Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

An optimization of composite sandwich structure with passive vibration absorber for vibration suppression

This article proposes the use of a support as a passive vibration absorber to a composite sandwich structure for vibration suppression of satellite structures. Based on continuous mass distributions, an approximate formulation is presented for conducting vibration (modal, frequency response) analyses of the composite sandwich structure with the support. This formulation is derived by the Ritz method; verified for accuracy and computational efficiency by comparing finite element analyses. Finally, we perform optimization of the composite sandwich structure with passive vibration absorber by the present method. This optimization is conducted to applying satellite structures for maximizing vibration suppression performance in limited mass. The optimization result allows a database to be obtained on the vibration characteristics of composite sandwich structures with passive vibration absorber for applying aerospace applications. Consequently, it is concluded that the approximate formulation is well suited to vibration analyses of composite sandwich structures with passive vibration absorber due to their relative simplicity and computational efficiency.

Crimp frequency of a viscoelastic fiber in a crimping process

Crimp frequency during the stuffer box crimping process is of great importance for controlling morphology of crimped fibers. A fiber is considered as a viscoelastic rheological fluid, and an approximate formulation for crimp frequency is obtained revealing the main factors affecting the crimping process.

Analytical Approximate Prediction of Thermal Post-Buckling Behavior of the Spring-Hinged Beam

This paper is concerned with thermal post-buckling of uniform isotropic beams with axially immovable spring-hinged ends. The ends of the beam with elastic rotational restraints represent the actual practical support conditions and the classical hinged and clamped conditions can be achieved as the limiting cases of the rotational spring stiffness. The governing differential–integral equation is solved by assuming suitable admissible function for lateral displacement and by employing the Galerkin method. A brief and explicit analytical approximate formulation is established to predict the thermal post-buckling behavior of the beam. The present analytical approximate expressions show excellent agreement with the corresponding numerical solutions based on the shooting method. This confirms the effectiveness and verifies the accuracy of the formulas established.

Nonlinear Interactions between Gravity Waves in Water of Constant Depth

The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.