External Load Frequency Research Articles

Structural Dynamic Effects on Interface Response: Formulation and Simulation Under Partial Slipping Conditions

A new formulation for dynamic sliding contact problems with partial slipping is presented and used to investigate the influence of structural dynamic response on interface behavior. The mixed differential-algebraic equation (MDAE) approach uses differential equations to describe the slipping dynamics and algebraic (constraint) equations to model interfacial sticking. An efficient method for solving the case of partial interface slipping has been developed, and special consideration has been given to the changing equations of motion (at the transition from stick-to-slip and slip-to-stick). An example is presented for the case of an elastic block pressed into a rigid foundation and loaded with cyclic tangential tractions at the top of the block. The full elastodynamic transient simulations illustrate that interface slip response is a strong function of loading frequency, reaching a maximum when the external loading frequency is near the theoretical (shear-mode) natural frequency of the structure. [S0021-8936(00)02204-2]

Nonlinear vibration modes of an elastic panel under periodic loading

The dynamic instability and nonlinear behavior of a nonshallow thin elastic cylindrical panel with simply supported rectilinear edges under uniformly distributed periodic load is studied. The regions of regular and chaotic dynamics are determined for symmetric and nonsymmetric bending modes of the panel. It is shown that depending on the external load frequency, the nonsymmetric buckling. which occurs when the load amplitude reaches a critical value, can lead to two different dynamic modes.

An exact method for cracked elastic strips under concentrated loads ? time-harmonic response

An exact method is presented for the determination of the near-tip stress field arising from the scattering of SH waves by a long crack in a strip-like elastic body. The waves are generated by a concentrated anti-plane shear force acting on each face of the crack. Time-harmonic variation of the external loading is assumed. The problem has two characteristic lengths, i.e. the strip width, and the distance between the point of application of the concentrated forces and the crack tip. It is well-known that the second characteristic length introduces a serious difficulty in the mathematical analysis of the problem: a non-standard Wiener-Hopf (W-H) equation arises, one that contains a forcing term with unbounded behavior at infinity in the transform plane. In addition, the presence of the strip's finite width results in a complicated W-H kernel. Nevertheless, a procedure is described here which circumvents the aforementioned difficulties and holds hope for solving more complicated problems (e.g. the plane-stress/strain version of the present problem) having similar features. The method is based on integral transform analysis, an exact kernel factorization and usage of certain theorems of analytic function theory. Numerical results for the stress-intensity-factor dependence upon the ratio of characteristic lengths and the external load frequency are presented.