Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

The differential quadrature method (DQM) is a numerical technique widely applied in structure mechanics problems. In this work, a top-tensioned riser conveying fluid is considered. The governing equation of this riser under parametric excitations is deduced. Through Galerkin’s method, the partial differential governing equation with respect to time t and vertical coordinate z is reduced into a 1D differential equation with respect only to time. Moreover, the DQM is applied to discretize the governing equation to give solution schemes for the risers’ parametric vibration problem. Furthermore, the instability region of Mathieu equation is studied by both the DQM and the Floquet theory to verify the effectiveness of the DQM, and the solutions of both methods show good consistency. After that, the influences of some factors such as damping coefficient, internal flow velocity, and wet-weight coefficient on the parametric instability of a top-tensioned riser are discussed through investigating the instability regions solved by the DQM solution scheme. Hence, conclusions are obtained that the increase of damping coefficient will save the riser from parametric resonance while increasing internal flow velocity, or the wet-weight coefficient will deteriorate the parametric instability of the riser. Finally, the time-domain responses of several specific cases in both stable region and unstable region are presented.

An efficient graphical acoustic computing (GRACO) method is introduced. Referring to the rendering of semi-transparent objects, the depth peeling (DP) technique is compounded with the GRACO method, forming a combined GRACO and DP method (GRACO–DP) to consider the backscattering of multiple-layered structures in which the contributions of inner structures are included. After that, some examples of GRACO and GRACO–DP are tested to evaluate the accuracy and efficiency of such methods. Through the examples of impedance sphere and benchmark models, GRACO can acquire results with higher efficiency and good consistency compared to the traditional KA method. Also, the TS of a pair of circular plates is determined by GRACO, GRACO–DP, and the finite element method (FEM). The results show that GRACO–DP can fit better with the FEM results. Moreover, the TS of a ribbed double shell is predicted by both GRACO and GRACO–DP; the features of a Bragg wave scattered by the periodically arranged inner ribs can be spotted from the result of GRACO–DP.