Static and dynamic analysis of beam assemblies using a differential system on an oriented graph

Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast

“…To re-emphasize the importance of geometric stiffness for the FEM solution, Cheng [26] employed it in the design optimization of a thermally loaded beam column under maximum vibration frequency or buckling temperature, where the geometric matrix is dependent on the compressive axial force that is linearly proportional to the given temperature rise. Furthermore, Náprstek and Fischer [27] analyzed the statics and dynamics of beam assemblies using a differential system on an oriented graph. Armand [28] employed a preloaded stiffness matrix of a mast of height 30 m in a dynamic solution to obtain its circular frequencies.…”

On the dynamics of nano-frames

“…-As for self-adjointness, see the work by Náprstek and Fischer (2015) proving that, upon enforcing the classical equilibrium equations at the nodes, the free-vibration problem of an arbitrarily-shaped frame is still governed by self-adjoint differential operators, if the free-vibration problem of every frame member is governed by selfadjoint differential operators.…”

Frequency dependent mass and stiffness matrices of bar and beam elements and their equivalency with the dynamic stiffness matrix

“…The publications of Williams and Wittrick [27], Akesson [28], Williams and Howson [29] and Howson et al [30] provide useful information about the application of the DSM in the context of bar and beam elements in frameworks. In a relatively recent publication, Naprstek and Fischer [31] presented a formulation for static and dynamic analysis of beam assembles using a differential system on an oriented graph. Their formulation was sufficiently general, but they considered the differential operators to be linear and symmetrical.…”