Laguerre Series Solutions of the Delayed Single Degree-of-Freedom Oscillator Excited by an External Excitation and Controlled by a Control Force

With increasing technologies, applications of delayed models are more frequently encountered in biology, physics and various fields of engineering. The single degree-of-freedom oscillator, on the other hand, is one of the fundamental systems in many physics and engineering problems; thus, solving the equation of this problem would serve for many other sophisticated problems. In this study, a novel and simple numerical method for the solution of this system is introduced in the matrix form based on Laguerre polynomials. The method is exemplified through a numerical application and the results obtained are compared with those of another method. In addition, an error analysis technique based on residual function is developed and applied to this problem to demonstrate the validity and applicability of the method. The convenience of the method is that it is quite simple to employ by using computer programs.

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Synthesizing Single DOF Linkages Via Transition Linkage Identification

Journal of Mechanical Design ◽

10.1115/1.2812418 ◽

2007 ◽

Vol 130 (2) ◽

Cited By ~ 5

Author(s):

Andrew P. Murray ◽

Michael L. Turner ◽

David T. Martin

Keyword(s):

Classification Scheme ◽

Degree Of Freedom ◽

Physical Parameters ◽

Single Degree Of Freedom ◽

Loop Closure ◽

Single Degree ◽

The Matrix ◽

Comprehensive Classification ◽

Insight Into ◽

Selection Of

A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the physical parameters that may alter this classification. The limits on the physical parameters that result in no change in the classification are defined by transition linkages. More rigorously, a transition linkage possesses a configuration at which the matrix defined by the derivative of the loop closure equations with respect to the joint variables loses rank. Transition linkages divide the set of all linkages into different classifications. In the simplest cases studied, transition linkage identification produces a comprehensive classification scheme. In all cases, this identification is used to alter a linkage’s physical parameters without changing its classification and produces insight into the selection of these parameters to produce a desired classification.

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Modelling of single degree of freedom SMA oscillators by using rheological schemes

MATEC Web of Conferences ◽

10.1051/matecconf/201819601049 ◽

2018 ◽

Vol 196 ◽

pp. 01049

Author(s):

Artur Zbiciak ◽

Kacper Wasilewski

Keyword(s):

Internal State ◽

Constitutive Relations ◽

Degree Of Freedom ◽

State Variables ◽

Numerical Application ◽

Single Degree Of Freedom ◽

Single Degree ◽

Internal State Variables ◽

Load Removal ◽

Modelling Approach

The article describes the approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Certain sets of rheological components are presented and their influence on the oscillator response is examined. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user's subroutines. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement.

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Modelling of single degree of freedom SMA oscillators by using rheological schemes

Vestnik MGSU ◽

10.22227/1997-0935.2019.4.427-434 ◽

2019 ◽

pp. 427-434

Author(s):

Artur Zbiciak ◽

Kacper Wasilewski

Keyword(s):

Civil Engineering ◽

Internal State ◽

Constitutive Relations ◽

Phenomenological Approach ◽

Degree Of Freedom ◽

State Variables ◽

Numerical Application ◽

Single Degree Of Freedom ◽

Single Degree ◽

Load Removal

Introduction. The interest to the SMA elements in civil engineering is constantly increasing. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. Materials and methods. The article describes the phenomenological approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Results. Certain sets of rheological components are presented and their influence on the oscillator response is examined. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement. Conclusions. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user’s subroutines.

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Optimization of PID controller parameters for active control of single degree of freedom structures

Challenge Journal of Structural Mechanics ◽

10.20528/cjsmec.2019.04.002 ◽

2019 ◽

Vol 5 (4) ◽

pp. 130

Author(s):

Serdar Ulusoy ◽

Sinan Melih Niğdeli ◽

Gebrail Bekdaş

Keyword(s):

Time Delay ◽

Active Control ◽

Pid Controller ◽

Structural Model ◽

Degree Of Freedom ◽

Control Force ◽

Single Degree Of Freedom ◽

Single Degree ◽

Near Fault ◽

Optimum Parameters

In active control of structures, the parameters of controllers used application must be perfectly tuned. In that case, a good vibration reduction performance can be obtained without a stability problem. During the tuning process, the limit of control force and time delay of controller system must be considered for applicable design. In the study, the optimum parameters of Proportional-Derivative-Integral (PID) type controllers that are proportional gain (K), integral time (Ti) and derivative time (Td) were optimized by using teaching learning-based optimization (TLBO). TLBO is a metaheuristic algorithm imitating the teaching and learning phases of education in classroom. The optimization was done according to the responses of the structure under a directivity pulse of near fault ground motions. In the study, time delay was considered as 20 ms and the optimum parameters of PID controller for a single degree of freedom (SDOF) structural model was found for different control force limits. The performances and feasibility of the method were evaluated by using sets of near fault earthquake records.

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