On Direct Computation of Beam Dynamic Stiffness Coefficients using MSC.Nastran

The forced frequency analysis is very important in the design of automotive structures. In particular, the Frequency Response Functions (FRF) computation is an important step in determining Noise, Vibration and Harshness (NVH) of any automotive vehicle. In general, the CAE engineer must address the severity and compliance of the design limits set in the NVH environment. Usually, a CAE engineer in the automotive industry will first compute the modal characteristic of the component or full body/trim structure, and then compute the frequency response functions to aid in the determination of its ability to withstand the random load input applied on the structure. There exists a second method in MSC.Nastran to compute the frequency response functions on structures without the need to compute its modal characteristics. This direct method of FRF computation is based on the lumped or coupled mass formulation in conjunction with the classical finite element stiffness matrices. It is to be noted that the effect of the distributed mass of the elements plays a critical role in the exact FRF computation. Such a formulation provides yet another method to compute FRF, and this method is henceforth named as the dynamic stiffness approach. To simplify the study of this method, only beam/frame structures will be considered for our purposes. In this paper, the direct numerical computation of the dynamic stiffness coefficients of beam structures using Euler-Bernoulli beam theory are discussed using the DMAP language of MSC.Nastran. There are other tools and compilers that can serve this purpose, but the future motivation of this work is in solving directly for the dynamic response of beam/frame structures using MSC.Nastran. The present dynamic stiffness analysis approach will also provide a direct method to compute the exact dynamic response on beam/frame structures using MSC.Nastran. It is easier to change the mass distribution of structure by changing mass density in the dynamic stiffness approach to perform mass parameter effect studies on the frequency response values. Accounting for the mass distribution exactly using the mass density in the dynamics stiffness approach is certainly better than the classical lumped or coupled mass approach. As a numerical study, a comparison of the dynamic stiffness coefficients between the direct method described in this paper and the classical approach is done using a beam example. In addition, the time history mid-span displacement due to a step load is compared using the two approaches.