A Clamped Plate with a Uniform Weight May Change Sign
نویسندگان
چکیده
It is known that the Dirichlet bilaplace boundary value problem, which is used as a model for a clamped plate, is not sign preserving on general domains. It is also known that the corresponding first eigenfunction may change sign. In this note we will show that even a constant right hand side may result in a sign-changing solution.
منابع مشابه
In any dimension a “ clamped plate ” with a uniform weight may change sign ∗
Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains Ω such that even the solution of ∆u = 1 in Ω with the homogeneous Dirichlet boundary conditions u = uν = 0 on ∂Ω is sign-changing. In two dimensions this corresponds to the Kirchhoff-Love model of a clamped pla...
متن کاملThermo-Elastic Analysis of Non-Uniform Functionally Graded Circular Plate Resting on a Gradient Elastic Foundation
Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. The plate is coupled by an elastic medium which is simulated as a Winkler- Pasternak foundation with gradient coefficients in the radial and circumferential...
متن کاملFree Vibration Analysis of Non-Uniform Circular Nanoplate
In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To ve...
متن کاملWhen is the first eigenfunction for the clamped plate equation of fixed sign ? ∗
It is known that the first eigenfunction of the clamped plate equation, ∆φ = λφ in Ω with φ = ∂ ∂n φ = 0 on ∂Ω, is not necessarily of fixed sign. In this article, we survey the relations between domains Ω and the sign of that first eigenfunction.
متن کاملActive Structural Acoustic Control of Clamped Flat Plates using a Weighted Sum of Spatial Gradients
In this paper, the weighted sum of spatial gradients, or WSSG (formerly known as composite velocity) is developed for use in active structural acoustic control (ASAC) on clamped flat rectangular plates. In previous work, WSSG was developed on a simply-supported flat rectangular plate\cite{pseudo}, and showed promise as a control metric. The displacement on the clamped plate has been modeled usi...
متن کامل