Extension of equivalent linearization method to design of TMD for linear damped systems

Anh, Nguyen Dong; Nguyen, N. X.

doi:10.1002/stc.446

Cited by 31 publications

(36 citation statements)

References 15 publications

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“…where x s and x T are the relative displacements of the primary structure and TMD to the base, respectively, and the dot over the symbol denotes the derivative with respect to time t. If τ is defined as τ = ω s t, d/dt = ω s (d/dτ) and d 2 =dt 2 ¼ ω 2 s d 2 =dτ 2 À Á . Then, Eqn (13) becomes…”

Section: Optimum Design Based On Smcmentioning

confidence: 99%

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

Xiang

Nishitani

2015

Earthq Engng Struct Dyn

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SUMMARYA variant type of tuned mass damper (TMD) termed as 'non-traditional TMD (NTTMD)' is recently proposed. Mainly focusing on the employment of TMD for seismic response control, especially for base-isolated or high-rise structures, this paper aims to derive design formulae of NTTMDs based on two methodologies with different targets. One is the fixed points theory with the performance index set as the maximum magnitude of the frequency response function of the relative displacement of the primary structure with respect to the ground acceleration, and the other is the stability maximization criterion (SMC) to make the free vibration of the primary structure decay in the minimum duration. Such optimally designed NTTMDs are compared with traditional TMDs by conducting both numerical simulations and experiments. The optimum-designed NTTMDs are demonstrated to be more effective than the optimum-designed traditional TMDs, with smaller stroke length required. In particular, the effectiveness of the TMDs combined with a base-isolated structure is investigated by small-scale model experimental tests subjected to a time scaled long period impulsive excitation, and it is demonstrated that the SMC-based NTTMD can suppress structural free vibration responses in the minimum duration and requires much smaller accommodation space. Additionally, a small-scale shaking table experiment on a high-rise bending model attached with a SMC-based NTTMD is conducted. This study indicates that NTTMD has a high potential to apply to seismic response control or retrofit of structures such as base-isolated or central column-integrated high-rise structures even if only a limited space is available for accommodating TMDs.

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Section: Optimum Design Based On Smcmentioning

confidence: 99%

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

Xiang

Nishitani

2015

Earthq Engng Struct Dyn

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“…Thus, it is difficult to find closed‐form solutions for the optimal parameters of the TMD in the case of damped structural systems. Most design methods for the optimal parameters are evaluated numerically or are based on the approximate equivalent model . Ghosh and Basu presented approximate closed‐form solutions for the optimal parameters of the TMD by assuming the existence of two fixed points.…”

Section: Introductionmentioning

confidence: 99%

“…Most design methods for the optimal parameters are evaluated numerically or are based on the approximate equivalent model. [15][16][17][18] Ghosh and Basu 15 presented approximate closed-form solutions for the optimal parameters of the TMD by assuming the existence of two fixed points. Ioi and Ikeda 17 introduced an empirical expression by minimizing the acceleration response of a lightly damped structure.…”

Section: Introductionmentioning

confidence: 99%

Tuned mass damper on a damped structure

Fang

Liu

Zhang

et al. 2019

Struct Control Health Monit

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Summary The classic design of the tuned mass damper on an undamped structure is based on the “fixed‐point” theory introduced by Den Hartog. Because of the lack of fixed points in the dynamic amplification of damped structures, a generalization of previous methods is presented in this study to identify the optimal parameters of the damper. The optimal frequency is identified by analyzing complex natural frequencies. The resulting frequency leads to a confluence point in the complex frequency locus and an equal modal damping ratio for the two vibration modes, provided that the damping ratio of the damper is less than a critical value. This critical value can be used as an upper bound of the damping ratio value in practice that can effectively restrict the relative motion of the damper. The optimal damping ratio is identified by ensuring that the dynamic amplification reaches an extremum value at a reference frequency. It is demonstrated that the resulting damping ratio accounts for the reduction in the motion of the primary structure and relative motion of the damper. Furthermore, a modified design procedure is proposed to determine the optimal parameters of the damper for damped structures with multiple degrees of freedom. Several numerical experiments indicate the efficiency of the proposed parameters and design procedure.

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“…In addition, despite standard analytic approaches used in solving linear analytical problems, these methods are impractical in handling nonlinearities. Among various proposed methods for the analysis of nonlinear systems under random excitations, the equivalent linearization (EL) can be applied into different fields such as state space, time domain, distribution space, frequency domain, and characteristic function space, which makes it useful for various applications . Generally, this technique includes two main steps.…”

Section: Introductionmentioning

confidence: 99%

Orthogonal function‐based equivalent linearization for sliding mode control of nonlinear systems

Baghaei

Ghaffarzadeh

Younespour

2019

Struct Control Health Monit

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This paper proposes the equivalent linearization (EL) and sliding mode control (SMC) methods to address nonlinearity and enhance the performance of nonlinear systems subjected to nonstationary random excitations. The EL methods are commonly used to propose approximate solutions for nonlinear systems under random excitations due to the high computational demands in the exact analyses. Considering the application of orthogonal functions in improving the accuracy and efficiency of approximate solutions, an orthogonal block pulse (BP) function is applied to the EL method in this study to approximate the nonlinear system responses under nonstationary random excitations. The SMC, as a robust control method for systems with uncertainties and external disturbances, is capable of achieving reliable and accurate tracking control. This method is applied to effectively reduce the dynamic responses predicted by the proposed EL method under nonstationary random excitations. The proposed approach is tested on single-degreeof-freedom and two-degree-of-freedom Duffing systems subjected to a seismic type excitation. The results indicate that not only the orthogonal functionbased EL method can approximate the dynamic responses more accurately, at lower computational cost, and by a high agreement with the exact solution, but also the proposed SMC can improve the performance of nonlinear systems by effectively reducing the responses compared with the linear quadratic regulator control method.KEYWORDS block pulse functions, equivalent linearization, nonlinearity, sliding mode control Nomenclature: A, plant matrix of the system; B,B u , control location matrices; B r , excitation orientation vector; C,C eq , damping matrix and its equivalent value; E[·], mathematical expectation; g, nonlinear function of displacement and velocity; h, unit impulse-response function; J, cost function; J G ,J F , convolution operational matrix; K,K eq , stiffness matrix and its equivalent value; k, linear stiffness; M, mass matrix; m, positive integer value; P, sliding surface coefficient vector; Q,R, positive semidefinite and definite weighting matrices; q, width of block pulse

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Extension of equivalent linearization method to design of TMD for linear damped systems

Cited by 31 publications

References 15 publications

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

Tuned mass damper on a damped structure

Orthogonal function‐based equivalent linearization for sliding mode control of nonlinear systems

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