Rotatory Inertia Influence on the highly prestressed orthotropic rectangular plates under travelling loads

Abstract

The problem of assessing the rotatory inertia influence on the highly prestressed orthotropic rectangular plates is investigated in this paper. The method of Composite Expansion (MCE),a singular perturbation technique, is employed in conjunction with the method of integral transformation and Cauchy Residue theorem to obtain to 0(ε) a uniformly valid solution in the entire domain of definition of the rectangular plate . Analyses show that material orthotropy does not affect the leading order solution but its effects are present in the first order correction. To O(ε) all the three pertinent parameters, the anisotropic prestress material orthotropy and rotatory inertial affect the response of the rectangular plate. It is also found that the critical velocities of the dynamical system increase with an increase in prestress for all values of rotatory inertia used. Thus resonance is reached ealier for lower values of prestress. Finally for high values of rotatory inertia correction factor, the critical velocity approaches a constant value indicating that resonant effect is remote for high values of rotatory inertia correction factor.

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 103-126