Reliability domain of the Timoshenko model in dynamics of rods and plates

Abstract

Comparing the frequency spectrum of rods and plates calculated with the rotation inertia and shear strain taken into account (the Timoshenko model) with the results of computations based on the solution of the stationary dynamic problem of the theory of elasticity for canonical bodies in rectangular and cylindrical coordinates, we determine the boundaries of the reliability domain for the Timoshenko model: we obtain the admissible (in the framework of accepted refined kinematic hypotheses) values of minimum flexibilities for rods of annular and quadratic cross-sections and of maximal relative thicknesses for plates with annular and square cross-sections. We present the basic dependencies for the solution of the problems of natural frequencies and mode shapes for rods and plates mentioned above (the Timoshenko model) and briefly describe the solutions of similar problems by methods of the theory of elasticity.