By Prof. Dr. Jan Awrejcewicz, Prof. Vadim A. Krys’ko, Prof. Alexander F. Vakakis (auth.)

ISBN-10: 3642058108

ISBN-13: 9783642058103

ISBN-10: 3662089920

ISBN-13: 9783662089927

This monograph is dedicated to contemporary advances in nonlinear dynamics of continuing elastic structures. a huge a part of the e-book is devoted to the research of non-homogeneous continua, e.g. plates and shells characterised by way of unexpected adjustments of their thickness, owning holes of their our bodies or/and edges, made of diversified fabrics with different dynamical features and intricate boundary stipulations. New theoretical and numerical ways for reading the dynamics of such continua are provided, equivalent to the tactic of additional plenty and the tactic of right orthogonal decomposition. The offered hybrid procedure results in effects that can't be got via different commonplace theories within the box. The validated equipment are illustrated through quite a few examples of software.

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**Sample text**

N) 1 ... (m, n) II p N AS . .. ...... ...... ,~ =amA ~ , ~nY i ' m. n "" L '" ... , ~(m , n) L IX) L '" m,' ~(m , nJ ... ...... ... (m, n) f .... .................. ...... ............. ...... ...... .................. . N 1

113) ← − −→ (1, 2), S = 2hA1212 ε12 , 3 M1 = 2h (A1111 ℵ11 + A1122 ℵ22 ) , 3 M12 = (0) T1i = Vi 2h3 A1212 ℵ12 , 3 Ai1111 εi11 + Ai1122 εi22 , (0) Si = Vi (2) M1i = Vi A1212 εi12 , Ai1111 ℵ11 + Ai1122 ℵ22 , (2) M2i = Vi ← − −→ (1, 2), ← − −→ (1, 2), ← − −→ (1, 2), A1212 ℵ12 . 114) The material stiﬀness of the added masses is deﬁned by the coeﬃcients Aijmkl . 114): εi11 = ∂w u i = u − zi , ∂x ← − ∂ui ∂ui ∂vi −→ + k1 w, (1, 2), εi12 = + , ∂x ∂x ∂y ← − −→ (1, 2), h+hi (k) Vi (z − zi )k dVi (z), = k = 0, 2.

For T1∗ one obtains h T1∗ = z∗ σ11 dz + −h σ11 dz. 29) and the properties of the characteristic function, the last term can be expressed by h + hi N σ11 Θ∗ Θ∗∗ dz. 105) h The i-th added mass dimension in the x, y directions are given by w˜ xi1 and 2˜ ci2 . 106) i=1 where h + hi T1i = σ11 dVi (z). 47) we obtain N T1i δ (x − xi ) δ (y − yi ). 109) i=1 where h T1 = σ11 dz. 111) i=1 where h T2 = h σ22 dz, S= -h h -h ← − −→ σ11 zdz, (1, 2), M1 = σ12 dz, h M12 = -h σ12 zdz, -h h + hi T2i = h + hi σ22 dVi (z), h Si = σ12 dVi (z), h h + hi ← − −→ σ11 (z − zi ) dVi (z), (1, 2), M1i = h h + hi σ12 (z − zi ) dVi (z), M12i = i = 1, N .

### Nonlinear Dynamics of Continuous Elastic Systems by Prof. Dr. Jan Awrejcewicz, Prof. Vadim A. Krys’ko, Prof. Alexander F. Vakakis (auth.)

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