The method of equivalent linearization

In this paper, the method design controller based on the feedback linearization control (FLC) method with optimal parameter for time response thanks to BAT algorithm for magnetic levitation system (MLS). Feedback linearization controller based on equivalent transformations brings a nonlinear system into linear form, then uses the poles-placement method to find parameters for the linear tracking controller.

17p viengels 25-08-2023 4 4   Download

The objectives of the thesis: The thesis has developed a technique by combining the equivalent linearization method and the weighted averaging value to analyze the responses of some undamped free nonlinear vibrations.

31p extraenglish 24-05-2021 11 2   Download

The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler–Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution.

23p nguaconbaynhay11 07-04-2021 19 2   Download

The thesis has developeda technique by combining the equivalent linearization method and the weighted averagingvalueto analyze the responses of some undamped free nonlinear vibrations.

31p capheviahe29 17-03-2021 23 2   Download

Propose the global – local mean square error criterion (GLOMSEC) for Gaussian equivalent linearization method (GEL) for randomly excited MDOF nonlinear system subjected to white noise or color noise excitation. The mean square of response solution will be concentrated to evaluate the accuracy of the proposed criterion by comparison with exact solution or other accepted solutions.

28p capheviahe26 25-01-2021 7 1   Download

The paper shows that the response of the random Rayleigh system, which is under harmonic and random excitations, can be found by a system of algebraic equations. The analytical approach is based on the stochastic averaging method and equivalent linearization method in Cartesian coordinates so that the Fokker-Planck equation associated with the linear equations obtained can be solved exactly by the technique of auxiliary function. The harmonic excitation frequency is taken to be in the neighborhood of the system natural frequency.

11p trinhthamhodang9 10-12-2020 19 0   Download

In this paper, a method for determining the limit load surface of fiber-reinforced nonlinear composites such as elasto-plastic composite is proposed. Using the stress approach of the homogeneous theory and the linear matching method (LMM).

12p tohitohi 19-05-2020 13 0   Download

This paper proposes an accurate, computationally efficient, and spectrum-free formulation of the heat diffusion smoothing on 3D shapes, represented as triangle meshes. The idea behind our approach is to apply a ðr;rÞ-degree Pade´–Chebyshev rational approximation to the solution of the heat diffusion equation. The proposed formulation is equivalent to solve r sparse, symmetric linear systems, is free of user-defined parameters, and is robust to surface discretization.

7p trinhthamhodang1 16-11-2019 25 2   Download

The objective of the thesis: Establishing thermal models of single-node, two-node and many-node associated with different thermal loading models acting on a small satellite in Low Earth Orbit. Finding analytical solutions of equations of thermal balance for small satellites by the dual criterion equivalent linearization method.

27p xacxuoc4321 08-07-2019 35 6   Download

A new method determining the equivalent dynamic parameters such as stiffness, vibrating mass, and air damping factor in motion direction of shuttle (i.e. in ydirection) is proposed, thence the differential motion equation of shuttle is established and solved to achieve a typical displacement formula.

10p danhdanh11 09-01-2019 19 1   Download

In this paper responses of beams subjected to random loading are analyzed by the dual approach of the equivalent linearization method. The external random loading is assumed to be a space-wise and time-wise white noise in which the exact solutions of the modal equations can be found.

14p thienthanquydu 23-10-2018 31 0   Download

The normalized weighting coefficient is suggested as a piecewise linear function of the squared correlation coefficient and is defined by the least square method based on the data of Lutes-Sarkani oscillator. The application to two typical nonlinear systems subjected to random excitation shows accurate approximations when the nonlinearity varies from the weak to strong levels.

15p thienthanquydu 21-10-2018 27 0   Download

In the study an extension of the Bubnov-Galerkin method in terms of the equivalent linearization method is presented. It is combined with sequential linearization and nonlinear procedure to yield a new method for solving nonlinear equations which can improve the accuracy when the nonlinearity is strong. For illustration the Duffing oscillator is considered to show the effectiveness of the proposed method.

6p thienthanquydu 17-10-2018 28 1   Download

In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing oscillator is considered to demonstrate the effectiveness of the proposed technique.

4p thienthanquydu 17-10-2018 42 0   Download