ABSTRACT
This chapter examines the Rayleigh quotient in a more general manner and develops strong supporting arguments for some physically inspired assertions made earlier concerning the Rayleigh and the Rayleigh-Ritz methods. It investigates the significance of the rotatory inertia term neglected in the development of the equations of motion of the beam. The chapter also examines variational aspects of the dynamics of beams and plates. Those who have studied dynamics of particles and rigid bodies at the intermediate level should recall Hamilton's principle as employed for discrete systems. The chapter presents an improved theory for the axisymmetric circular plate wherein the effect of transverse shear was taken into account. It considers the rectangular plate and takes into account the effects of transverse shear and rotatory inertia while formulating the free vibration problem for this case. The theory was given for statics by Reissner and extended to dynamics by Mindlin.
