Transient response of a thin linearly elastic plate with Norton or Tresca friction

2021 ◽  
pp. 1-16
Author(s):  
Oana Iosifescu ◽  
Christian Licht
Keyword(s):  
Rigid Body ◽  
Transient Response ◽  
Hilbert Spaces ◽  
Elastic Plate ◽  
Lateral Boundary ◽  
Asymptotic Modeling ◽  
Nonlinear Version ◽  
Bilateral Contact

By using a nonlinear version of Trotter’s theory of approximation of semi-groups acting on variable Hilbert spaces, we propose an asymptotic modeling for the behavior of a linearly elastic plate in bilateral contact with a rigid body along part of its lateral boundary with Norton or Tresca friction.

Generalized Modes in Time-Domain Seakeeping Calculations

2012 ◽  
Vol 56 (04) ◽  
pp. 215-233
Author(s):  
Johan T. Tuitman ◽  
Šime Malenica ◽  
Riaan van't Veer
Keyword(s):  
Rigid Body ◽  
Transient Response ◽  
Time Domain ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Nonlinear Load ◽  
Large Amplitude Motions ◽  
Rigid Body Modes ◽  
The Time Domain

The concept of "generalized modes" is to describe all degrees of freedom by mode shapes and not using any predefined shape, like rigid body modes. Generalized modes in seakeeping computations allow one to calculate the response of a single ship, springing, whipping, multibody interaction, etc., using a uniform approach. The generalized modes have already been used for frequency-domain seakeeping calculations by various authors. This article extents the generalized modes methodology to be used for time-domain seakeeping computations, which accounts for large-amplitude motions of the rigid-body modes. The time domain can be desirable for seakeeping computations because it is easy to include nonlinear load components and to compute transient response, like slamming and whipping. Results of multibody interaction, two barges connected by a hinge, whipping response of a ferry resulting from slamming loads, and the response of a flexible barge are presented to illustrate the theory.

Transient Response of Inelastically Constrained Rigid-Body Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 1041-1047 ◽  
Author(s):  
K. C. Park ◽  
K. J. Saczalski
Keyword(s):  
Structural Material ◽  
Rigid Body ◽  
Transient Response ◽  
Equations Of Motion ◽  
Coupling Mechanism ◽  
System Of Equations ◽  
Structural System ◽  
Lagrangian Multipliers ◽  
Nonlinear Geometric ◽  
Incremental Equations

An energy rate balance is employed to develop the incremental equations of motion for a shock loaded, inelastically constrained rigid-body structural system. Lagrangian multipliers provide the coupling mechanism necessary to reduce the overall system of equations to a set of modified rigid-body equations which include the nonlinear geometric and structural material effects. Kinematic material hardening and a modified yield criteria are used. Examples illustrate the technique and are compared with experimental results.

Elastic cables–rigid body coupled dynamics: asymptotic modeling and analysis

2017 ◽  
Vol 90 (3) ◽  
pp. 1941-1963 ◽  
Author(s):  
Tieding Guo ◽  
Houjun Kang ◽  
Lianhua Wang ◽  
Yueyu Zhao
Keyword(s):  
Rigid Body ◽  
Coupled Dynamics ◽  
Modeling And Analysis ◽  
Asymptotic Modeling ◽  
Elastic Cables

Dynamics of a Plate in Large Overall Motion

1989 ◽  
Vol 56 (4) ◽  
pp. 887-892 ◽  
Author(s):  
A. K. Banerjee ◽  
T. R. Kane
Keyword(s):  
Rigid Body ◽  
Reference Frame ◽  
Elastic Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Present Theory ◽  
Thin Elastic Plate ◽  
Vibration Modes ◽  
Simply Supported ◽  
Rigid Body Motions

Equations of motion are formulated for a thin elastic plate that is executing small motions relative to a reference frame undergoing large rigid body motions (three-dimensional rotation and translation) in a Newtonian reference frame. As an illustrative example, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening.

scholarly journals MODELLING OF THE EFFECT OF A THIN STIFFENER ON THE BOUNDARY OF A NONLINEAR THERMOELASTIC PLATE

2009 ◽  
Vol 14 (3) ◽  
pp. 353-368 ◽  
Author(s):  
Leila Rahmani
Keyword(s):  
Thermal Conductivity ◽  
Asymptotic Analysis ◽  
Rigid Body ◽  
Nonlinear Model ◽  
Elastic Plate ◽  
Thermal Effects ◽  
Nonlinear Oscillations ◽  
Thin Body ◽  
Thermoelastic Plate ◽  
Approximate Boundary Conditions

We consider a dynamic nonlinear model for a heterogeneous thermoelastic plate consisting of a thin highly rigid body of high thermal conductivity perfectly glued on a portion of the boundary of an elastic plate. This model, which describes the nonlinear oscillations of a plate subjected to thermal effects is referred to as the “full von Karman thermoelastic system”. Our aim is to model this junction and reproduce the effect of the thin body by means of approximate boundary conditions, obtained by an asymptotic analysis with respect to the thickness of this body.

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