Department of Mechanical Engineering

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https://hdl.handle.net/10919/23261

The Virginia Tech Mechanical Engineering Department serves its students, alumni, the Commonwealth of Virginia, and the nation through a variety of academic, research and service activities. Our missions are to: holistically educate our students for professional leadership as creative problem-solvers in a diverse society, conduct advanced research for societal advancement, train graduate students for scholarly inquiry, and engage with alumni, industry, government, and community partners through outreach activities. In order to produce engineers prepared for success across a range of career paths, our academic program integrates training in engineering principles, critical thinking, hands-on projects, open-ended problem solving, and the essential skills of teamwork, communication, and ethics.

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Transverse vibrations of double-tapered cantilever beams with end support and with end mass
Mabie, Hamilton H.; Rogers, C. B. (Acoustical Society of America, 1974)
The free vibrations of a double-tapered cantilever beam with (1) end support and (2) end mass have been investigated using the Bernoulli-Euler equation. The beam was tapered linearly in the horizontal and in the vertical planes simultaneously with the taper ratio in the horizontal plane equal to that in the vertical plane. A table is presented for the first case from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. A chart, plotted from this table, shows the effect of taper ratio on the various harmonics. For the second case, a table and resulting charts show the effect of taper ratio and ratio of end mass to beam mass on the fundamental frequency and higher harmonies. Although previously presented, the case of the beam with free end is also included for purposes of comparison.
Sound transmission between absorbing parallel planes
Hurst, Charles J.; Mitchell, Larry D. (Acoustical Society of America, 1976)
Partially absorbing parallel surfaces can be dominant acoustical feature of many rooms. The sound fields in such rooms are not diffuse, which causes difficulty in predicting sound pressure levels. A method is developed for predicted sound pressure levels in these rooms. It rests on the prediction of sound pressure levels caused by a nondirectional source of known sound power radiating between absorbing parallel planes. The development proceeds from a geometrical acoustics viewpoint. Good correlation has been found between predicted and measured levels in existing rooms having simple geometries. [Work supported by NSF.]
Acoustic performance of a stretched membrane and porous blanket combination
Thomas, W. A. Jr.; Hurst, Charles J. (Acoustical Society of America, 1976)
The sound absorption performance of an acoustic absorber consisting of a stretched circular membrane placed a short distance in front of a fiberglass blanket was both measured and predicted. Both theoretical and experimental analyses were restricted to plane acoustic waves. Theoretical predictions indicated that the membrane-blanket combination would have a sound power absorption coefficient nearly equal to the sound power absorption coefficient of the blanket alone if the incident acoustic plane wave drove the membrane at one of its resonance frequencies. Theoretical analysis also predicted that the sound power absorption coefficient would approach zero when the membrane was driven at an antiresonance frequency by the incident acoustic plane wave. Experimental agreement with theoretical predictions was good for several membrane-blanket combinations. The results show that membrane-blanket combinations can be effective acoustic absorbers in frequency ranges which do not include the antiresonance frequencies of the membrane. The equations developed may be used to predict the acoustic performance of any membrane-blanket combination.
Prediction of sound pressure levels in irregularly shaped factory spaces
Zinskie, John H.; Mitchell, Larry D.; Hurst, Charles J. (Acoustical Society of America, 1976)
The prediction of sound pressure levels in irregularly shaped factory spaces is approached through an analysis of acoustically coupled rooms. Previous work has indicated that room surface sound absorption characteristics create a theoretical interdependence between the sound pressure fields in each coupled volume. Whenever a barrier is interposed between a sound source and observer, the effects of diffraction must also be considered. A computer algorithm was developed to predict sound pressure levels in irregularly shaped rooms using a modified statistical acoustic theory. The program is based on a conversational technique and requires the user to enter information regarding room geometry, surface absorptions, receiver placements, and source sound power and placement information. Several output options are provided, among which is a plan view print-plot of sound pressure level contours in the analysis room. [Work supported by NSF.]
