Steady planar vibrations of an isotropic body with cavities

1995 ◽  
Vol 77 (6) ◽  
pp. 3524-3528
Author(s):  
V. G. Zhitnyaya
Keyword(s):  
Isotropic Body ◽  
Planar Vibrations ◽  
Body With Cavities

Symmetric Planar Vibrations of a Rotating Disk

1963 ◽  
Vol 35 (7) ◽  
pp. 982-989 ◽  
Author(s):  
Pravin G. Bhuta ◽  
John P. Jones
Keyword(s):  
Rotating Disk ◽  
Planar Vibrations

scholarly journals Some Remarks Concerning Jones Eigenfrequencies and Jones Modes

2005 ◽  
Vol 12 (2) ◽  
pp. 337-348
Author(s):  
David Natroshvili ◽  
Guram Sadunishvili ◽  
Irine Sigua
Keyword(s):  
Exterior Domain ◽  
Thermal Stresses ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Isotropic Body ◽  
Oscillation Parameter ◽  
Uniqueness Of Solutions ◽  
Fluid Solid Interaction

Abstract Three-dimensional fluid-solid interaction problems with regard for thermal stresses are considered. An elastic structure is assumed to be a bounded homogeneous isotropic body occupying a domain , where the thermoelastic four dimensional field is defined, while in the unbounded exterior domain there is defined the scalar (acoustic pressure) field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface ∂Ω±. We show that uniqueness of solutions strongly depends on the geometry of the boundary ∂Ω±. In particular, we prove that for the corresponding homogeneous transmission problem for a ball there exist infinitely many exceptional values of the oscillation parameter (Jones eigenfrequencies). The corresponding eigenvectors (Jones modes) are written explicitly. On the other hand, we show that if the boundary surface ∂Ω± contains two flat, non-parallel sub-manifolds then there are no Jones eigenfrequencies for such domains.

Planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov

2020 ◽  
pp. 27-38
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Vertical Direction ◽  
Experimental Program ◽  
Response Analysis ◽  
Considerable Decrease ◽  
Rigid Structure ◽  
Initial Excitation ◽  
Parametric Studies ◽  
The Impact ◽  
Planar Vibrations ◽  
Gap Closing

The author carries out parametric studies for the equation of planar vibrations of rigid structure resting on kinematical rolling supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. Varied parameter is the width of the bottom. Horizontal structural acceleration is studied. Three variants of the possible behavior are shown: (i) minor rocking with little decrease in response accelerations as compared to the initial excitation; considerable rocking with considerable decrease in the response accelerations; intensive rocking leading to the overturn of the supports. In vertical direction there appear shocks (infinite accelerations) during gap closings of the supports. The importance of the problem for the seismic response analysis of the unanchored items is noted. The author gives recommendations for the experimental program, aimed to obtain data about damping both for rotation and for the gap closing, and also about the impact of the flexibility of the supports and underlying surface.

On the Plasticity Conditions of an Isotropic Body

2020 ◽  
pp. 181-193
Author(s):  
Valentin Molotnikov ◽  
Antonina Molotnikova
Keyword(s):  
Isotropic Body

scholarly journals A Simple Derivation of the Birch–Murnaghan Equations of State (EOSs) and Comparison with EOSs Derived from Other Definitions of Finite Strain

Minerals ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 745 ◽  
Author(s):  
Tomoo Katsura ◽  
Yoshinori Tange
Keyword(s):  
Finite Strain ◽  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Isotropic Body ◽  
Simple Derivation ◽  
Scale Free ◽  
Free Data ◽  
Pressure Scale ◽  
Derivatives Of ◽  
Lagrangian Scheme

Eulerian finite strain of an elastically isotropic body is defined using the expansion of squared length and the post-compression state as reference. The key to deriving second-, third- and fourth-order Birch–Murnaghan equations-of-state (EOSs) is not requiring a differential to describe the dimensions of a body owing to isotropic, uniform, and finite change in length and, therefore, volume. Truncation of higher orders of finite strain to express the Helmholtz free energy is not equal to ignoring higher-order pressure derivatives of the bulk modulus as zero. To better understand the Eulerian scheme, finite strain is defined by taking the pre-compressed state as the reference and EOSs are derived in both the Lagrangian and Eulerian schemes. In the Lagrangian scheme, pressure increases less significantly upon compression than the Eulerian scheme. Different Eulerian strains are defined by expansion of linear and cubed length and the first- and third-power Eulerian EOSs are derived in these schemes. Fitting analysis of pressure-scale-free data using these equations indicates that the Lagrangian scheme is inappropriate to describe P-V-T relations of MgO, whereas three Eulerian EOSs including the Birch–Murnaghan EOS have equivalent significance.

scholarly journals Thermo-mechanically coupled ice-sheet response — cold, polythermal, temperate

1993 ◽  
Vol 39 (131) ◽  
pp. 65-86 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Isotropic Body ◽  
Interaction Force ◽  
Moisture Diffusivity ◽  
Darcy Law ◽  
Momentum Balance ◽  
Mathematical Representation ◽  
Heat Conducting ◽  
Two Phase ◽  
Alpine Glacier ◽  
Diffusive Model

AbstractClassical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character.As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored.The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law.When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail.

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