Solving and Numerical Simulations of Fractional-Order Governing Equation for Micro-Beams

This paper applies a recently proposed numerical algorithm to discuss the deflection of viscoelastic micro-beams in time domain with direct access. A nonlinear-fractional order model for is constructed. Before solving governing equations, operator matrices shifted Chebyshev polynomials are derived first. Shifted used approximate function, and nonlinear fractional equation expressed form matrices. Next, collocation method discretize equations into algebraic solution. It simplifies calculation. MATLAB software was program this simulate solution deflection. The effectiveness accuracy verified by example. Finally, simulations carried out on micro-beams. found that viscous damping coefficient inversely proportional deflection, length scale parameter micro-beam also In addition, stress strain micro-beam, change under different simple harmonic loads, potential energy discussed. results study fully demonstrated polynomial effective