Prediction of the sound diffracted around barriers in large rooms using an extension of Maekawa's approach
Johnson, R. A.; Hurst, Charles J.; Mitchell, Larry D. (Acoustical Society of America, 1977)
A computer program has been developed for the prediction of sound pressure levels in large, irregular rooms utilizing a geometric acoustics approach. Experiments indicated that the program gave good predictive accuracy when receiver positions were in the line of sight of the sound source. However, the accuracy was poor when the receiver was out of the line of sight. The present discussion reports on the further development of the program to include diffraction effects using an extension of Maekawa's approach for thin screens and right angle wedges. The program is capable of finding all valid diffracted rays which undergo three or fewer reflections before diffraction and three or fewer reflections after diffraction. Limited experimental work indicates good predictive accuracy.
Computer-aided, interactive design routine for the prediction of sound levels in irregularly shaped factory spaces
Blanding, James M.; Mitchell, Larry D.; Hurst, Charles J. (Acoustical Society of America, 1977)
An interactive computer algorithm is presented which utilizes modified room acoustics theory to predict dBA sound pressure levels in regularly- and irregularly-shaped factory spaces. Irregularly positioned and nonuniform room absorptions are treated. The user-oriented algorithm, suited to remote interactive terminal operation, employs a conversational format to facilitate input of room dimensions, of absorption data, and of locations and noise levels of machinery. A redesign feature is included which employs three options. These allow the user to change sound source data and acoustic treatments in the process of finding the most economical accommodation of OSHA regulations during any phase of the factory design or redesign. [Work supported by NSF.]
Temperature-Jump Problem with Arbitrary Accommodation
Loyalka, S. K.; Siewert, C. E.; Thomas, J. R. (AIP Publishing, 1978)
A concise and accurate result for the temperature‐jump coefficient based on the linearized BGK model and arbitrary accommodation is reported. The jump coefficient is expressed as a power series in (1‐α), and values of the expansion coefficients are given.
A geometric acoustics approach to the study of sound propagation in ducts containing sheared flows
Grimm, Denny W.; Hurst, Charles J. (Acoustical Society of America, 1979-12-01)
Geometric acoustics has been used to study the propagation of sound waves in a homogeneous moving medium with sheared flow bounded by the hard walls of a duct. Differential equations describing the ray trajectories and the spreading losses along each ray were developed and solved numerically for a range of centerline Mach numbers and shear boundary-layer thicknesses. Results were obtained which show the effects of upstream and downstream sound propagation on the ray paths. A method was also developed to allow the calculation of intensity loss profiles at specified downstream cross sections of the duct.
Sound transmission between absorbing parallel planes
Hurst, Charles J. (Acoustical Society of America, 1980-01-01)
Partially absorbing parallel surfaces can be the dominant acoustical feature of many rooms. The sound fields in such rooms are not diffuse, which causes difficulty in predicting sound pressure levels. A method is developed for predicting sound pressure levels in these rooms. It rests on the prediction of sound pressure levels caused by a nondirectional source of known sound power radiating between absorbing parallel planes. The development proceeds from a geometrical acoustics viewpoint. Good correlation has been found between predicted and measured levels in existing rooms having simple geometries.
Heat Transfer in a Rarefied Gas Enclosed Between Parallel Plates: Role of Boundary Conditions
Loyalka, S. K.; Thomas, J. R. (AIP Publishing, 1982)
The influence of boundary conditions of accomodation coefficients and Maxwellian diffuse specular reflection on heat transfer through a rarefied gas enclosed between two parallel plates is examined. An exact expression for heat transfer for accomodation coefficient boundary conditions and the Bhatnagar–Gross–Krook (BGK) model is constructed by using results of Cercignani and Pagani and Thomas, Chang, and Siewert. These results are compared with some variational results of Cipolla and Cercignani and some exact results of Thomas, Chang, and Siewert and Thomas for the BGK model and Maxwellian diffuse specular reflection boundary conditions. It is concluded that the two boundary conditions provide results that agree within about 3% for a range of Knudsen numbers and boundary parameters. It is found that the variational results are remarkably accurate for the BGK model and both types of boundary conditions. Further, it is noted that the heat transfer between parallel plates with different accommodation coefficients at the two surfaces can be calculated exactly by using a harmonic mean for each surface.
