The dynamic response of an axially traveling laminated composite beam is investigated analytically,with special consideration to natural frequencies,complex mode functions and critical speeds of the system.The equatio...The dynamic response of an axially traveling laminated composite beam is investigated analytically,with special consideration to natural frequencies,complex mode functions and critical speeds of the system.The equation of motion for a symmetrically laminated system,which is in the form of a continuous gyroscopic system,is considered;the equation of motion is not discretized — no spatial mode function is assumed.This leads to analytical expressions for the complex mode functions and critical speeds.A parametric study has been conducted in order to highlight the effects of system parameters on the above-mentioned vibration characteristics of the system.展开更多
Maxwell-Vlasov PDEs system describes the dynamics of plasma consisting of charged particles with long-range inter-action. Their solutions can be written using some Stokes potentials. Section 1 presents the experimenta...Maxwell-Vlasov PDEs system describes the dynamics of plasma consisting of charged particles with long-range inter-action. Their solutions can be written using some Stokes potentials. Section 1 presents the experimental devices which can produce a magnetic trap. Magnetic geometric dynamic provides mathematical tools for describing the magnetic flow (see [1-7]). Stokes representation for the solutions of PDEs as Maxwell PDEs or Maxwell-Vlasov PDEs are used analyzing electromagnetic energy in magnetic traps. Section 2 studies Maxwell-Vlasov PDEs system. Stokes represen-tation of its solutions, using Maximum Principle for a multitime optimal control problem, is obtained. Section 3 dis-cusses a method for changing a given ODEs system into a geodesic motion under a gyroscopic field of forces (geomet-ric dynamics). Section 4 proposes a modified form for Maxwell-Vlasov PDEs, by replacing the classical gyroscopic force with the one appearing in geometric dynamics. Stokes representation for the solutions of modified Max-well-Vlasov PDEs is also obtained.展开更多
The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed ...The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.展开更多
文摘The dynamic response of an axially traveling laminated composite beam is investigated analytically,with special consideration to natural frequencies,complex mode functions and critical speeds of the system.The equation of motion for a symmetrically laminated system,which is in the form of a continuous gyroscopic system,is considered;the equation of motion is not discretized — no spatial mode function is assumed.This leads to analytical expressions for the complex mode functions and critical speeds.A parametric study has been conducted in order to highlight the effects of system parameters on the above-mentioned vibration characteristics of the system.
文摘Maxwell-Vlasov PDEs system describes the dynamics of plasma consisting of charged particles with long-range inter-action. Their solutions can be written using some Stokes potentials. Section 1 presents the experimental devices which can produce a magnetic trap. Magnetic geometric dynamic provides mathematical tools for describing the magnetic flow (see [1-7]). Stokes representation for the solutions of PDEs as Maxwell PDEs or Maxwell-Vlasov PDEs are used analyzing electromagnetic energy in magnetic traps. Section 2 studies Maxwell-Vlasov PDEs system. Stokes represen-tation of its solutions, using Maximum Principle for a multitime optimal control problem, is obtained. Section 3 dis-cusses a method for changing a given ODEs system into a geodesic motion under a gyroscopic field of forces (geomet-ric dynamics). Section 4 proposes a modified form for Maxwell-Vlasov PDEs, by replacing the classical gyroscopic force with the one appearing in geometric dynamics. Stokes representation for the solutions of modified Max-well-Vlasov PDEs is also obtained.
文摘The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.
