In linear system, in-plane motions are decoupled from out-of-plane motions for planar frame structures. A theoretical method is proposed that permits the efficient calculations of modal characteristics of planar multi-story frame structures. There are 3 × m beam components for a planar m-story frame structure. By analyzing the transverse and longitudinal motions of each component simultaneously and considering the compatibility requirements across each frame joint, the undetermined variables of the entire m-story frame structure system can be reduced to six, regardless of the number of stories, and that can be determined by the application of the boundary conditions. The main feature of this method is to decrease the dimensions of the matrix involved in the finite element methods and certain other analytical methods.

An exact analysis of deformation and stress field in a laminated elastic tube under extension and uniform pressuring is presented. The problem of finite laminated tube is considered with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic layer. The transfer matrix transmits the state vector in radial direction from inner surface to outer surface and takes into account the interfacial continuity and lateral boundary conditions in a rigorous manner. Upon delineating the symplectic orthogonality relations of the eigenvectors and by using eigenfunction expansion, an exact solution which satisfies the end conditions is determined. The results show that the end effect is significant but confined to a local region near the base where the displacement and stress distributions are remarkably different from those according to the simplified solutions that only satisfy lateral BC.

The formulation of a beam on which a pair of piezoelectric segments bonded is presented. The method of transfer matrix is adopted to study the structural responses of the surface-mounted actuation beam induced by an external force on the beam and by a voltage on the actuator. Furthermore, the modal frequencies and the corresponding mode shape functions of the beam also are obtained by the method. The orthogonality of any two distinct sets of mode shape functions of the beam is shown. The method of modal analysis is presented to study the forced vibration of the beam due to a concentrated transient force. The effects of length, location and thickness of the piezoelectric pairs on the structural responses and the modal frequencies of the beam are investigated.

This paper deals with the linear dynamic responses of beams with a flexible support under a moving load with a constant speed. The entire system is modeled as a two-span beam and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements on the flexible constraint, the relationships between two segments can be obtained. By using a transfer matrix method, the characteristic equation of the entire system can then be determined. The forced responses of the system under a moving load can then be obtained through modal expansion theory. Some numerical results are presented to the effects of support stiffness and the different speeds of the moving load.

The purpose of this paper is to apply Biot theory on analyzing honeycomb core to investigate the sound insulation characteristics of honeycomb sandwich panels. At first, the honeycomb core was regarded as a porous material and the sandwich panel is made of layered media. Thus Biot theory developed for fluid saturated porous material is adopted to analyze the waves propagated in honeycomb core. Then the transfer matrix for waves propagated between two ends of each panel is established. The combination of these related matrices can be conducted on evaluating the sound propagation characteristic in the layered media. The comparison of the transmission loss between the available experimental measurements and numerical predictions shows that the present method is reliable. With the present method, the numerical results reveal that the coincident frequency decreases apparently as the thickness of core increases. Therefore, the transmission loss is also increased in the analyzed frequency range. Further, the effect of core density and cell size are also investigated.

This work explores the sound transmission loss provided by the orthotropic multi-layers to elucidate the sound insulation of FRP (Fiber Reinforced Plastics). Mat is the major material considered in the numerical works. The transfer matrices of a single layer of the orthotropic laminate and the fluid are determined. Further, the boundary conditions on the various interface planes are arranged into matrix form. Combining the transfer matrixes and the boundary conditions and applying the transfer matrix method (TMM) yields the surface impedance and the sound transmission loss. The sound-propagation characteristics are studied. Additionally, the STC (Sound Transmission Class) of FRP and steel are compared and discussed.