| Abstract: | We develop spectral and asymptotic analysis for a class of nonselfadjoint operators which are the dynamics generators for the systems governed by the equations of the spatially nonhomogeneous Timoshenko beam model with a 2–parameter family of dissipative boundary conditions. Our results split into two groups. We prove asymptotic formulas for the spectra of the aforementioned operators (the spectrum of each operator consists of two branches of discrete complex eigenvalues and each branch has only two points of accumulation: +∞ and —∞), and for their generalized eigenvectors. Our second main result is the fact that these operators are Riesz spectral. To obtain this result, we prove that the systems of generalized eigenvectors form Riesz bases in the corresponding energy spaces. We also obtain the asymptotics of the spectra and the eigenfunctions for the nonselfadjoint polynomial operator pencils associated with these operators. The pencil asymptotics are essential for the proofs of the spectral results for the aforementioned dynamics generators. |
