Index of content:
Volume 103, Issue 6, June 1998
- STRUCTURAL ACOUSTICS AND VIBRATION 
103(1998); http://dx.doi.org/10.1121/1.423050View Description Hide Description
It is well known that a stretched string subjected to symmetric harmonic excitation in a single plane may exhibit large amplitude, coupled motion between the th in-plane mode and the th out-of-plane mode ( coupling). Significant coupling between modes of different indices ( coupling) is not expected in the steady state; if the th in-plane mode is directly excited, it can be shown that the amplitude of the th mode both in-plane and out-of-plane, will decay monotonically, for any The present study illustrates that steady-state coupled motion of the string may exist, provided that a constant in-plane bias force is superimposed on the harmonic excitation, thereby breaking the symmetry of the problem. In particular, the case of 2:1 coupling between in-plane and out-of-plane modes is examined using a perturbation approach. Results are confirmed by numerical simulations and physical experiments.
103(1998); http://dx.doi.org/10.1121/1.423051View Description Hide Description
Effects of tensile loading on the properties of longitudinal-mode elastic-wave propagation in a 1.52-cm-diam, seven-wire strand used for prestressed concrete structures were investigated experimentally. In an unloaded state, the wave propagationproperties in strand matched those seen in individual wires comprising the strand, namely, straight center wire and helical outer wires. In the strand, however, extraneous signals were found to be produced from the propagating wave due to physical interactions between the adjacent wires. Under tensile loading, it was observed that a certain portion of the frequency components of the wave became highly attenuative and, thus, absent in the frequency spectrum of the wave. The center frequency of this missing portion, called notch frequency, was found to increase linearly with where is the applied tensile load. In addition, on both sides of the notch frequency, the wave exhibited a large dispersion in a manner similar to the behavior near a cutoff frequency. Possible causes of the observed behavior under tensile loading are discussed.
103(1998); http://dx.doi.org/10.1121/1.423078View Description Hide Description
A new substructuring technique is proposed to perform vibration analysis of line-coupled structures. In dividing the whole structure into a master structure and several auxiliary structures, a variational formulation is used to model the master structure, enabling one to introduce the effects of all auxiliary structures by using their compliance characteristics at several observation points along the junction. Continuous functions of the compliance are obtained via a regression analysis. Given the problem of using the compliance inverse to attain a straightforward formulation, a “Coupling Load Decomposition” technique is proposed since a direct formulation using the compliance inverse is not feasible. By decomposing the interactive load between substructures, relations with displacement decomposition of the master structure can be found. This new formulation permits the direct use of the compliance of the junction, which may be obtained analytically, numerically, or experimentally. Numerical examples using both calculated and experimentally measured compliance data are given. Simulation results are also compared to those obtained experimentally, showing good agreement in low- and medium-frequency ranges.
103(1998); http://dx.doi.org/10.1121/1.423081View Description Hide Description
This paper presents an analytical framework for understanding and controlling the physical mechanisms which govern power flow to infinitely long cylindrical shells from applied point forces. It has been observed by others that the power flow to an empty shell peaks dramatically when the excitation frequency is near the cutoff frequency of a wave in the shell. In this paper, these observations are explained and generalized by a new analytical expression for power flow based on classic analyses of a shell’s response to an applied point force. This expression quantifies the partition of power among propagating waves excited by an applied force. Furthermore, the expression confirms that power flow increases dramatically as a propagating wave is excited in the vicinity of its cutoff frequency. In the context of this understanding, the attachment of a passive structure to the shell is explored as a means of controlling power flow. The nonlinear problem of designing a structure which satisfies practical constraints and minimizes power flow is formulated in such a way as to be solvable by a variety of optimization techniques. The formulation, which can be extended to other structures, is based on an expression for power flow in which the impedance of the attached structure acts in mechanical parallel with the shell’s impedance at the points of attachment. An example indicates that a significant reduction in power flow can be achieved by the attachment of a passive structure whose parameters have been optimized by a genetic algorithm.
103(1998); http://dx.doi.org/10.1121/1.423052View Description Hide Description
This paper presents a theoretical approach for constructing a reduced model in the medium-frequency range in the area of structural acoustics for a general three-dimensional dissipative structure made of an anisotropic, inhomogeneous, viscoelastic bounded medium coupled with an external acoustic fluid. All the results presented can be used if the structure is made of beams, plates, and shells. The boundary value problem in the frequency domain and its variational formulation are presented. For a fixed medium-frequency band, an energy operator related to the structural-acoustic system is introduced. This operator is symmetric positive definite and has a countable set of positive eigenvalues. Its dominant eigensubspace allows a reduced model to be constructed using the Ritz–Galerkin method. A finite dimension approximation of the three-dimensional continuous case is presented and an effective construction of the dominant subspace using the subspace iteration method is developed. As an example, the reduced model is used for constructing the time-stationary random response of the structural-acoustic system submitted to a random wall pressure field. Finally, the theory is validated for a finite length circular cylindrical shell coupled with several dashpots and springs and immersed in a gas (air) and in a liquid (water).