Abstract: Approximate representation of a transcendental or a non-linear dynamic stiffnessmatrix K(p) by a quadratic eigen-matrix is studied theoretically in this paper, The quadraticmatrix is formed by expressing the elements of K(p)as parabolic functions based on choosingthree fixed values of the eigenparameter. General bounds on the exact eigenvalues of thetranscendental eigenvalue problem provided by the quadratic matrix are shown to exist ifthe three fixed values chosen are below the lowest pole of the transcend...