Search results for "Biharmonic equation"
showing 10 items of 14 documents
A class of shear deformable isotropic elastic plates with parametrically variable warping shapes
2017
A homogeneous shear deformable isotropic elastic plate model is addressed in which the normal transverse fibers are allowed to rotate and to warp in a physically consistent manner specified by a fixed value of a real non-negative warping parameter ω. On letting ω vary continuously (at fixed load and boundary conditions), a continuous family of shear deformable plates Pω is generated, which spans from the Kirchhoff plate at the lower limit ω=0, to the Mindlin plate at the upper limit ω=∞; for ω=2, Pω identifies with the third-order Reddy plate. The boundary-value problem for the generic plate Pω is addressed in the case of quasi-static loads, for which a principle of minimum total potential …
Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system
1999
Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.
A COMPARATIVE STUDY BETWEEN ´ BIHARMONIC BEZIER SURFACES AND BIHARMONIC EXTREMAL SURFACES
2009
AbstractGiven a prescribed boundary of a Bezier surface, we compare the Bezier surfaces generated by two different methods, i.e., the Bezier surface minimising the biharmonic functional and the unique Bezier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we provide a theoretical argument showing why the two types of surfaces are not always the same.
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
2011
We approach surface design by solving second-order and fourth-order Partial Differential Equations (PDEs). We present many methods for designing triangular Bézier PDE surfaces given different sets of prescribed control points and including the special cases of harmonic and biharmonic surfaces. Moreover, we introduce and study a second-order and a fourth-order symmetric operator to overcome the anisotropy drawback of the harmonic and biharmonic operators over triangular Bézier surfaces. © 2010 Elsevier B.V. All rights reserved.
Horseshoe-shaped maps in chaotic dynamics of long Josephson junction driven by biharmonic signals
2000
Abstract A collective coordinate approach is applied to study chaotic responses induced by an applied biharmonic driven signal on the long Josephson junction influenced by a constant dc-driven field with breather initial conditions. We derive a nonlinear equation for the collective variable of the breather and a new version of the Melnikov method is then used to demonstrate the existence of Smale horseshoe-shaped maps in its dynamics. Additionally, numerical simulations show that the theoretical predictions are well reproduced. The subharmonic Melnikov theory is applied to study the resonant breathers. Results obtained using this approach are in good agreement with numerical simulations of …
Strong Instability of Ground States to a Fourth Order Schrödinger Equation
2019
Abstract In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectures from [1–3, 11].
Extension of the line element-less method to dynamic problems
2020
The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized harmonic polynomials as approximation functions, we extend the line element-less method to the inhomogeneous Helmholtz equation and to the eigenvalue problem for the Helmholtz equation. The obtained approximate solutions are critically discussed and advantages as well as limitations of the approach are pointed out.
Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the -biharmonic
2012
By using critical point theory, we establish the existence of infinitely many weak solutions for a class of elliptic Navier boundary value problems depending on two parameters and involving the p-biharmonic operator. © 2012 Elsevier Ltd. All rights reserved.
Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal
2013
Abstract Using a nonlinear circuit ruled by the FitzHugh–Nagumo equations, we experimentally investigate the combined effect of noise and a biharmonic driving of respective high and low frequency F and f. Without noise, we show that the response of the circuit to the low frequency can be maximized for a critical amplitude B∗ of the high frequency via the effect of Vibrational Resonance (V.R.). We report that under certain conditions on the biharmonic stimulus, white noise can induce V.R. The effects of colored noise on V.R. are also discussed by considering an Ornstein–Uhlenbeck process. All experimental results are confirmed by numerical analysis of the system response.