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- W2798182237 abstract "In this paper we consider a linear system modeling the vibrations of two nonhomogeneous Euler-Bernoulli beams connected by a point mass. This system is generated by the following equationsbea &&rho(x)y_{tt}(t,x)+(sigma(x)y_{xx}(t,x))_{xx}-(q(x)y_{x}(t,x))_{x}=0,~t>0,~x in (-1,0)cup(0,1), &&M y_{tt}(t,0)=({T}y(t,x))_{mid_{x=0^-}}-({T}y(t,x))_{mid_{x=0^+}},~~t>0,eea with hinged boundary conditions at both ends, where ${T}y = (se(x)y_{xx})_{x} - q(x)y_x$. We prove that all the associated eigenvalues $(la_n)_{ngeq1}$ are algebraically simple, furthermore the corresponding eigenfunctions $(phi_n)_{ngeq1}$ satisfy $phi_n'{T}{phi}_{n}(-1)>0$ and $phi_n'{T}{phi}_{n}(1)<0$ for all $ngeq1$. These results give a key to the solutions of various control and stability problems related to this system." @default.
- W2798182237 created "2018-04-24" @default.
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- W2798182237 date "2018-04-17" @default.
- W2798182237 modified "2023-10-01" @default.
- W2798182237 title "On the Simplicity of Eigenvalues of Two Nonhomogeneous Euler-Bernoulli Beams Connected by a Point Mass." @default.
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