By Alexey V. Porubov

ISBN-10: 9812383263

ISBN-13: 9789812383266

ISBN-10: 9812794298

ISBN-13: 9789812794291

A remedy of the amplification of nonlinear pressure waves in solids. It addresses difficulties concurrently: the sequential analytical attention of nonlinear pressure wave amplification and choice in wave publications and in a medium; and the demonstration of using even specific analytical options to nonintegrable equations in a layout of numerical simulation of unsteady nonlinear wave methods. The textual content comprises a variety of targeted examples of the tension wave amplification and choice as a result of the effect of an exterior medium, microstructure, relocating element defects, and thermal phenomena. The volume's major beneficial properties are: nonlinear types of the stress wave evolution in a rod subjected by means of a number of dissipative/active elements; and an analytico-numerical process for strategies to the governing nonlinear partial differential equations with dispersion and dissipation. The paintings will be compatible for introducing readers in mechanics, mechanical engineering and utilized arithmetic to the idea that of lengthy nonlinear pressure wave in one-dimensional wave publications. it's going to even be important for self-study through execs in all parts of nonlinear physics.

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**Additional info for Amplification of Nonlinear Strain Waves in Solids (Series on Stability, Vibration and Control of Systems, Series a, 9)**

**Example text**

4) connecting the Weierstrass function with the Jacobi function en, regular along the real axes. Here k = \/{&2 — e-3)/{ei — ez) is the modulus of the Jacobian elliptic function, while r = em ( m = 1,2,3 , e^ < e-i < e\ ) are the real roots of the cubic equation 4T3 _ g2T _ fl3 = 0. 5) Expressing these results in terms of an appropriate choice of parameters, the wave number K = \ / e i ~ e 3 a n d the Jacobian elliptic modulus k, we have e3 = —K , e2 = «r, ei = —-—«T, 34 Amplification of Nonlinear Strain Waves in Solids 92 = 1^(1 -k2 + k% g3 = ^n\k2 + 1)(2 - k2){l - 2k2).

16 keep their width, while their shapes vary in time. 9). Moreover, at negative values of / the exact solution doesn't predict propagation to the right of the solitary wave with positive amplitude. Absence of linear dispersive terms. We have found an exact solitary wave solution that may be supported by higher -order nonlinear terms even without linear dispersive terms, at d = 0 or / = 0. Numerical simulations show that there are no solitary waves at both zero d and / . Some solutions from previous subsections keep their features at d = 0, in particular, this relates to the case r j ^ O .

In case of the solitary wave solution the initial condition should be have the shape of the solitary wave itself. Moreover, travelling wave solutions for the dissipative equations usually have not free parameters, and additional relationships on the equation coefficients are required for the existence of the solutions Porubov (1993); Porubov (1996); Porubov and Velarde (1999); Porubov and Parker (1999); Porubov and Parker (2002); Samsonov (1995); Samsonov (2001). 2 Painleve analysis Recently it was developed the theory of nonlinear ordinary differential equations whose solutions have not movable singularities, other than poles.

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