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Delft University of Technology

1. Dall'Acqua, A. Higher order elliptic problems and positivity.

Degree: 2005, Delft University of Technology

The main subject of this thesis concerns positivity for fourth order elliptic problems. By positivity we mean that a positive source term in the differential equation leads to a positive solution. For second order elliptic partial differential equations such a result is known and referred to by the name maximum principle. It is also well known that such a maximum principle does not have a straightforward generalization to higher order elliptic equations. A fourth order elliptic equation describes the displacement of an elastic plate loaded by some weight. In general the displacement is not everywhere in one direction. However, the mechanical model seems to indicate that some positivity remains. The main result of the thesis is a splitting of the solution operator as the sum of two terms: a positive singular term and a sign-changing regular one. As a consequence, we prove that the sign preserving effects are much stronger than the opposite ones. Advisors/Committee Members: Clement, Ph.P.J.E..

Subjects/Keywords: clamped equation; maximum principle; dirichlet boundary conditions; biharmonic operator

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Dall'Acqua, A. (2005). Higher order elliptic problems and positivity. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441

Chicago Manual of Style (16th Edition):

Dall'Acqua, A. “Higher order elliptic problems and positivity.” 2005. Doctoral Dissertation, Delft University of Technology. Accessed May 09, 2021. http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441.

MLA Handbook (7th Edition):

Dall'Acqua, A. “Higher order elliptic problems and positivity.” 2005. Web. 09 May 2021.

Vancouver:

Dall'Acqua A. Higher order elliptic problems and positivity. [Internet] [Doctoral dissertation]. Delft University of Technology; 2005. [cited 2021 May 09]. Available from: http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441.

Council of Science Editors:

Dall'Acqua A. Higher order elliptic problems and positivity. [Doctoral Dissertation]. Delft University of Technology; 2005. Available from: http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; urn:NBN:nl:ui:24-uuid:dc26e6ac-c0f7-4313-8236-9d4742968441 ; http://resolver.tudelft.nl/uuid:dc26e6ac-c0f7-4313-8236-9d4742968441

2. Johnson, William Richard. Active Structural Acoustic Control of Clamped and Ribbed Plates.

Degree: MS, 2013, Brigham Young University

A control metric, the weighted sum of spatial gradients (WSSG), has been developed for use in active structural acoustic control (ASAC). Previous development of WSSG [1] showed that it was an effective control metric on simply supported plates, while being simpler to measure than other control metrics, such as volume velocity. The purpose of the current work is to demonstrate that the previous research can be generalized to plates with a wider variety of boundary conditions and on less ideal plates. Two classes of plates have been considered: clamped flat plates, and ribbed plates. On clamped flat plates an analytical model has been developed for use in WSSG that assumes the mode shapes are the product of clamped-clamped beam mode shapes. The boundary condition specific weights for use in WSSG have been derived from this formulation and provide a relatively uniform measurement field, as in the case of the simply supported plate. Using this control metric, control of radiated sound power has been simulated. The results show that WSSG provides comparable control to volume velocity on the clamped plate. Results also show, through random placement of the sensors on the plate, that similar control can be achieved regardless of sensor location. This demonstrates that WSSG is an effective control metric on a variety of boundary conditions. Ribbed plates were considered because of their wide use in aircraft and ships. In this case, a finite-element model of the plate has been used to obtain the displacement field on the plate under a variety of boundary conditions. Due to the discretized model involved, a numerical, as opposed to analytical, formulation for WSSG has been developed. Simulations using this model show that ASAC can be performed effectively on ribbed plates. In particular WSSG was found to perform comparable to or better than volume velocity on all boundary conditions examined. The sensor insensitivity property was found to hold within each section (divided by the ribs) of the plate, a slightly modified form of the flat plate insensitivity property where the plates have been shown to be relatively insensitive to sensor location over the entire surface of the plate. Improved control at natural frequencies can be achieved by applying a second control force. This confirms that ASAC is a viable option for the control of radiated sound power on non-ideal physical systems similar to ribbed plates.

Subjects/Keywords: active structural acoustic control; ASAC; clamped plate vibration; ribbed plate vibration; active noise control; ANC; wave equation; Bernoulli-Euler beam theory; composite velocity; weighted sum of spatial gradients; WSSG; Mechanical Engineering

…application on flat plate . . . . . . . . . . . . . . WSSG terms for the clamped flat plate first… …mode . . . . . . . . . . . . . . . . WSSG field on the clamped flat plate… …Simulated control of the clamped plate . . . . . . . . . . . . . . . . . . . . . . Modal… …controlled sound power levels of the clamped plate . . . . . . . . . . . Sound radiated by the… …first radiation mode on the clamped rectangular plate. . . Sound radiated by the second… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Johnson, W. R. (2013). Active Structural Acoustic Control of Clamped and Ribbed Plates. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5010&context=etd

Chicago Manual of Style (16th Edition):

Johnson, William Richard. “Active Structural Acoustic Control of Clamped and Ribbed Plates.” 2013. Masters Thesis, Brigham Young University. Accessed May 09, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5010&context=etd.

MLA Handbook (7th Edition):

Johnson, William Richard. “Active Structural Acoustic Control of Clamped and Ribbed Plates.” 2013. Web. 09 May 2021.

Vancouver:

Johnson WR. Active Structural Acoustic Control of Clamped and Ribbed Plates. [Internet] [Masters thesis]. Brigham Young University; 2013. [cited 2021 May 09]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5010&context=etd.

Council of Science Editors:

Johnson WR. Active Structural Acoustic Control of Clamped and Ribbed Plates. [Masters Thesis]. Brigham Young University; 2013. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5010&context=etd

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