Dynamic stiffness formulation and response analysis of stiffened shells

Continuous Element Formulations for Composite Ring-Stiffened Cylindrical Shells

“…First, the dynamic transfer matrix T m can be divided into four blocks as: 12 11 T T T T T m (14) Finally, the dynamic stiffness matrix K(ω) m for the cylindrical shell or the ring is determined as: …”

“…Therefore, our study exploited another efficient method widely used in experiment for measuring and testing vibrations of structures. This alternative consists of plotting the harmonic responses and then recognizing natural frequencies from those curves [13][14][15][16].…”

“…Then the construction of the dynamic stiffness matrix K(ω) for the ring-stiffened cylindrical shells based on the continuity conditions at the connecting is illustrated in Figure 3. Once K(ω) is obtained, natural frequencies of ringstiffened cylindrical shells will be extracted from harmonic responses [13][14][15][16].…”

“…The Dynamic Stiffness Method (DSM) or the Continuous Element Method (CEM) [12][13][14][15][16] has been developed in order to overcome these difficulties of the FEM in dynamic problems. The CEM is based on the exact closed form solution of the governing differential equations of motion which lead to the dynamic stiffness matrix relating a state vector of loads to the corresponding state vector of displacements at the edges of the structure [12,13].…”

“…Therefore, new dynamic stiffness formulations for building new isotropic and composite continuous elements are in strong development. Recent formulations have concerned all kinds of structural elements such as isotropic and composite shells [12][13], and stiffened isotropic cylindrical shells [14]. Recently, Casimir et al [15], Thinh and Nguyen [16] considered the dynamic response of a cross-ply laminated composite shell with the dynamic stiffness method.…”