A temperature correlation for the radiation resistance of a thick-walled circular duct exhausting a hot gas
Mahan, J. Robert; Cline, J. G.; Jones, J. D. (Acoustical Society of America, 1984-01-01)
It is often useful to know the radiation impedance of an unflanged but thick-walled circular duct exhausting a hot gas into relatively cold surroundings. The reactive component is shown to be insensitive to temperature, but the resistive component is shown to be temperature dependent. A temperature correlation is developed permitting prediction of the radiation resistance from a knowledge of the temperature difference between the ambient air and the gas flowing from the duct, and a physical basis for this correlation is presented.
Flux formulation of hyperbolic heat conduction
Frankel, Jay Irwin; Vick, Brian L.; Ozisik, M. Necati (American Institute of Physics, 1985)
The development of the general flux formulation for heat conduction based on the modified Fourier's law is presented. This new formulation produces a hyperbolic vector equation in heat flux which is more convenient to use for analysis in situations involving specified flux conditions than the standard temperature formulation. The recovery of the temperature distribution is obtained through integration of the energy conservation law with respect to time. The Green's function approach is utilized to develop a general solution for hyperbolic heat conduction in a finite medium. The utility of the flux formulation and the unusual nature of heat conduction based on the hyperbolic formulation are demonstrated by developing analytical expressions for the heat flux and temperature distributions in a finite slab exposed to a pulsed surface heat flux.
Exact Numerical Results for Poiseuille And Thermal Creep Flow in a Cylindrical Tube
Valougeorgis, D.; Thomas, J. R. (AIP Publishing, 1986-02-01)
The F N method is used, in the field of rarefied gas dynamics, to develop a complete solution for the cylindrical Poiseuille flow and thermal creep problems. The linearized Bhatnagar–Gross–Krook (BGK) model and purely diffuse reflection at the surface are used to describe the physical problem. The derived set of singular integral equations is solved by polynomial expansion and collocation. By choosing suitable F N approximations, the solution of both problems under consideration is accomplished with a single matrix inversion, minimizing computational time and effort. The converged numerical results for the flow rates and the velocity profiles are correct to four significant figures, thus supporting the results of previous authors achieved by other methods.
Hyperbolic heat conduction with temperature-dependent thermal conductivity
Glass, D. E.; Ozisik, M. Necati; McRae, D. S.; Vick, Brian L. (American Institute of Physics, 1986-03-15)
Hyperbolic heat conduction in a semi-infinite slab with temperature-dependent thermal conductivity is studied numerically, and the results are compared with those obtained from the classical parabolic equation for the following cases: (a) constant applied temperature at x=0.0, (b) constant applied heat flux at x=0.0, and (c) a pulsed heat source released instantaneously at t=0.0 in the region [] adjacent to an insulated boundary. In addition to changing the temperature profiles, the nonlinear thermal conductivity also altered the speed of the thermal front. An increase in the thermal conductivity increased the wave speed, while a decrease in the thermal conductivity decreased the wave speed.
A Simple Model for the Average Local Entrainment Rate
Dancey, Clinton L. (AIP Publishing, 1986-07-01)
A new expression for the mean local entrainment rate in a turbulent intermittent flow is obtained. This expression is used to obtain a simple model for the entrainment rate assuming that an indicator function can be defined for the flow, that the interface defined by the indicator function is homogeneous in two directions, and that the turbulent Reynolds number is very large. A particularly simple form is obtained if the intermittency is in a scalar imbedded in a turbulence field and the correlation coefficient for the indicator function is self_similar. The final expression compares favorably with the limited existing data and with other model expressions. Recommendations for experimental verification are presented.
