• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.75-84
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• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• 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.

• Journal of Ocean Engineering and Technology
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• v.1 no.1
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• pp.57-64
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• 1987

Methods of nonlinear stochastic analysis of guyed towers are studied in this paper. Two different kinds of nonlinearities are considered. They are the nonlinear restoring force from the guying system and the nonlinear hydrodynamic force. Analyses are carried out mainly in the frequency domain using linearization techniques. Two methods for the linearization of the nonlinear stiffness are presented, in which the effects of the steady offset and the oscillating component of the structural motion can be adequately analyzed. those two methods are the equivalent linearization method and the average stiffness method. The linearization of the nonlinear drag force is also carried out considering the effect of steady current as well as oscillatory wave motions. Example analyses are performed for guyed tower in 300m water. Transfer functions and the expected maximum values of the deck displacement and the bending moment near the middle of the tower are calculated. Numerical results show that both of the frequency domain methods presented in this paper predict the responses of the sturcture very reasonably compared with those by the time integration method utilzing the random simulations wave particla motions.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.747-756
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• 2022

This study presents the nonlinear free and forced vibrations of a cracked atomic force microscopy (AFM) cantilever by using the modified couple stress. The cracked section of the AFM cantilever is considered and modeled as rotational spring. In the frame work of Euler-Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory, the nonlinear equation of motion for the cracked AFM is derived by Hamilton's principle and then discretized by using the Galerkin's method. The semi-inverse method is utilized for analysis nonlinear free oscillation of the system. Then the method of multiple scale is employed to investigate primary resonance of the system. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, Tip-Mass, the magnitude and the location of the external excitation force on the nonlinear free and forced vibration behavior of the system.

• Steel and Composite Structures
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• v.25 no.1
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• pp.19-34
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• 2017

The widespread damage to steel Moment Resisting Frames (MRFs) in past major earthquakes have underscored the need to understand the nonlinear inelastic behaviour of such systems. To assess the seismic performance of steel MRF, it is essential to model the nonlinear force-deformation behaviour of beam to column joints. To determine the extent of inelasticity in a beam to column joint, nonlinear finite element analysis is generally carried out, which is computationally involved and demanding. In order to obviate the need of such elaborate analyses, a simplistic method to predict the force-deformation behaviour is required. In this study, a simple, mechanics driven, hand calculation method is proposed to obtain the forcedeformation behaviour of strong axis beam to column moment joints. The force-deformation behaviour for twenty-five interior and exterior beam to column joints, having column to beam strength ratios ranging from 1.2 to 10.99 and 2.4 to 22, respectively, have been obtained. The force-deformation behaviour predicted using the proposed method is compared with the results of finite element analyses. The results show that the proposed method predicts the force-deformation behaviour fairly accurately, with much lesser computational effort. Further the proposed method has been used to conduct Nonlinear Dynamic Time History Analyses of two benchmark frames; close correspondence of results obtained with published results establishes the usefulness and computational accuracy of the method.

• The Journal of the Acoustical Society of Korea
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• v.14 no.5
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• pp.29-35
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• 1995

Nonlinear distortion arising from the nonlinear movement of the loudspeaker diaphragm degradates the tone quality. The distortion is, in low frequency range, mainly caused by nonlinear characteristics of the suspension stiffness and the force factor. In this paper, the nonlinear suspension stiffness and the nonlinear force factor are modeled to the quadratic functions and a method is proposed to determine their coefficients. An additional mass to the diaphragm moved the quiescent point of the diaphragm and uncoupled the stiffness and the force factor. This made it possible to deter mine the coefficients of the nonlinear suspension stiffness by measuring the resonance frequencies at several quiescent points. The coefficients of the nonlinear force factor are then determined by fitting the curve which is calculated from the waveforms of input voltage and input current, and the displacement of the diaphragm at resonance frequency.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.105-112
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• 2006

The nonlinear damping force model is made to identify the properties of the ER (electro-rheological) fluid suspension damper. The instrumentation is carried out to measure the damping force of the ER damper. The higher order spectral analysis method is used to investigate the nonlinear frequency coupling phenomena with the damping force signal according to the sinusoidal excitation of the damper. The distinctive higher order nonlinear characteristics are observed. The nonlinear damping force model, which has the higher order velocity terms, is proposed with the result of higher order spectrum analysis. The higher order terms coefficients, which vary according to the strength of the electric field, are calculated using the least square method.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1045-1059
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• 2015

Form-finding for cable-membrane structures is a delicate operation. During the last decades, the force density method (FDM) was considered to be an efficient method to address the problem. Many researchers were devoted to improving this method and proposed many methods such as natural force density method (NFDM), improved nonlinear force density method (INFDM), et al. In this paper, a modified nonlinear force density method (MNFDM) is proposed. In this method, the stresses of membrane elements were transformed to the force-densities of cable nets by an equivalent relationship, and then they can be used as initial conditions. By comparing with the forming finding results by using the FDM, NFDM, INFDM and MNFDM, it had demonstrated that the MNFDM presented in this paper is the most efficient and precise.

• Journal of Korean Association for Spatial Structures
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• v.21 no.4
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• pp.49-56
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• 2021

This study aims to develop a form-finding algorithm for a single-layered pneumatic membrane. The initial shape of this pneumatic membrane, which is an air-supported type pneumatic membrane, is to find a state in which a given initial tension and internal pneumatic pressure are in equilibrium. The algorithm developed to satisfy these conditions is that a nonlinear optimization problem based on the force method considering the deformed shape is formulated, and, it's able to find the shape by iteratively repeating the process of obtaining a solution of the governing equations. An computational technique based on the Gauss-Newton method was used as a method for obtaining solutions of nonlinear equations. In order to verify the validity of the proposed form-finding algorithm, a single-curvature pneumatic membrane example and a double-curvature air pneumatic membrane example were adopted, respectively. In the results of these examples, it was possible to well observe the step-by-step convergence process of the shape of the pneumatic membrane, and it was also possible to confirm the change in shape according to the air pressure. In addition, the calculation results of the shape and internal force after deformation due to initial tension, air pressure, and self-weight were obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.458-466
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• 1998

In this work, a frequency domain method is tested numerically and experimentally to improve nonlinear model parameters using the frequency response function at the nonlinear element connected point of structure. This method extends the force-state mapping technique, which fits the nonlinear element forces with time domain response data, into frequency domain manipulations. The force-state mapping method in the time domain has limitations when applying to complex real structures because it needd a time domain lumped parameter model. On the other hand, the frequency domain method is relatively easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of each substurcture. Since this mehtod is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude bot also selecting excitation frequency domain method has some advantages over the classical force-state mapping technique in the number of data points needed in curve fit and the sensitivity to response noise.