On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff–Love Constraints
نویسندگان
چکیده
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff–Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it simultaneously performs one-dimensional oscillations orthogonal to this central plane. For the polar decomposition we obtain the stationary ellipsoids as special solutions of the general, strongly nonlinear equations of motion. It is also shown that these solutions are conceptually different from those obtained earlier for the two-polar (singular value) decomposition.
منابع مشابه
Dynamics of Love-Type Waves in Orthotropic Layer Under the Influence of Heterogeneity and Corrugation
The present problem deals with the propagation of Love-type surface waves in a bedded structure comprises of an inhomogeneous orthotropic layer and an elastic half-space. The upper boundary and the interface between two media are considered to be corrugated. An analytical method (separation of variables) is adapted to solve the second order PDEs, which governs the equations of motion. Equations...
متن کاملThermoelastic Damping and Frequency Shift in Kirchhoff Plate Resonators Based on Modified Couple Stress Theory With Dual-Phase-Lag Model
The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dual-phase-lag model. The basic equations of motion and heat conduction equation are written with the help of Kirchhoff-Love plate theory and dual phase lag model. The analytical expressions for thermoelastic damping and frequency ...
متن کاملAll You Need Is Force: a constraint-based approach for rigid body dynamics in computer animation
Over the last few years, simulating the motion of linked articulated rigid bodies based on classical rigid body dynamics has become a valuable paradigm for making realistic 3-D computer animations. Although several operational methods for dynamical simulation have been developed, in general these are both conceptually and computationally complex. To inspire further research in devising alternat...
متن کاملQuantization of the planar affinely-rigid body
This paper is a continuation of [1] where the classical model was analyzed. Discussed are some quantization problems of two-dimensional affinely rigid body with the double dynamical isotropy. Considered are highly symmetric models for which the variables can be separated. Some explicit solutions are found using the Sommerfeld polynomial method.
متن کاملSimulation and Derivation of Deflection Equation for Suspended Diaphragm for MEMS Application Using Kirchhoff-Love Theory
In this paper, using theory of sheets, the deflection of suspended diaphragm has been obtained under uniform and circular loading. This type of diaphragm, unlike other diaphragms, has a central support which is recommended to be used in MEMS applications. The relationship between diaphragm deflection and static analysis of this diaphragm enjoys a great significance in investigating and understa...
متن کامل