Comparison Of The Measured And Predicted Response Of The Earth Radiation Budget Experiment Active Cavity Radiometer During Solar Observations
Mahan, J. Robert; Tira, N. E.; Lee, R. B.; Keynton, R. J. (Optical Society of America, 1989-05-01)
The Earth Radiation Budget Experiment consists of an array of radiometric instruments placed in earth orbit by the National Aeronautics and Space Administration to monitor the longwave and visible components of the earth's radiation budget. Presented is a dynamic electrothermal model of the active cavity radiometer used to measure the earth's total radiative exitance. Radiative exchange is modeled using the Monte Carlo method and transient conduction is treated using the finite element method. Also included is the feedback circuit which controls electrical substitution heating of the cavity. The model is shown to accurately predict the dynamic response of the instrument during solar calibration.
Active vibration and structural acoustic control of shape memory alloy hybrid composites: Experimental results
Rogers, Craig A. (Acoustical Society of America, 1990-12-01)
Shape memory alloy hybrid composites have been shown both by analytical simulations and experiments to be effective adaptive materials for active vibration and structural acoustics control [Rogers and Robertshaw, Engineering Science Preprints 25, ESP25.88027, Society of Engineering Sciences (1988) and ASME Paper 88-WA/DE-9 ( 1988); Rogers et al., in Proceedings of the 30th Structures, Structural Dynamics, and Materials Conference, AIAA Paper 89-1389 (1989)]. Structural acoustics is the study of how elastic structures radiate or receive sound, and in its most fundamental form involves the simultaneous solution of the differential equations describing the structure and fluid media with appropriate boundary conditions between the two, i.e., a "fully" coupled analysis. This paper will review the state-ofthe-art of active control utilizing shape memory alloy hybrid composites and present experimental results showing active dynamic tuning by a method called active strain energy tuning (ASET), active control of sound radiation from a clamped-baffled beam, and transient vibration control of a cantilevered beam.
Modeling of shape memory alloy hybrid composites for structural acoustic control
Rogers, Craig A.; Liang, Chen; Fuller, Chris R. (Acoustical Society of America, 1991-01-01)
Experimental demonstration of active vibration and structural acoustic control using shape memory alloy (SMA) hybrid composites [C. A. Rogers, in Proceedings of the International Congress on Recent Developments in Air and Structure Borne Sound and Vibration (to be published)[ has provided the motivation for investigating new control schemes and developing more accurate models. This paper will briefly describe newly developed constitutive models for shape memory alloy actuators and the hybrid material system. A general dynamical model for laminated SMA hybrid composite beams and plates will be presented with several theoretical results. A new structural acoustic model for laminated composite plates [Liang et al., J. Sound Vib. (to be published)] will be briefly described and the potential for active structural acoustic control using SMA hybrid composites demonstrated by numerical simulation.
Characterization of multiple piezoelectric actuators for structural excitation
Clark, Robert L.; Fuller, Chris R.; Wicks, Alfred L. (Acoustical Society of America, 1991-07-01)
The thrust of the present work is to analytically and experimentally study the response of a simply supported beam driven by multiple piezoelectric actuators in an effort to understand distributed excitation of the structure. The results indicate that the theoretical model provides the basis for a viable means of determining appropriate locations for piezoelectric actuators for exciting desired modal distributions in the structural response.
Active control of sound radiation due to subsonic wave scattering from discontinuities on fluid-loaded plates. I: Far-field pressure
Gu, Yi; Fuller, Chris R. (Acoustical Society of America, 1991-10-01)
Active control of sound radiation due to subsonic wave scattering from discontinuities represented by a line constraint or by a uniform reinforcing rib positioned on a fluid-loaded infinite plate is analytically studied. The mathematical models are based on the plate vibration and sound radiation due to a line force or a line moment solved in the spectral k domain. For simplicity, the far-field pressure is estimated by the stationary phase approach. Feed-forward control is achieved by adding secondary line forces applied to the plate near the discontinuity. The amplitudes of control forces are determined by the optimal solution of a cost function that integrates the far-field radiated acoustic intensity in a semicylindrical space around the discontinuity. The results show that for subsonic incident waves, high reduction in radiated pressure due to spectral wave scattering at the discontinuities is possible with two active control forces located near the discontinuity. The amount of sound reduction as well as the residual directivity pattern is shown to depend upon the number and location of the control forces.

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