scholarly journals The Krylov problem in the case of a beam on Vlasov inertial foundation

2018 ◽  
Vol 19 (6) ◽  
pp. 728-736
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Closed Form ◽  
Compressive Force ◽  
Elastic Beam ◽  
Forced Vibrations ◽  
Critical Force ◽  
Winkler Foundation ◽  
Static Deflection ◽  
Numerical Examples ◽  
Moving Force ◽  
Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

scholarly journals Closed-Form Solutions for Gradient Elastic Beams with Geometric Discontinuities by Laplace Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mustafa Özgür Yayli
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Elastic Beam ◽  
Form Solution ◽  
Static Deflection ◽  
Closed Form Solutions ◽  
Geometric Discontinuities ◽  
Algebraic Forms

The static bending solution of a gradient elastic beam with external discontinuities is presented by Laplace transform. Its utility lies in the ability to switch differential equations to algebraic forms that are more easily solved. A Laplace transformation is applied to the governing equation which is then solved for the static deflection of the microbeam. The exact static response of the gradient elastic beam with external discontinuities is obtained by applying known initial conditions when the others are derived from boundary conditions. The results are given in a series of figures and compared with their classical counterparts. The main contribution of this paper is to provide a closed-form solution for the static deflection of microbeams under geometric discontinuities.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

scholarly journals Conditional and Unconditional Deterministic Bounds on the MSE of the Non-Uniform Linear Co-centered Orthogonal Loop and Dipole Array

2021 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Tao Bao ◽  
Mohammed Nabil EL KORSO
Keyword(s):  
Theoretical Analysis ◽  
Closed Form ◽  
Mean Square Error ◽  
Source Localization ◽  
Threshold Region ◽  
Observation Model ◽  
Mean Square ◽  
Numerical Examples ◽  
Cramer Rao Bound ◽  
Deterministic Bounds

The co-centered orthogonal loop and dipole (COLD) array exhibits some interesting properties, which makes it ubiquitous in the context of polarized source localization. In the literature, one can find a plethora of estimation schemes adapted to the COLD array. Nevertheless, their ultimate performance in terms the so-called threshold region of mean square error (MSE), have not been fully investigated. In order to fill this lack, we focus, in this paper, on conditional and unconditional bounds that are tighter than the well known Cramér-Rao Bound (CRB). More precisely, we give some closed form expressions of the McAulay-Hofstetter, the Hammersley-Chapman-Robbins, the McAulaySeidman bounds and the recent Todros-Tabrikian bound, for both the conditional and unconditional observation model. Finally, numerical examples are provided to corroborate the theoretical analysis and to reveal a number of insightful properties.

scholarly journals Influence of the Parameterization in the Interval Solution of Elastic Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Stefano Gabriele ◽  
Valerio Varano
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Interval Analysis ◽  
Elastic Beam ◽  
Elastic Beams ◽  
Analysis Theory ◽  
Set Intersection ◽  
Interval Solution ◽  
Uncertain Boundary

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.

CONTROL OF STEADY-STATE VIBRATIONS OF RECTANGULAR PLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 535-562 ◽  
Author(s):  
K. A. ALSAIF ◽  
M. A. FODA
Keyword(s):  
Steady State ◽  
Function Method ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Selected Lines ◽  
Numerical Examples ◽  
Nodal Lines ◽  
Free And Forced Vibrations ◽  
Concentrated Masses ◽  
The Given

The focus of the present research is to eliminate the undesired steady-state vibrations at selected lines or locations in a vibrating plate by means of adding attachments at arbitrary selected locations. These attachments can be either added concentrated masses and/or translational or rotational springs which are connected to the plate at one end and grounded at the other. The case of attachment of translational and/or rotational oscillators systems is examined. In addition, imposing lines of zero displacements (nodal lines) at selected locations are also investigated. The dynamic Green's function method is employed. Several numerical examples are cited to verify the utility of the proposed method. In addition, sample experiments to measure the plate free and forced vibrations for the given boundary conditions are conducted and the experimental measurements are compared with the analytical results.

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

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