Wireless sensors applied to modal analysis (2003)

In traditional modal analysis test setups, much effort is expended dealing with the limitations of interconnecting wires. This article examines the potential for wireless sensor and data acquisition methods to mitigate some of the inherent problems associated with experimental modal analysis as it is currently performed with “hard wire” technology. Approaches to wireless hardware and software are suggested that could parallel calculations and thus reduce calculation time and improve data quality by elimination of wires. Modal analysis has become a widely applied tool for understanding complex energy concentrations and dispersions in materials and structures. The engineering purposes of modal analysis include solution designs for noise suppression, diagnosis of dynamic vehicle performance, measurement of structural responses to potentially destructive excitations (impulses), stress analysis for system components, and structural health and prognostic measurements. The wide variety of applications of modal analysis has engendered an equally wide variety of mathematical methods for computation of modal parameters. However, for purposes of discussion, applications of modal analysis can be subdivided into two categories: 1. The analysis performed by the test and evaluation community for purposes of characterizing system performance. 2. The analysis performed within system designs for purposes of improving performance in an operating environment. In the first case, modal test setups are installed, tests are performed, and the system is dismantled to be used for other testing. In the second case, the modal analysis hardware and software are an integral part of a working environment. In either case, certain physical limitations exist. Generally, these limitations include requirements for a large number of sensors, limits on the mass of the sensors so as not to ‘load’ the test article, and support and security of the interconnecting wires which, if not secured, will add ‘noise’ modes to the test article. These difficulties exist because each of the sensors in a conventional modal test setup must be connected to both a power source and a wire or optical signal path. The exact nature and configuration of the power and data connections may vary somewhat with the characteristics of the sensor; however, in some form, an interconnect path must be provided from the sensor to a central location. At this location, the analog information can be utilized to provide the modal characteristics. In many cases, the output from the transducer (sensor) may be a signal that is inherently susceptible to additive noise. Thus, the interconnect must also contain shielding that adequately protects the signal level produced by the source transducer from contamination to outside noise sources. The experimental contingent of the modal community has historically labored diligently to overcome the data contamination inherent in the mechanical, electrostatic and electromagnetic effects associated with wire. In some cases, the design of these solutions and their implementation far exceed the time needed to perform the testing. Analytical Modal Analysis Analytical modal analysis starts with the measurement of the geometry of a structure, its boundary conditions, and the characteristics of its materials. The mass, stiffness and damping of the structure are expressed in terms of the matrices for these three parameters (M, K and C, respectively). Depending on the complexity of the structure, these matrices can contain thousands, tens of thousands, or even more elements. Individual equations of motion are first formed for each discrete element of the structure. The coordinates for these individual elements are then aligned in system space through a linear transformation, after which the elements are combined, resulting in the matrix formulation of the structure. Generalized displacement and force matrices can be combined into specified and unspecified segments, and this structure matrix formulation transforms so that its left side is expressed only in terms of unspecified coordinates. Once this final formulation is achieved, sufficient information is available to extract the system modal parameters (natural frequencies, damping factors and vibratory mode shapes). Subsequently, the system frequency response matrix can be determined in terms of these modal parameters.