摘要 :
Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However...
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Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However, in large scale industrial applications, there is no general methodology for dynamicists to extract nonlinear parameters from measured vibration data so that these can be then included in the associated numerical models. In this paper, a simple method based on the information contained in the frequency response function (FRF) properties of a structure is studied. This technique falls within the category of single-degree-of-freedom (SDOF) modal analysis methods. The principle upon which it is based is effectively a linearisation whereby it is assumed that at given amplitude of displacement response the system responds at the same frequency as the excitation and that stiffness and damping are constants. In so doing, by extracting this information at different amplitudes of vibration response, it is possible to estimate the amplitude-dependent 'natural' frequency and modal loss factor. Because of its mathematical simplicity and practical implementation during standard vibration testing, this method is particularly suitable for practical applications. In this paper, the method is illustrated and new analyses are carried out to validate its performance on numerical simulations before applying it to data measured on a complex aerospace test structure as well as a full-scale helicopter.
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In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member ...
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In this paper, a nonlinear analysis of three-dimensional steel frames is developed. This analysis accounts for material and geometric nonlinearities. The material nonlinearity considers the gradual yielding associated with member forces. The geometric nonlinearioty includes the second-order effects associated with P-δ and P-△. The material nonlinearity at a section is considered using the concept of the P-m hinge consisting of many fibers. The geometric nonlinearity is considered by the use of stability functions. The modified incremental displace- ment method is used as the solution technique. The load-displacement relationships predicted by the proposed analysis compare well with those given by other approaches.
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The conventional switching strategy for solving the inverted pendulum control problem is based on two steps: swinging-up and stabilization. In this note, first, a new strategy for swinging the Furuta pendulum up towards the desire...
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The conventional switching strategy for solving the inverted pendulum control problem is based on two steps: swinging-up and stabilization. In this note, first, a new strategy for swinging the Furuta pendulum up towards the desired upright position is designed using the Speed-Gradient method, which uses only directly measured coordinates. Then, a nonlinear controller, based on the Forwarding approach, stabilizes the upright position. As a new contribution the latter leads to a nonlinear stabilizer around the upright position, whose Lyapunov function yields a larger size estimation of the domain of attraction than the one obtained with the traditional linear approach. This estimation allows us to use it in a global switching strategy in the practical implementation and guarantees almost-global asymptotic stability of the equilibrium. Successful experimental results are reported with the available laboratory Furuta pendulum.
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The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled sys...
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The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.
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Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to com...
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Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources.
Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration.
Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as:
equivalent reduced model technique (ERMT);
modal modification response technique (MMRT); and
component element method (CEM);
are presented in this paper and are compared to traditional methods.
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We present in this paper a short survey of some recent interactions between Nonlinear Analysis and Nonlinear Complementarity. Considering the new relations between Nonlinear Analysis and Complementarity Theory, put in evidence in ...
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We present in this paper a short survey of some recent interactions between Nonlinear Analysis and Nonlinear Complementarity. Considering the new relations between Nonlinear Analysis and Complementarity Theory, put in evidence in this paper, we define several open research subjects profitable to both domains.
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Diodes and transistors, which are widely used in microwave frequencies, have nonlinearities in current-voltage (I-V) and capacitance-voltage (C-v) characteristics of their junction. Their nonlinear characteristics are utilized to ...
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Diodes and transistors, which are widely used in microwave frequencies, have nonlinearities in current-voltage (I-V) and capacitance-voltage (C-v) characteristics of their junction. Their nonlinear characteristics are utilized to implement large-signal microwave devices, e.g., frequency converters, frequency multipliers, frequency dividers, and amplifiers. This report presents how we analyze the performance characteristics of these devices. The report focuses the analysis that is based upon time-domain concept, partly incorporating frequency-domain technique.
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A new design method of three-dimensional truss bridges using practical advanced analysis is presented. Separate member capacity checks encompassed by the code specifications are not required, because the stability of separate memb...
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A new design method of three-dimensional truss bridges using practical advanced analysis is presented. Separate member capacity checks encompassed by the code specifications are not required, because the stability of separate members and the structure as a whole can be rigorously treated in determing the maximum strength of the structures. The geometric nonlin- earity is considered using the updated Lagrangian formulation.
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Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear s...
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Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is non-zero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity-norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L-infinity. These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class of nonlinear feedback systems. Copyright (C) 2000 John Wiley & Sons, Ltd. [References: 21]
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The signals that originate from the human cardiovascular system were analysed using methods of both linear and nonlinear system theory. The analyses in the time domain and in the phase space revealed the deterministic and almost c...
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The signals that originate from the human cardiovascular system were analysed using methods of both linear and nonlinear system theory. The analyses in the time domain and in the phase space revealed the deterministic and almost conservative nature of the cardiovascular control system on the time scale of minutes. Five characteristic frequencies were found in the signal of peripheral blood flow. Some of them had already been found in other cardiovascular functions, the breathing, blood pressure, ECG and HRV. Each characteristic peak reflects the periodic action of one of the subsystems, involved in the regulation of the blood flow. These systems are mutually dependent, via the couplings among them. Their strength plays an essential role in the performance of the system. In some cases their importance is indicted, thus pointing to practical applications in the diagnosis and prediction of cardiovascular functions.
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