• Another approach

• Based on the calculation of the frequency of the first mode of vibration from the general expression:

• Values of coefficients A_i for different types of support are given in following table:

• Beam containing several layers of different materials
  • Bending stiffness EI and mass m terms must be replaced with composite bending stiffness and composite mass:

where

N is the number of layers in the composite beam
E_i, I_i, m_i are properties of the ith layer in the cross-section of the beam