Dynamic equations of motion for inextensible beams and plates

The large deflections of cantilevered beams and plates are modeled discussed. Traditional nonlinear elastic models (e.g., that von Karman) employ restoring forces based on the effect stretching bending, these less applicable to cantilevers. Recent experimental work indicates cantilevers subject inertial stiffness effects. We review a recently established (quasilinear nonlocal) beam model, consider some natural extensions two dimensions -- namely, inextensible plates. Our principal configuration is thin, isotropic, homogeneous rectangular plate, clamped one edge free remaining three. proceed through geometric modeling obtain equations motion via Hamilton's principle for appropriately specified energies. enforce {\em effective} inextensibility constraints Lagrange multipliers. Multiple plate analogs 1D model obtained, various assumptions. For each we present hypotheses resulting motion. It total, three distinct partial differential equation models, and, additionally, describe class ``higher order" models. Each has particular advantages drawbacks both mathematical engineering analyses. conclude with an in depth discussion comparison systems analytical problems.