A variational principle for the photocatalytic NOx abatement

Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.

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“…The variational principle of Eq. ( 1) can be constructed by the semi-inverse method [40][41][42][43], which is…”

Section: Hamiltonian-based Frequency-amplitude Formulationmentioning

confidence: 99%

Hamiltonian-Based Frequency-Amplitude Formulation for Nonlinear Oscillators

Hou

Qie

et al. 2021

FU Mech Eng

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“…According to the variational theory [36][37][38], the Lagrange's equation for conservative dynamical systems is…”

Section: Problem's Descriptionmentioning

confidence: 99%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

Axioms

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The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

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“…where λ is the Lagrange multiplier, which is determined by the variational theory [10][11][12][13]. By the standard process of the variational iteration method, the multiplier can be identified:…”

Section: Solution Property Of Langmuir Kinetic Equationmentioning

confidence: 99%