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At least 109 records · Page 6

Stress waves in isotropic elastic plate excited by circular transducer

Steady state harmonic stress waves in an isotropic elastic plate excited on one face by a circular transducer are analyzed theoretically. The transmitting transducer transforms an electrical voltage into a uniform normal stress at the top of the plate. To solve the boundary value problem,the radiation into a half-space is considered. The receiving transducer produces an electrical voltage proportional to the average spatially integrated normal stress over its face due to an incident wave. A numerical procedure is given to evaluate the frequency response at a receiving point due to a multiply reflected wave in the near field. Its stability and convergence are discussed. Parameterization plots which determine the particular wave whose frequency response has maximum magnitude compared with other multiple reflected waves are given for a range of values of dimensionless parameters. The effects of changes in the values of the parameters are discussed.

Williams, J. H., Jr.↗

Intermittency and Cessation of Vortex Shedding in the Wake of a Thin Flat Plate with a Circular Trailing Edge

The near and very near wake of thin flat plates with both sharp and circular trailing edges (TEs) are investigated with direct numerical simulations (DNSs). The TE is circular in two of the cases (IN & NS) and sharp in one of them (ST). The separating boundary layers are turbulent in all cases. The objectives of this study are twofold. The first is to explore the effect of significantly reducing Re(sub D) (Reynolds number based on circular TE diameter, D) on the flow in the TE region, and the shedding process (Cases IN and NS). The second is to better understand the reasons underlying the findings of an earlier experimental wake investigation (sharp TE) where (1) the center-line values in normal intensity, and the peak in shear stress profiles in the cross-stream direction, were found to first increase in the streamwise direction (x), from that obtained at the TE, before diminishing further downstream, and (2) a broadband peak was observed in centerline cross-stream velocity (v) spectra (indicating quasi-periodicity, possibly due to vortices or wave-like motions). Case ST from the present study showed a near wake instability resulting in spanwise vortices (with a streamwise component). The instability is intermittent and contributes to both the broadband peak in the v spectrum and the initial increases in normal intensity and shear stress (as in the experiment). Case NS, with the lower value of ReD is an "essentially" non-shedding case where the flow in the TE region continually changes direction (upward/downward) because of turbulence. Case IN, with twice the value of ReD as Case NS, also exhibits a swaying motion in the TE region. In addition, vortex shedding is initiated during periods when the flow direction changes rapidly. Shedding in this case is intermittent. It results in a peak in the v spectrum obtained at the centerline (x/D = 1.0).

direct numerical simulations↗

Total-internal-reflection elastic metasurfaces: Design and application to structural vibration isolation

This letter presents the concept of the Total Internal Reflection metasurface (TIR-MS) which supports the realization of structure-embedded subwavelength acoustic shields for elastic waves propagating in thin waveguides. The proposed metasurface design exploits extreme phase gradients, implemented via locally resonant elements, in order to achieve operating conditions that are largely beyond the critical angle. Such artificial discontinuity is capable of producing complete reflection of the incoming waves regardless of the specific angle of incidence. From a practical perspective, the TIR-MS behaves as a sound hard barrier that is impenetrable to long-wavelength modes at a selected frequency. The TIR metasurface concept is first conceived for a flat interface embedded in a rectangular waveguide and designed to block longitudinal S 0 -type guided modes. Then, it is extended to circular plates in order to show how enclosed areas can be effectively shielded by incoming waves. Given the same underlying physics, an equivalent dynamic behavior was also numerically and experimentally illustrated for flexural A 0 -type guided modes. This study shows numerical and experimental evidence that, when the metasurface is excited at the target frequency, significant vibration isolation can be achieved in the presence of waves having any arbitrary angle of incidence. Furthermore, these results open interesting paths to achieve vibration isolation and energy filtering in certain prototypical structures of interest for practical engineering applications.

