ABSTRACT
The assumed deflection shapes used in the approximate methods such asin the Rayleigh–Ritz
method were normally formulated by inspection andsometimes by trial and error, until recently,
when a systematic method ofconstructing such a function in the form of characteristic orthogonal
polynomials(COPs) was developed in 1985. However, vibrational analyses of plates with all
edges free or clamped are much more complicated. This project aims at establishing particular
expressions for the fundamental natural frequency of rectangular plates using Rayleigh Ritz
Method by obtaining approximate shape functions of plate of different support conditions
through characteristics orthogonal polynomials. To this end, new sets of stress – strain relations
for orthotropic plates were derived. The principle of force of inertia was introduced, yielding the
corresponding dynamic governing equation of orthotropic plate and hence the strain energy
equation of orthotropic plate.Rayleigh – Ritz quotient was obtained by equating the strain energy
equation of the plate to the kinetic energy equation of the plate. From the rayleigh’s quotient, an
expression for the natural frequency of the plate was obtained in terms of the shape functions of
the plate. The shape function of plate of different support conditions was obtained through
characteristics orthogonal polynomials. A spreadsheet programme was developed to aid the
solutions of the equations and the results show that values of fundamental natural frequencies
obtained using the present studies (Rayleigh - Ritz Method) for all round clamped plates with
aspect ratio, r between 0.5 to 1.2 are four times greater than that obtained from that of previous
studies (Galerkin’s method). Moreso, for plates with mixed support conditions, values of
fundamental natural frequencies obtained using the present study are higher than that of previous
studies (Galerkin’s Method) their difference ranging from 33% for r = 0.5 to 95% for r = 1.2
while results for plate all round simply supported for both present and previous studies are the
same.
EMMANUEL, J (2021). Analysis Of Orthotropic Plates In Free Vibration Regime Using Rayleigh – Ritz Method.. Afribary. Retrieved from https://tracking.afribary.com/works/analysis-of-orthotropic-plates-in-free-vibration-regime-using-rayleigh-ritz-method-1
EMMANUEL, JAMESIME "Analysis Of Orthotropic Plates In Free Vibration Regime Using Rayleigh – Ritz Method." Afribary. Afribary, 20 May. 2021, https://tracking.afribary.com/works/analysis-of-orthotropic-plates-in-free-vibration-regime-using-rayleigh-ritz-method-1. Accessed 13 Nov. 2024.
EMMANUEL, JAMESIME . "Analysis Of Orthotropic Plates In Free Vibration Regime Using Rayleigh – Ritz Method.". Afribary, Afribary, 20 May. 2021. Web. 13 Nov. 2024. < https://tracking.afribary.com/works/analysis-of-orthotropic-plates-in-free-vibration-regime-using-rayleigh-ritz-method-1 >.
EMMANUEL, JAMESIME . "Analysis Of Orthotropic Plates In Free Vibration Regime Using Rayleigh – Ritz Method." Afribary (2021). Accessed November 13, 2024. https://tracking.afribary.com/works/analysis-of-orthotropic-plates-in-free-vibration-regime-using-rayleigh-ritz-method-1