Vibration tailoring of heterogeneous beams and annular plates

In this study, it is demonstrated that clamped–clamped heterogeneous Bernoulli–Euler beams and the Kirchhoff–Love annular plate that is clamped along both inner and outer perimeters possess the common fundamental mode shape that is a fourth-order polynomial. This remarkable finding leads to the possibility of vibration tailoring, namely, the analytical design of annular heterogeneous plate with a pre-specified natural frequency.