Variational principle for nonlinear oscillator arising in a fractal nano/microelectromechanical system
Kang‐Le Wang
Abstract
In this work, a nonlinear oscillator model with a fractal derivative is successfully established for a fractal nano/microelectromechanical system (MEMS), and its variational principle is obtained by the semi‐inverse method. The established variational formulation suggests an energy conservation for the fractal nonlinear oscillator, and its approximate analytical solution is found by the two‐scale transform and homotopy perturbation method; Laplace transform is used in the solution process. This paper sheds a new light on fractal MEMS.
Topics & Concepts
FractalMathematicsFractal derivativeNonlinear systemLaplace transformVariational principleHomotopy perturbation methodMathematical analysisInverseHomotopyVariational methodFractal dimensionGeometryFractal analysisPhysicsQuantum mechanicsPure mathematicsFractional Differential Equations SolutionsThermoelastic and Magnetoelastic PhenomenaNumerical methods in engineering