General theory of the solutions of the equations of motion of an elastic medium of different moduli

Self-similar waves in media with bimodular elastic nonlinearity and relaxation

“…«Неанали-тичность» некоторых твердых тел проявляется в так называемой разномодульности. Разно-модульными (или бимодульными) упругими свойствами, то есть различными модулями E 1 и E 2 упругости при растяжении и сжатии, обладает довольно широкий класс твердых тел: некоторые полимеры, композиционные и конструкционные материалы [6], грунты [7][8][9], а также твердые тела, содержащие трещины [10,11]. Распространение нелинейных аку-стических волн в разномодульных материалах исследовалось во многих работах [11][12][13][14], однако влияние релаксационных свойств на эволюцию нелинейных волн в таких средах не рассматривалось.…”

Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading

“…(3) was investigated in detail. We need some definitions and facts from [5,6]. Following to [5,6] we call a line x ¼ lðtÞ in the characteristic plane for Eq.…”

“…Wave propagation in one-dimensional media with a o 0 r1 was considered in [5,6], where the structure of a solution of Eq. (3) was investigated in detail.…”

“…If a ¼1 (the special case of no-tension medium), Eq. (3) can be used to describe a one-dimensional non-cohesive granular material [5][6][7]. In the latter case the theory was successfully applied to simulate processes in the disaster reactor of Chernobyl nuclear plant [10].…”

“…Khachatryan [13] (see also [2]) considered oscillation of a finite bar and obtained the solution the form of the Fourier series. Wave propagation in a no-tension medium was considered by Maslov and Mosolov [5], Maslov and Antsiferova [7] and by Maslov et al [10]. In the above referenced studies the solutions are constructed based on the general form of the D'Alembert solution for the wave equation.…”