Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments

1996 ◽  
Vol 118 (1) ◽  
pp. 70-77 ◽  
Author(s):  
I. Y. Shen
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Characteristic Equation ◽  
Matrix Equation ◽  
Homogeneous Equation ◽  
Transform Domain ◽  
Threshold Control ◽  
Control Gain ◽  
The Laplace Transform ◽  
The Stability

This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer function approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.

Noncolocated Control of a Damped String Using Time Delay

1992 ◽  
Vol 114 (4) ◽  
pp. 736-740 ◽  
Author(s):  
B. Yang
Keyword(s):  
Control System ◽  
Time Delay ◽  
Laplace Transform ◽  
Feedback Loop ◽  
Transform Domain ◽  
Flexible Systems ◽  
Specific Time ◽  
Bode Plot ◽  
Control Gain ◽  
The Laplace Transform

Recent research studies noncolocated control of flexible mechanical systems using time delay. The developments are limited to undamped flexible systems; damped flexible systems have not been considered. This paper investigates noncolocated vibration control of a viscously damped string using time delay. The control system is formulated in the Laplace transform domain. Based on the understanding of the system eigenstructure, a modified Bode plot of the feedback controller is introduced in a design region. The Bode plot designed, along with a specific time delay in the feedback loop, proper sensor and actuator positions, and proper control gain, guarantees stabilization of vibration of the damped string.

scholarly journals Pricing the Zero-Coupon Bond and its Fair Premium Under a Structural Credit Risk Model with Jumps

2011 ◽  
Vol 48 (02) ◽  
pp. 404-419 ◽  
Author(s):  
Yinghui Dong ◽  
Guojing Wang ◽  
Rong Wu
Keyword(s):  
Laplace Transform ◽  
Credit Risk ◽  
Closed Form ◽  
Risk Model ◽  
Market Value ◽  
Credit Spread ◽  
The Laplace Transform ◽  
Credit Risk Model ◽  
Coupon Bond ◽  
Fair Premium

In this paper we consider a structural form credit risk model with jumps. We investigate the credit spread, the price, and the fair premium of the zero-coupon bond for the proposed model. The price and the fair premium of the bond are associated with the Laplace transform of default time and the firm's expected present market value at default. We give sufficient conditions under which the Laplace transform and the expected present market value of a firm at default are twice continuously differentiable. We derive closed-form expressions for them when the jumps have a hyperexponential distribution. Using the closed-form expressions, we obtain numerical solutions for the default probability, the credit spread, and the fair premium of the bond.

Propagation of Discontinuities in Coupled Thermoelastic Problems

1968 ◽  
Vol 35 (3) ◽  
pp. 489-494 ◽  
Author(s):  
B. A. Boley ◽  
R. B. Hetnarski
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Applied Strain ◽  
Transform Domain ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Thermoelastic Problems

The character and magnitude of traveling discontinuities in one-dimensional coupled transient thermoelastic problems are studied. For this purpose, 16 different fundamental problems are considered in detail, by examination of the nature of the solutions in the Laplace-transform domain. These problems correspond to various combinations of applied strain or stress as mechanical variables, and of applied temperature or heat flux as thermal variables. A system of classification of discontinuities is devised, which permits the results of the 16 problems to be extended to some general conclusions as to the character of the discontinuities in cases of arbitrary boundary conditions.

scholarly journals On solutions of local fractional Schrodinger equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1929-1934
Author(s):  
Resat Yilmazer ◽  
Neslihan Demirel
Keyword(s):  
Fourier Transform ◽  
Schrödinger Equation ◽  
Laplace Transform ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Fractional Schrödinger Equation ◽  
The Laplace Transform ◽  
Fractional Schrodinger Equation

In this study, we obtain the solution of a local fractional Schrodinger equation. The solution is obtained by the implementation of the Laplace transform and Fourier transform in closed form in terms of the Mittag-Leffler function.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

scholarly journals Transient Analysis of Dynamic Crack Propagation With Boundary Effect

1995 ◽  
Vol 62 (4) ◽  
pp. 1029-1038 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Fundamental Solution ◽  
Crack Propagation ◽  
Laplace Transform ◽  
Fundamental Problem ◽  
Boundary Effect ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, a dynamic antiplane crack propagation with constant velocity in a configuration with boundary is investigated in detail. The reflected cylindrical waves which are generated from the free boundary will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. Numerical results of dynamic stress intensity factors for the propagation crack are evaluated in detail.

scholarly journals Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2181
Author(s):  
Daniela Inoan ◽  
Daniela Marian
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Polynomial Functions ◽  
Integro Differential Equation ◽  
The Laplace Transform ◽  
The Stability ◽  
Rassias Stability

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

scholarly journals A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Chunlin Su ◽  
Bin Zhen ◽  
Zigen Song
Keyword(s):  
Laplace Transform ◽  
Chaotic Behavior ◽  
Integral Form ◽  
Nonlinear Coupling ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform ◽  
Analytical Criterion ◽  
Linear And Nonlinear ◽  
The Stability

In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.

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