Analytical Study of Coupling Effects for Vibrations of Cable-Harnessed Beam Structures

Abstract

This paper presents a distributed parameter model to study the effects of the harnessing cables on the dynamics of a host structure motivated by space structures applications. The structure is modeled using both Euler–Bernoulli and Timoshenko beam theories (TBT). The presented model studies the effects of coupling between various coordinates of vibrations due to the addition of the cable. The effects of the cable's offset position, pretension, and radius are studied on the natural frequencies of the system. Strain and kinetic energy expressions using linear displacement field assumptions and Green–Lagrange strain tensor are developed. The governing coupled partial differential equations for the cable-harnessed beam that includes the effects of the cable pretension are found using Hamilton's principle. The natural frequencies from the coupled Euler, Bernoulli, Timoshenko and decoupled analytical models are found and compared to the results of the finite element analysis (FEA).

Coupled Dynamics of Cable-Harnessed Structures: Experimental Validation

“…As previously shown in Ref. [31], the offset position induces an asymmetry in the system that results in coupling between various coordinates of vibrations such as the out-of-plane and in-plane bending, axial and torsion. Depending on the system parameters, stronger coupling may be observed between some of the coordinates.…”

“…In this regard, Yerrapragada et al [30][31][32], extends the work by Martin et al [16][17][18][19][20][21] to develop analytical models that include these coupling effects. Yerrapragada et al, [31] presents analytical models based on both Euler-Bernoulli and Timoshenko beam theories to study these coupling effects for a harnessed beam structure where longitudinal cables are attached along the length of a host beam structure. The energy transfer between various coordinates of vibrations are studied and the effects of various cable parameters on the system's dynamic behavior and frequencies are studied.…”

“…The details for the displacement field assumptions, derivations of the strain and kinetic energy expressions, the resultant governing partial differential equations, natural frequencies and mode shapes are presented in Ref. [31]. Both Euler Bernoulli and Timoshenko models are considered.…”

“…They have shown that as the cables become dominant, these coupling behaviors are not to be neglected and must, therefore, be included in the system's dynamic modeling for better accuracy. The current paper focuses on the experimental validation of the analytical models developed in [31] for the coupled vibrations of these cable-harnessed structures. The experimentally validated coupled model is also compared to the previous modeling techniques on the decoupled vibrations by Martin et al [16][17][18][19][20][21] for accuracy.…”

Partitioned Coupling for Structural Acoustics

“…Structural acoustics involves the interaction between a vibrating structure and the pressure fluctuations in an acoustic field, and it can be useful in identifying the noise radiated from a structure or how a structure responds to acoustic waves. Applications of coupled structural acoustics include shock loads on ships [1,2], tire-road interaction [3][4][5], and aero-structures [6][7][8][9]. Computational structural acoustics is used at Sandia National Laboratories to predict structural responses in various acoustic environments.…”