A Multi-Parameter Perturbation Solution for the Inverse Eigenproblem of Nearly-Resonant N-Dimensional Hamiltonian Systems

2012 ◽  
Author(s):  
M. Lepidi
Keyword(s):  
Hamiltonian Systems ◽  
Perturbation Solution ◽  
Parameter Perturbation

scholarly journals A Multi-Parameter Perturbation Solution and Experimental Verification for Bending Problem of Piezoelectric Cantilever Beams

Polymers ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1934 ◽  
Author(s):  
Zhi-Xin Yang ◽  
Xiao-Ting He ◽  
Hong-Xia Jing ◽  
Jun-Yi Sun
Keyword(s):  
Cantilever Beam ◽  
Perturbation Solution ◽  
Experimental Results ◽  
Cantilever Beams ◽  
Parameter Perturbation ◽  
Analysis And Design ◽  
Piezoelectric Polymers ◽  
Piezoelectric Cantilever ◽  
Piezoelectric Structure ◽  
Coupling Characteristics

The existing studies indicate that the application of piezoelectric polymers is becoming more and more extensive, especially in the analysis and design of sensors or actuators, but the problems of piezoelectric structure are usually difficult to solve analytically due to the force–electric coupling characteristics. In this study, the bending problem of a piezoelectric cantilever beam was investigated via theoretical and experimental methods. First, the governing equations of the problem were established and non-dimensionalized. Three piezoelectric parameters were selected as perturbation parameters and the perturbation solution of the equations was finally obtained using a multi-parameter perturbation method. In addition, the relevant experiments of the piezoelectric cantilever beam were carried out, and the experimental results were in good agreement with the theoretical solutions. Based on the experimental results, the effect of piezoelectric properties on the bending deformation of piezoelectric cantilever beams was analyzed and discussed. The results indicated that the multi-parameter perturbation solution obtained in this study is effective and it may serve as a theoretical reference for the design of sensors or actuators made of piezoelectric polymers.

Dynamics of the parameter-perturbation process

1966 ◽  
Vol 113 (6) ◽  
pp. 1077 ◽  
Author(s):  
J.L. Douce ◽  
K.C. Ng ◽  
M.M. Gupta
Keyword(s):  
Parameter Perturbation

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

scholarly journals Comment on ,,On the integrability of 2D Hamiltonian systems with variable Gaussian curvature” by A. A. Elmandouh

2021 ◽  
Author(s):  
Wojciech Szumiński ◽  
Andrzej J. Maciejewski
Keyword(s):  
Hamiltonian Systems ◽  
Gaussian Curvature ◽  
Necessary Conditions ◽  
Constant Gaussian Curvature ◽  
Local Coordinates ◽  
Hamiltonian Functions

AbstractIn the paper [1], the author formulates in Theorem 2 necessary conditions for integrability of a certain class of Hamiltonian systems with non-constant Gaussian curvature, which depends on local coordinates. We give a counterexample to show that this theorem is not correct in general. This contradiction is explained in some extent. However, the main result of this note is our theorem that gives new simple and easy to check necessary conditions to integrability of the system considered in [1]. We present several examples, which show that the obtained conditions are effective. Moreover, we justify that our criterion can be extended to wider class of systems, which are given by non-meromorphic Hamiltonian functions.

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