Free vibration analysis of the completely free rectangular plate by the method of superposition

Gorman, Daniel

doi:10.1016/0022-460x(78)90322-x

Cited by 107 publications

(39 citation statements)

References 3 publications

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“…order a few Hz assuming the elastic parameters given in Table S1, and maximum length scales of a few tens of kilometers [e.g., Gorman, 1978]. The spectral peak at 53.2 min is not associated with the 0 S 2 eigen-oscillation of the Earth because the frequency is slightly too high -313.28 vs. 309.45 ± 0.15 mHz [Masters and Widmer, 1995] and because the oscillations are continuous over the entire six-month recording interval and, therefore, not associated with strong earthquakes, the usual source of episodic Earth oscillations.…”

Section: Source Modelmentioning

confidence: 99%

Bottom pressure signals at the TAG deep‐sea hydrothermal field: Evidence for short‐period, flow‐induced ground deformation

Sohn¹,

Thomson²,

Rabinovich³

et al. 2009

Geophysical Research Letters

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[1] Bottom pressure measurements acquired from the TAG hydrothermal field on the Mid-Atlantic Ridge (26°N) contain clusters of narrowband spectral peaks centered at periods from 22 to 53.2 minutes. The strongest signal at 53.2 min corresponds to 13 mm of water depth variation. Smaller, but statistically significant, signals were also observed at periods of 22, 26.5, 33.4, and 37.7 min (1 -4 mm amplitude). These kinds of signals have not previously been observed in the ocean, and they appear to represent vertical motion of the seafloor in response to hydrothermal flow -similar in many ways to periodic terrestrial geysers. We demonstrate that displacements of 13 mm can be produced by relatively small flow-induced pressures (several kPa) if the source region is less than $100 m below the seafloor. We suggest that the periodic nature of the signals results from a nonlinear relationship between fluid pore pressure and crustal permeability.

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Section: Source Modelmentioning

confidence: 99%

Bottom pressure signals at the TAG deep‐sea hydrothermal field: Evidence for short‐period, flow‐induced ground deformation

Sohn¹,

Thomson²,

Rabinovich³

et al. 2009

Geophysical Research Letters

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“…Gorman [7] je predložio analitičko rešenje problema slobodnih vibracija pravougaone ploče, koje je nezavisno od graničnih uslova, u obliku sume jednostrukih Fourier-ovih redova. Ovaj metod se naziva metod superpozicije i korišćen je, uz metod projekcije kojim su diskretizovani granični uslovi, za izvođenje dinamičke matrice krutosti pravougaone ploče po Kirchhoff-oj teoriji [8].…”

Section: Introductionunclassified

“…Gorman [7] applied the method of superposition and obtained analytical solution for free vibration of a rectangular Kirchhoff plate with arbitrary boundary conditions, in the form of the Fourier series. Casimir [8] used the method of superposition, along with the method of projection for discretization of boundary conditions, and derived dynamic stiffness matrix of a rectangular Kirchhoff plate [8].…”

Section: Introductionmentioning

confidence: 99%

Dynamic stiffness method in the vibration analysis of circular cylindrical shell

Kolarević¹,

Nefovska-Danilović²,

Petronijević³

2016

Gra mat konstru

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UVODLjuske se često koriste kao elementi inženjerskih konstrukcija, naročito u mašinstvu, građevinarstvu, avio i brodskom inženjeringu. Razlog je u tome što ljuske mogu da se koriste za konstrukcije velikih raspona, bez potrebe za međuosloncima, i što ovakve konstrukcije imaju povoljan odnos krutosti i težine. Ljuske se koriste za konstrukcije rezervoara, delova trupova aviona, delova konstrukcija brodova i slično. Tokom životnog veka, odnosno tokom njihove primene, ove konstrukcije izložene su složenim uslovima okruženja koji podrazumevaju najrazličitije granične uslove i opterećenja, kao što su npr. dinamički uticaji velikog intenziteta koji mogu da dovedu do kolapsa konstrukcije. Potpuno poznavanje dinamičkih karakteristika ovih konstruktivnih elemenata od velike je važnosti da bi se obezbedilo sigurno, uspešno i ekonomski isplativo projektovanje.Metod dinamičke krutosti (MDK), koji u poslednje vreme privlači pažnju sve većeg broja istraživača, predstavlja alternativu metodu konačnih elemenata (MKE) u analizi vibracija. Kao što je poznato, veličina konačnog elementa mora da bude manja od petine talasne dužine koja odgovara najvišoj frekvenciji u analizi da bi se dobili rezultati zadovoljavajuće tačnosti. Zato proračun konstrukcija primenom MKE u oblasti visokih frekvencija, koje se javljaju u akustici ili kod vibracija mašina visokih frekvencija, postaje glomazan i Nevenka Kolarević, M.Sc, Univerzitet u BeograduGrađevinski fakultet, Bulevar kralja Aleksandra 73,

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“…By using the method of superposition, Gorman [1] proposed a new theoretical approach to analyze the free vibration of the completely free rectangular plate. The method involves choosing auxiliary plate problems for which accurate solutions are easily obtained, superimposing these solutions, and constraining them such that their combined solution satisfies the boundary conditions of interest.…”

Section: Introductionmentioning

confidence: 99%

“…Using a similar approach as in reference [1], Gorman [2] exploited the method of superposition to obtain a solution for the free vibration of thin rectangular plates resting on elastic edge supports of arbitrarily distributed stiffness in which step discontinuities exist. In that study, it was found that the eigenvalues approach their known proper limits as the stiffness approach their limits of zero and infinity.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of a Rectangular Plate with Kelvin Type Boundary Conditions

Kırışık

Yüksel

2006

Shock and Vibration

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Abstract. The transverse vibrations of a rectangular plate with the Kelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented.

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Free vibration analysis of the completely free rectangular plate by the method of superposition

Cited by 107 publications

References 3 publications

Bottom pressure signals at the TAG deep‐sea hydrothermal field: Evidence for short‐period, flow‐induced ground deformation

Bottom pressure signals at the TAG deep‐sea hydrothermal field: Evidence for short‐period, flow‐induced ground deformation

Dynamic stiffness method in the vibration analysis of circular cylindrical shell

Free Vibration Analysis of a Rectangular Plate with Kelvin Type Boundary Conditions

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