Peng Wang

University of Jinan | UJN · mechanics

The aim of this paper is to study the electro-mechanical coupling responses of functionally graded (FG) piezoelectric cantilever nanobeam under the concentrated load, and the material properties follow an exponential distribution in the thickness direction. The constitutive equations are derived from the electric Gibbs free energy density function....

Noether theorem is applied into a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics. The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics, is given. The variable orders fractional Noether symmetry criterion and Noether conser...

A fractional generalization of the gradient system to the Birkhoff mechanics, that is, a new fractional gradient representation of the Birkhoff system is investigated, in this paper. The definitions of the fractional gradient system are generalized to Birkhoff mechanics. Based on the definition, a general condition that a Birkhoff system can be a f...

Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equati...

By Kirchhoff dynamic analogy, the thin elastic rod static equals to rotation of rigid body dynamic. The analytical mechanics methods reflect their advantages in the study of the modeling and equilibrium and stability of elastic rod static, especially for the constrained problems. The Lagrangian structure of the equation of motion for elastic rod is...

In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables: time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obta...

We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can...

Perturbation to Noether symmetries and adiabatic invariants of discrete nonholonomic nonconservative mechanical systems on an uniform lattice are investigated. Firstly, we review Noether symmetry and conservation laws of a nonholonomic nonconservative system. Secondly, we study continuous Noether symmetry of a discrete nonholonomic system, give the...

Conserved quantities of the Cosserat elastic rod dynamics are studied according to the general theorems of dynamics. The rod dynamical equation takes the cross section of the rod as its objective of study and is expressed by two independent variables, the arc coordinate of the rod and the time, so the conserved quantities are written in the integra...

Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated. First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained...

This paper investigates perturbation to the Noether symmetry of discrete holonomic nonconservative dynamical systems on a uniform lattice. Firstly, we give the Noether theorem of system. Secondly, both criterion of perturbation to the Noether symmetry and the Noether adiabatic invariants of system are obtained. Finally, an example is given to illus...

This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given. An example is given to illustrat...

We study a new symmetric perturbation, i.e. weakly Noether symmetric perturbation (WNSP). The criterion and definition of WNSP and Noether symmetric perturbation (NSP) are given. A theorem between WNSP and adiabatic invariants is established. It is concluded that WNSP is different from NSP, the sufficient condition when WNSP is NSP can be presented...

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the No...

Based on the concept of adiabatic invariant, perturbation to Lie symmetry and Lutzky adiabatic invariants for Lagrange systems are studied by using different methods from those of previous works. Exact invariants induced from Lie symmetry of the system without perturbation are given. Perturbation to Lie symmetry is discussed and Lutzky adiabatic in...

The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of...

In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the result...

This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are propose...

In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.

A new type of conserved quantity which is directly induced by Mei symmetry of Hamilton system is studied. Firstly, the definition and criterion of Mei symmetry for Hamilton system are given. Secondly, a coordination function is introduced; the conditions from which the new type of conserved quantity can be induced by Mei symmetry and the form of th...

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether–Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether–Lie symmet...

In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the res...

In this paper, a new symmetry, i.e., Noether-Lie symmetry and its conserved quantities of the non-holonomic mechanical system is studied. The definition and the criterion of the Noether-Lie symmetry for the system are given. A theorem asserting that the Noether-Lie symmetry for the system leads to both the Noether conserved quantity and the general...

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized...