Two-Dimensional Systems

• Longitudinal Waves in a Plate

Phase velocity

   where E_P ... plate modulus

• Transverse Waves in a Plate

Phase velocity

   where    M  ...  mass of the plate per unit surface
                                                          ...   stiffness of the plate for bending

 

 Boundary conditions for flexural waves in a plate:

Displacement disribution depends on the boundary conditions

 

Distribution of nodal lines of the first vibration modes on a clamped rectangular plate:

 

Distribution of nodal lines of the first vibration modes on a clamped circular plate:

 

 

Frequencies of free vibrations of circular plate with the radius a:

  

Coefficients ε_mn for the first modes of vibrations are in the following table: