Response Suppression of FGM Plate Using Piezoelectric Layers Under Parametric Uncertainty Conditions with Markovian Jump Approach

2021 ◽  
pp. 2150049
Author(s):  
Habib Arabi ◽  
Ahmad Bagheri ◽  
Gholam Reza Zarepour
Keyword(s):  
Transient Response ◽  
Power Law ◽  
External Disturbance ◽  
Structural Equations ◽  
Time Response ◽  
Core Material ◽  
Markovian Jump ◽  
Constituent Material ◽  
Piezoelectric Layers ◽  
Internal Radius

It should be noted that in addition to the geometry, constituent material also affects the strength and rigidity of the cylindrical shell, some factors that determine the transient response are its geometry and the constituent material. The capability of piezoelectric materials to adept their properties in reaction to environmental factors including electricity and loading is one of the major reasons for using in this work. Therefore, in this study, the transient response of a symmetric annular sandwich plate incorporating functionally graded core and piezoelectric layers under external harmonic force and electrical voltage is investigated. The properties of the core material vary along its thickness according to a power law model. The displacement field is represented by the third-order shear deformation theory. With the aid of Hamilton’s principle, the structural equations are obtained in terms of displacement components, then solved using the differential quadrature method. In addition, the time response is evaluated with respect to effective parameters including the internal radius, power law index, core thickness, and external voltage. According to the simulation results, the oscillation amplitude decreases as the internal radius of the plate increases over the desired time interval. Also, a higher index parameter is associated with a wider time response range. Moreover, the stability analysis of a piezoelectric system with [Formula: see text] performance is considered based on the theory of Markovian jump systems. To this end, a Markovian jump state-space model of the piezoelectric system obtained using system identification under the effect of external disturbance is presented. The [Formula: see text] stability index is selected based on a candidate Lyapunov function that leads to a set of linear matrix inequalities for each region. The uncontrolled and controlled transient responses of the coupled system under external disturbance are calculated and compared, indicating the satisfactory controller performance in the presence of external disturbance and jump in the sensor and system dynamics.

Finite, Dynamic Motions of Thin Rate-Dependent Sheets

1990 ◽  
Vol 57 (4) ◽  
pp. 821-827 ◽  
Author(s):  
J. A. Blume
Keyword(s):  
Transient Response ◽  
Power Law ◽  
Thin Sheet ◽  
Power Law Model ◽  
Axially Symmetric ◽  
Varying Thickness ◽  
Rate Dependent ◽  
Axially Symmetry ◽  
Constitutive Response

The transient response of a thin sheet comprised of a rate-dependent solid is determined. The material is assumed to be incompressible, and the constitutive response is governed by a nonlinearly viscous power-law model. The sheet has axially symmetry, but an otherwise arbitrarily varying thickness. Axially symmetric, finite, dynamic motions of the sheet are identified.

A Microcomputer-Based S-Plane Transient Response Plotter

1986 ◽  
Vol 23 (2) ◽  
pp. 167-177
Author(s):  
S. J. Cahill
Keyword(s):  
Linear System ◽  
Transient Response ◽  
Time Response ◽  
Tabular Form ◽  
System Specification ◽  
Excitation System ◽  
User Friendly

A CAD package running on the Apple IIe microcomputer is presented to plot the time response of a linear system to a number of forms of excitation. System specification is in either pole-zero or S-plane polynomial, both up to the 9th order. Output is in graphical or tabular form. The programs are user-friendly, and may be used by students with a minimum of formal introduction.

Finite Element Analysis of Subsea Pipelines Subjected to Underwater Explosion

2013 ◽  
Author(s):  
F. Van den Abeele ◽  
P. Verleysen
Keyword(s):  
Shock Wave ◽  
Finite Element ◽  
Transient Response ◽  
Acoustic Pressure ◽  
Underwater Explosion ◽  
Structural Response ◽  
Added Mass ◽  
Radiation Damping ◽  
Time Response ◽  
Subsea Pipelines

Underwater mines and explosives, left in ports and harbours after World War II, can still pose a threat to subsea pipelines. In case of an accidental explosion, or even during controlled detonation, such explosives can cause significant damage to subsea pipelines. To assess the safety of pipelines exposed to an underwater explosion, finite element analyses are performed to predict the transient response of the pipeline to an acoustic pressure shock wave. This type of problem is characterized by a strong coupling between the structural response of the pipe and the acoustic pressure on the wetted interface between the pipe surface and the surrounding seawater. The spherical pressure wave induced by an underwater explosion is characterized by a very steep wave front, where the maximum pressure is attained over an extremely short rise time. The pressure then drops off exponentially over a significantly longer period of time. As a result, the structural behaviour is a combination of a long time response, dominated by an added mass effect (low frequency), a short time response, governed by radiation damping (high frequency), and an intermediate time-frequency response, where both added mass and radiation damping effects are present. In this paper, a finite element model is presented to simulate the transient response of a subsea pipeline subjected to an underwater explosion. The close coupling between acoustic pressure and structural response gives rise to numerical challenges like the accurate formulation and representation of the shock wave, the mesh requirements for the acoustic domain, and the position of the surface based absorbing radiation boundaries. An explicit dynamic solver is used to tackle these challenges, and to predict the behaviour of subsea pipelines exposed to an underwater explosion. The numerical results are compared to published experimental data, and can be used to assess the safety of submerged pipelines in the vicinity of explosives.

Observer-based robust H∞ control for uncertain Markovian jump systems via fuzzy Lyapunov function

2018 ◽  
Vol 41 (3) ◽  
pp. 657-667 ◽  
Author(s):  
Jun Chen ◽  
Tieqing He ◽  
Fei Liu
Keyword(s):  
Lyapunov Function ◽  
External Disturbance ◽  
Optimization Techniques ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Congruent Transformation ◽  
Fuzzy Lyapunov Function ◽  
Jump Systems ◽  
Takagi Sugeno

This paper investigates the problem of observer-based robust [Formula: see text] control for a class of continuous-time nonlinear Markovian jump systems (MJSs) with uncertainties, external disturbance and unavailable states that can be represented by Takagi-Sugeno (T-S) fuzzy models. Based on a mode-dependent fuzzy Lyapunov function and by introducing slack matrix variables, a sufficient condition for the existence of the state observer and observer-based robust [Formula: see text] controller for such MJSs are derived by constructing an augmented fuzzy system. Further, by means of congruent transformation in matrix and linear matrix inequality (LMI) method, the results are given in the form of LMIs that can be easily solved by using the convex optimization techniques. Moreover, we also give the result obtained via common stochastic Lyapunov function to compare with the proposed approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

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