Nonlinear parametric vibration of axially accelerating viscoelastic strings is investigated via an approximate analytical approach. The standard linear solid model using the material time derivative is employed to describe the string viscoelastic behaviors. A coordinate transformation is introduced to derive Mote’s model of transverse motion from the governing equation of the stationary string....

Aiming at reducing the vibration of CNC machine tools and increasing manufacturing quality, an interpolation method for parametric tool pathes with confined jounce, jerk, acceleration, and speed is proposed. An acceleration/deceleration profile with confined jounce, jerk, acceleration, and speed is proposed and it is proved that this profile is time-optimal to change the speed from one value to...

We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite a steadily growing wave via parametric autoresonance. The method of averaging is employed to derive the governing equations for the primary mode....

This work investigates the nonlinear behavior of a representative parametrically amplified macroscale structure. Specifically, the effort examines the effects of structural and inertial nonlinearities on the near-resonant response of a base-excited, flexible cantilever beam driven by a combined (simultaneously parametric and direct) excitation. The prototypical structure is modeled using classi...