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Eigen-vibration representation of transfer functions for structures by considering arbitrary excitations
A control system based on a two-channel narrow-band LMS algorithm is used to isolate periodic vibration at low frequencies on a structure composed of a rigid top plate mounted on a flexible receiving plate. The control performance of distributed PVDF error sensors and accelerometer point sensors is compared. For both sensors, high levels of global reduction, up to 32 dB, have been obtained. It is found that, by driving the PVDF strip output voltage to zero, the controller may force the structure to vibrate so that the integration of the strain under the length of the PVDF strip is zero. This ability of the PVDF sensors to act as spatial filters is especially relevant in active control of sound radiation. It is concluded that the PVDF sensors are flexible, nonfragile, and inexpensive and can be used as strain sensors for active control applications of vibration isolation and sound radiation.
This MQP is an ongoing part of the NASA Advanced Space Design Program which examines the integration of the WPI/MITRE Get Away Special Canister (GASCan 2). GASCan 2 contains the Ionospheric Properties and Propagation, Micro-Gravity Ignition, and Rotational Fluid Flow experiments, as well as the integrated support structure. The objectives this year were to finalize the power supply system, connections for experiments, mechanical design of the IPPE's antenna, and to update the structural and vibrational analysis of the integrated support structure.
Impedance-based structural-health-monitoring uses piezoelectric (PZT) patches that are bonded onto or embedded in a structure. Each individual patch behaves as both an actuator of the surrounding structural area as well as a sensor of the structural response. The size of the excited area varies with the geometry and material composition of the structure, and an active patch is driven by a sinusoidal voltage sweep. When a PZT patch is subjected to an electric field, it produces a mechanical strain; and when it is stressed, it produces an electric charge. Since the patch is bonded to the structure, driving a patch deforms and vibrates the structure. The structure then produces a localized dynamic response. This structural system response is transferred back to the PZT patch, which in turn produces an electrical response. The electromechanical impedance method is based on the principle of electromechanical coupling between the active sensor and the structure, which allows researchers to assess local structural dynamics directly by interrogating a distributed sensor array. Because of mechanical coupling between the sensor and the host structure, this mechanical effect is picked up by the sensor and, through electromechanical coupling inside the active element, is reflected in electrical impedance measured at the sensor s terminals.
Equilibrium and free vibration problems of centrifugally stabilized disk and shell structures
Larger and more powerful space based instruments are needed to meet increasingly sophisticated scientific demand. To support this need, concepts for telescopes with apertures of 100 meters are being investigated, but the required technologies are not in hand today. Due to the capacity limits of launch vehicles, the idea of deploying, erecting, or inflating large structures in space is being considered. Recently, rigidization concepts of large inflatable structures have demonstrated the capability of weight reductions of up to 50% from current concepts with packaging efficiencies near 80%. One of the important aspects of inflatable structures is vibration mitigation and line-of-sight control. Such control tasks are possible only after actuators/sensors are properly integrated into a rigidizable concept. To study these issues, we have developed an inflatable/rigidizable hexapod structure testbed. The testbed integrates state of the art piezo-electric self-sensing actuators into an inflatable/rigidizable structure and a flat membrane reflector. Using this testbed, we plan to experimentally demonstrate achievable vibration and line-of-sight control. This paper contains a description of the testbed and an outline of the test plan.
A fluid finite element has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.
Fluctuating pressure requirements for calculation of flight vehicle vibration environments - structural response equations
State of the art ab initio electronic structure methods have been used to investigate the (FHCl)- molecular anion. It is proposed that the geometric structure and binding energies of the complex are r(e)(H-F) = 0.963 +/- 0.003 A, R(e)(H-Cl) = 1.925 +/- 0.015 A, and D0(HF + Cl(-)) = 21.8 +/- 0.4 kcal/mol. A Morokuma decomposition of the ion-molecular bonding give the following electrostatic, polarization, exchange repulsion, dispersion, and charge-transfer plus higher-order mixing components of the vibrationless complexation energy: -27.3, -5.2, +18.3, -4.5, and -5.0 kcal/mol, respectively. A couples cluster single and doubles global surface is constructed from 208 and 228 energy points for linear and bent configurations, respectively, these being fit to rms errors of only 3.9 and 9.3/cm, respectively, below 8000/cm. Converged J = 0 and J = 1 variational eigenstates of the (FHCl)- surface to near the HF + Cl(-) dissociation threshold are determined. The fundamental vibrational frequencies are found to be nu1 = 247/cm, nu2 = 876/cm, and nu3 = 2884/cm. The complete vibrational eigenspectrum is analyzed.
