Consider the transverse vibrations of three beams, all with dimensions compatible with the...

Consider the transverse vibrations of three beams, all with dimensions compatible with the Euler-Bernoulli assumptions and all with cantilevered boundary conditions. Suppose two of the beams have constant stiffness denoted by E 1 I 1 and E 2 I 2 respectively and that the third beamhas a variable stiffness denoted EI ( x ). Show that if E 1 I 1 <> EI ( x ) <> E 2 I 2 , then the eigenvalues of the variable stiffness beam fall in between those of the constant stiffness beams.