC structures, designed according to the Iranian concrete code (ABA) and the Iranian seismic code (2800), are evaluated using nonlinear dynamic and static analyses. The investigation is performed using nonlinear dynamic and static pushover analysis considering the deformations due to anchorage slip. The nonlinear analysis results confirm that bond slip significantly influences the seismic behavior of RC structure leading to an increase of lateral deformations by up to 30% depending on the height of building. The outcomes also identify important parameters affecting the extent of this influence.