Measured vibration response of residential structures excited by mechanical and acoustical loadings
In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or finite element analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid frequencies between the optimum frequency regimes for FEA and SEA. Power flow analysis has in general been used on one-dimensional beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to two-dimensional plate like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.
Power generation schemes that could be used downhole in an oil well to produce about 1 Watt average power with long-life (decades) are actively being developed. A variety of proposed energy harvesting schemes could be used to extract energy from this environment but each of these has their own limitations that limit their practical use. Since vibrating piezoelectric structures are solid state and can be driven below their fatigue limit, harvesters based on these structures are capable of operating for very long lifetimes (decades); thereby, possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. An initial survey identified that spline nozzle configurations can be used to excite a vibrating piezoelectric structure in such a way as to convert the abundant flow energy into useful amounts of electrical power. This paper presents current flow energy harvesting designs and experimental results of specific spline nozzle/ bimorph design configurations which have generated suitable power per nozzle at or above well production analogous flow rates. Theoretical models for non-dimensional analysis and constitutive electromechanical model are also presented in this paper to optimize the flow harvesting system.
Theoretical aspects of a new capability developed and implemented in NASTRAN level 17.7 to analyze forced vibration of a cyclic structure rotating about its axis of symmetry are presented. Fans, propellers, and bladed shrouded discs of turbomachines are some examples of such structures. The capability includes the effects of Coriolis and centripetal accelerations on the rotating structure which can be loaded with: (1) directly applied loads moving with the structure and (2) inertial loas due to the translational acceleration of the axis of rotation (''base' acceleration). Steady-state sinusoidal or general periodic loads are specified to represent: (1) the physical loads on various segments of the complete structure, or (2) the circumferential harmonic components of the loads in (1). The cyclic symmetry feature of the rotating structure is used in deriving and solving the equations of forced motion. Consequently, only one of the cyclic sectors is modelled and analyzed using finite elements, yielding substantial savings in the analysis cost. Results, however, are obtained for the entire structure. A tuned twelve bladed disc example is used to demonstrate the various features of the capability.
A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn lead to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.
Cantilevered structure supports heat exchanger coils against vibration loading while allowing freedom for differential thermal growth. The support channels will accept a variety of coil angles with the same coil pitch, thus reducing the number of parts required. This design, with slight modification, could be used to support parallel rows of straight piping.
There is a need for a long-life power generation scheme that could be used downhole in an oil well to produce 1 Watt average power. There are a variety of existing or proposed energy harvesting schemes that could be used in this environment but each of these has its own limitations. The vibrating piezoelectric structure is in principle capable of operating for very long lifetimes (decades) thereby possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. In order to determine the feasibility of using piezoelectrics to produce suitable flow energy harvesting, we surveyed experimentally a variety of nozzle configurations that could be used to excite a vibrating piezoelectric structure in such a way as to enable conversion of flow energy into useful amounts of electrical power. These included reed structures, spring mass-structures, drag and lift bluff bodies and a variety of nozzles with varying flow profiles. Although not an exhaustive survey we identified a spline nozzle/piezoelectric bimorph system that experimentally produced up to 3.4 mW per bimorph. This paper will discuss these results and present our initial analyses of the device using dimensional analysis and constitutive electromechanical modeling. The analysis suggests that an order-of-magnitude improvement in power generation from the current design is possible.
The paper develops an efficient free-vibration analysis procedure of two-dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free-vibration analysis presented herein clearly indicate that these dynamic elements combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.
The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms.