Flexural waves in nonlocal strain gradient high-order shear beam mounted on fractional-order viscoelastic Pasternak foundation

The flexural wave propagation in a micro-beam mounted on viscoelastic foundation is considered in the present work. The mechanical behavior of the micro-beam is modeled by nonlocal strain gradient elasticity with the size-effects taken into account. The constraint is modeled by the Pasternak foundation with the rheology behavior modeled by fractional-order viscoelasticity. The main concerns are the dispersion and attenuation feature of five kinds of possible flexural waves derived from the governing equations of the presented micro-beam model. The influences of the nonlocal effects, strain gradient effects and the fractional-order viscoelastic effects are investigated by a parameter study in the numerical examples. This research is helpful for the design of micro-sensor, micro-actuator and energy-harvest devices in micro electric-mechanic system (MEMS).