42 ENGINEERING↗

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗

Compendium of modal densities for structures

Expressions and graphs for estimating average modal densities for various structural elements of engineering importance including beams, rods, circular plates, and conical shells

Hart, F. D.↗

Electromagnetic rheometer

Force required to pull free a small circular plate imbedded in gel liquid is determined. Procedure for measuring the structure of a gel is given.

Globus, R. H.↗

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

Stricklin, J. A.↗

Automated Shell Theory for Rotating Structures (ASTROS)

Computer program can be used to analyze any disk or shell of revolution of arbitrary cross section under inertial loads caused by rotation about shell axis and under various static loads, including thermal gradients. Geometric shapes incorporated in program are ellipsoidal, spherical, ogival, toroidal, conical, circular plate, cylindrical, and parabolic.

Foster, B. J.↗

Thermoelastic flutter models for elements of flexible satellites

Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiations. The partial differential equations for all the elements of the satellite are linear in the space dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations. In the succeeding paper, a further reduction of these equations is made into singular perturbation equations, which are amenable to solution for complex problems of extremely large number of degrees of freedom.

Huang, T. C.↗

Thermoelastic flutter models for elements of flexible satellites

Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells, have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiation. The partial differential equations for all the elements of the satellite are linear in the space-dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations.

Huang, T. C.↗

Calculation of planar-truss modal frequencies

Simplified method for calculating modal frequencies of four types of large area planar trusses (tetrahedral, pentahedral, hexahedral, and radial rib) treat trusses as equivalent circular plates thus allowing classical plate theories to be used.

Gates, R. M.↗

Control of large space structures: Status report on achievements and current problems

The objectives, state-of-the-art, and problems of large space structures control are outlined. The general objectives range from basic deployment and maneuvering, where some vibration modes may be suppressed, to disturbance rejection for very high performance imaging applications. The controls selected generally must produce some combination of eigenvalue/eigenvector and loads modification in order to achieve the mission objectives. An experiment illustrating the dynamic control of a suspended circular plate is described. Analysis methods used in system modelling, signal processing, and process control and monitoring are discussed. Sensor and actuator performance are assessed.

Lyons, M. G.↗

Embedded gage impact study

Impact damage in graphite/epoxy laminates was characterized and transient strain history during impact was correlated. The material investigated was AS-4/3501-6 graphite/epoxy. Eight-ply and sixteen-ply quasi-isotropic laminates of 45/0/-45/90 sub s and 45/0/-45/90 sub 2s layups were fabricated with strain gages embedded between plies during the strain gages and leads from the highly conductive graphite fibers. The specimens were circular plates 12.7 cm (5 in.) in diameter and clamped along their circumference. The specimens were impacted with a 185 gm impactor, dropped from heights of 1.20 m and 1.65 m. An accelerometer was attached to the back surface of the specimen opposite the impact point and was used to trigger the recording instrumentation. The transient strain data were recorded with an eight channel waveform digitizer capable of sampling data at 0.5 microsec intervals. The data were stored, processed, and plotted by means of a microcomputer. Transient strain data were correlated with results from ultrasonic inspection of the specimens.

Schramm, S. W.↗

Vibration and flutter of mistuned bladed-disk assemblies

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Kaza, K. R. V.↗

A deformation analysis of flat flexible gear and its equation of original curved surfaces

The equation of the original curved surface of end harmonic gearing is determined by displacement analysis of flat flexible gear. The displacement analysis is also used to calculate the strength and rigidity of the gear. The latter is regarded as a circular plate with two concentrated loads, since its torsional rigidity is much larger than its bending rigidity. Small-deflection theory of thin plates is used to solve for the displacement of any point in the middle plane of the gear. New expressions are given for radial and tangential displacements of the middle plane under asymmetrical loading. A digital computer is used to obtain numerical values for the displacements.

Yunwen, S.↗

Vibration and flutter of mistuned bladed-disk assemblies

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbufans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Rao, K.↗