Free transversal vibrations of the plate at cantilever boundary conditions are given by using Rayleigh-Ritz method
in Section 3.
Ramesh and Rao  studied the natural frequencies of a pretwisted rotating FG cantilever beam by using Lagrange's equation and the Rayleigh-Ritz method
. The influences of different parameters and coupling between chordwise and flapwise bending modes on the natural frequency were investigated.
Their model is formulated by using Rayleigh-Ritz method
that is based on the characteristic functions of the beam.
[7-9] applied the modified Fourier series and Rayleigh-Ritz method
to analyze the free vibrations of functionally graded open and closed shells including cylindrical, conical, and spherical ones with general boundary conditions based on first-order shear deformation theory.
Balmes [7, 8] proposed the Parametric Reduced Order Model (PROM) method by expanding the Rayleigh-Ritz method
. He used the mode shapes from a few selected design configurations to predict the response at any design point throughout the design domain.
Dyakonov's monograph on optimization for elliptic problems  and its Chapter 9 on the Rayleigh-Ritz method
for spectral problems.
According to the to the Rayleigh-Ritz method
, the following equation is obtained, corresponding to (45) of the paper :
El sayad and Ghazy  applied Rayleigh-Ritz method
for free vibration of Mindlin trapezoidal plates.
2007) derived the frequency equation in the form of eigen-value problem by employing Rayleigh-Ritz method
. Love's thin shell theory was used for strain-displacement and curvature-displacement relation.
After reviewing the primary methods of analysis for vibration problems in shaped structures, this mechanical engineering graduate textbook develops boundary characteristic orthogonal polynomials and applies the Rayleigh-Ritz method
to transverse vibration of elliptic and circular plates, triangular plates, rectangular and skew plates, and annular plates.
The finite element method based on the Rayleigh-Ritz method
used is set out in Section 2.
 derived a unified solution for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports by using an improved trigonometric series and the Rayleigh-Ritz method
. Messina  studied the free vibrations of multilayered doubly curved shells based on a mixed variational approach and global piecewise-smooth functions.