C.W. Cai

Dynamic response of infinite continuous beams subjected to a moving force: an exact method

This paper describes an exact method for investigating the dynamic response of an infinite uniform beam resting on periodic rolle supports and subjected to a moving force. At first, an exact solution for a rotationally periodic continous beam subjected to a moving force is obtained by the U -transformation and mode method. Then, by a limiting process, with the number of spans approaching infinity, the result is generalized to give a solution for an infinite continuous beam subjected to a moving force. This method will be applicable to the forced vibration analysis of an infinite continuous beam under arbitrary excitation.

Localized modes in a two-degree-coupling periodic system with a nonlinear disordered subsystem

Abstract The localized modes in a two-degree-coupling periodic system with infinite number of subsystems and having one nonlinear disorder are analyzed by using the Lindstedt–Poincare (LP) method. The governing equation with the standard form in which the linear terms are uncoupled for subsystems, is derived by using the U-transformation technique. Three types of localized modes, i.e., symmetric, anti-symmetric and asymmetric modes, are found by the LP method. It is shown that the nondimensional parameter η ( i.e., (16k c /3γ 0 )A max −2 ) controls the type, number, stability and localized level of the modes.

A static solution of stiffened plates

Abstract Rectangular plates with periodic stiffening ribs which are symmetrical about the middle plane of the plate and with all edges simply supported are considered. The exact solution for the deflection function of a stiffened plate subjected to uniform load is derived by using the U-transformation method. Solutions for other loading cases can also be derived in a similar manner. A comparison between the results obtained by this exact model and the orthotropic plate model is made.

Moments and Deflections of Simply Supported Rectangular Grids — An Exact Method

An exact method for obtaining the solutions for the bending moments, twisting moments and deflections of simply supported rectangular grids subjected to static concentrated loads applied at the nodes is presented in this paper. It is developed by employing the cyclic periodicity in two directions of the equivalent systems of the original grid structure. A simple example is worked out to demonstrate the accuracy of this method which is applicable to orthogonal grids subjected to nodal loads only at this stage but will be further developed to extend its applicability to other types of grids such as diagonal grids subjected to arbitrary loading.

Exact analysis of localized modes in bi-periodic mono-coupled mass–spring systems with a single disorder

Abstract The frequency bands of perfect bi-periodic mass–spring systems and the localized modes in the same systems with one disordered subsystem are exactly analyzed using the U-transformation method. The linear bi-periodic system with an infinite number of subsystems may be considered as an equivalent cyclic bi-periodic system having infinite subsystems. The governing equation for such an equivalent system with cyclic bi-periodicity can be uncoupled by applying the U-transformation twice to form a set of single-degree-of-freedom equations. These equations can be used to analyze the pass bands and localized modes corresponding to the considered system with and without disorder, respectively. Some specific systems are taken as examples to demonstrate how to apply the formulas obtained in this paper and to find the localized modes and frequencies.

An Analytical Method for Static Analysis of Double Layer Grids

An analytical method for the static analysis of double layer grids consisting of diagonals and top and bottom layers which are plane orthogonal grids is presented. It is assumed that the double layer grid is simply supported at all nodes located at the boundary of the top layer. By using the double U-transformation technique, exact solutions for the nodal displacements and axial forces of the bars in the double layer grid can be derived. The validity of the method is demonstrated with a simple example.

Dynamic response of an orthogonal cable network subjected to a moving force

Abstract The double U-transformation and mode method are employed to analyze the dynamic response of rectangular cable networks which can be considered as cyclic periodic structures in two orthogonal directions after being converted into an equivalent system. As an example, the dynamic response of the deflection of a network subjected to a moving force along the middle cable is derived. The present approach can be used with any loading condition and is an exact method for rectangular cable networks.