ANALYTICITY, HYPERBOLICITY AND UNIFORM STABILITY OF SEMIGROUPS ARISING IN MODELS OF COMPOSITE BEAMS

2000 ◽  
Vol 10 (04) ◽  
pp. 555-580 ◽  
Author(s):  
SCOTT W. HANSEN ◽  
IRENA LASIECKA
Keyword(s):  
Boundary Conditions ◽  
Analytic Semigroup ◽  
Inner Core ◽  
Sandwich Beam ◽  
Composite Beams ◽  
Rotational Inertia ◽  
Viscous Resistance ◽  
Stability Properties ◽  
Exponentially Stable ◽  
The Stability

We examine the stability properties of a sandwich beam consisting of two outer layers and a thin core. The outer layers are modeled as Euler Bernoulli beams and the inner core provides both elastic and viscous resistance to shearing. We show for both clamped and hinged boundary conditions that (i) if rotational inertia terms are neglected, the model is described by an analytic semigroup, and (ii) if rotational inertia is retained in the outer layers, the model is uniformly exponentially stable.

scholarly journals Effects of Lower Boundary Conditions on the Stability of Radiative Shocks

2002 ◽  
Vol 19 (2) ◽  
pp. 282-292 ◽  
Author(s):  
Curtis J. Saxton
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Lower Boundary ◽  
Stationary Flow ◽  
Physical Models ◽  
Lower Boundary Condition ◽  
Stability Properties ◽  
Shock Region ◽  
Post Shock ◽  
The Stability

AbstractThermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties depend on the cooling processes, the electron–ion energy exchange, and the boundary conditions. This paper considers the effects of the lower boundary condition on the post-shock flow, both ideally and for some specific physical models. Specific cases include constant perturbed velocity, pressure, density, flow rate, or temperature at the lower boundary, and the situation with nonzero stationary flow velocity at the lower boundary. It is found that for cases with zero terminal stationary velocity, the stability properties are insensitive to the perturbed hydrodynamic variables at the lower boundary. The luminosity responses are generally dependent on the lower boundary condition.

Stability analysis for positive solutions for classes of semilinear elliptic boundary-value problems with nonlinear boundary conditions

2017 ◽  
Vol 147 (5) ◽  
pp. 1019-1040 ◽  
Author(s):  
Jerome Goddard ◽  
Ratnasingham Shivaji
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Stability Properties ◽  
Linearized Stability ◽  
Stability And Instability ◽  
The Stability

We investigate the stability properties of positive steady-state solutions of semilinear initial–boundary-value problems with nonlinear boundary conditions. In particular, we employ a principle of linearized stability for this class of problems to prove sufficient conditions for the stability and instability of such solutions. These results shed some light on the combined effects of the reaction term and the boundary nonlinearity on stability properties. We also discuss various examples satisfying our hypotheses for stability results in dimension 1. In particular, we provide complete bifurcation curves for positive solutions for these examples.

scholarly journals An Extension of Explicit Coupling for Fluid–Structure Interaction Problems

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1747
Author(s):  
Martina Bukač
Keyword(s):  
Boundary Conditions ◽  
Original Method ◽  
Robin Boundary Conditions ◽  
Stability Properties ◽  
Optimal Accuracy ◽  
Original Scheme ◽  
The Stability ◽  
Robin Boundary ◽  
Partitioned Method ◽  
Excellent Stability

We present an extension of a non-iterative, partitioned method previously designed and used to model the interaction between an incompressible, viscous fluid and a thick elastic structure. The original method is based on the Robin boundary conditions and it features easy implementation and unconditional stability. However, it is sub-optimally accurate in time, yielding only O(Δt12) rate of convergence. In this work, we propose an extension of the method designed to improve the sub-optimal accuracy. We analyze the stability properties of the proposed method, showing that the method is stable under certain conditions. The accuracy and stability of the method are computationally investigated, showing a significant improvement in the accuracy when compared to the original scheme, and excellent stability properties. Furthermore, since the method depends on a combination parameter used in the Robin boundary conditions, whose values are problem specific, we suggest and investigate formulas according to which this parameter can be determined.

Stability results for constrained calculus of variations problems: an analysis of the twisted elastic loop

2005 ◽  
Vol 461 (2057) ◽  
pp. 1357-1381 ◽  
Author(s):  
Kathleen A Hoffman
Keyword(s):  
Boundary Conditions ◽  
Calculus Of Variations ◽  
Perturbation Expansion ◽  
Variational Problems ◽  
Physical Sciences ◽  
Stability Properties ◽  
Variational Structure ◽  
Isoperimetric Constraints ◽  
The Stability ◽  
Parameter Dependent

Problems with a variational structure are ubiquitous throughout the physical sciences and have a distinguished scientific history. Constrained variational problems have been much less studied, particularly the theory of stability, which determines which solutions are physically realizable. In this paper, we develop stability exchange results appropriate for parameter-dependent calculus of variations problems with two particular features: either the parameter appears in the boundary conditions, or there are isoperimetric constraints. In particular, we identify an associated distinguished bifurcation diagram, which encodes the direction of stability exchange at folds. We apply the theory to a twisted elastic loop, which can naturally be formulated as a calculus of variations problem with both isoperimetric constraints and parameter-dependent boundary conditions. In combination with a perturbation expansion that classifies certain pitchfork bifurcations as sub- or super-critical, the distinguished diagram for the twisted loop provides a classification of the stability properties of all equilibria. In particular, an unanticipated sensitive dependence of stability properties on the ratio of twisting to bending stiffness is revealed.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

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