Regularity and energy transfer for a nonlinear beam equation

نویسندگان

چکیده

In this paper we study some key effects of a discontinuous forcing term in fourth order wave equation on bounded domain, modeling the adhesion an elastic beam with substrate through elastic-breakable interaction. By using spectral decomposition method show that main induced by nonlinearity at transition from attached to detached states can be traced loss regularity solution and migration total energy scales.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Positive Solutions for Singular Nonlinear Beam Equation

In paper, we study the existence of solutions for the singular pLaplacian equation` |u′′|p−2u′′ ́′′ − f(t, u) = 0, t ∈ (0, 1) u(0) = u(1) = 0, u′′(0) = u′′(1) = 0, where f(t, u) is singular at t = 0, 1 and at u = 0. We prove the existence of at least one solution.

متن کامل

Global Solution for the Nonlinear Beam Equation

We prove the existence and uniqueness of global solution for the nonlinear beam equation with initial boundary condition: Q in x f u g t u u M u u ) ( ) ( ) ( ) ( 2 2 2 = ′ + Δ ∇ − Δ + ′ ′ φ α where tt u t x u = ′ ′ ) , ( , t u t x u = ′ ) , ( , 0 > α , φ , , g M is nonlinear functions and Δ is Laplacian in n R .

متن کامل

Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u) ( c(u)ux ) x = 0. For an open dense set of C initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a sem...

متن کامل

Nonlinear Beam Equation with Indefinite Damping

We consider the nonlinear beam equation utt + a(x)ut − f(ux)x + uxxxx = 0 in a bounded interval (0, 1) ⊂ R. The equation has an indefinite damping term, i.e., with a damping function a = a(x) possibly changing sign. For this non-dissipative situation we prove the exponential stability of the corresponding linearized system provided ā = ∫ 1 0 a(x)dx > 0 and ‖ a− ā ‖L2≤ τ , for τ small enough. We...

متن کامل

A periodic folded piezoelectric beam for efficient vibration energy harvesting

Periodic piezoelectric beams have been used for broadband vibration energy harvesting in recent years. In this paper, a periodic folded piezoelectric beam (PFPB) is introduced. The PFPB has special features that distinguish it from other periodic piezoelectric beams. The Adomian decomposition method (ADM) is used to calculate the first two band gaps andtwelve natural frequencies of the PF...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Applied Mathematics Letters

سال: 2021

ISSN: ['1873-5452', '0893-9659']

DOI: https://doi.org/10.1016/j.aml.2020.106959