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The nonlinear longitudinal wave propagation in a rod is studied by the homotopy analysis method and obtained analytical solutions which are the same as earlier known results. We also employed the explicit and implicit finite difference methods to solve this nonlinear equation, respectively. The numerical results showed the wave form depends on many factors such as driving frequency, amplitude, nonlinear elastic constant, and wave velocity. We found that compared with the explicit finite difference method, the implicit finite difference method need less amount of the grid but require more computational time to obtain reliable solutions. We also found out that the energy of multiple-frequency components becomes larger with longer traveling distance. [ABSTRACT FROM PUBLISHER]

In the present study, results are presented on the development of superlenses based on left-handed elastic phononic crystals (PC). Numerical simulations are performed to design left-handed elastic PC in terms of constitutive materials, lattice geometry and filling fraction of the inclusion. Wave injection phenomenon inside the PC is studied and shows the importance of the interface geometry between the PC and the external fluid domain to increase the energy transmitted to the PC [ABSTRACT FROM PUBLISHER]

Propagation of bulk solitary density waves is studied in lengthy elastic wave guides, which have strong dispersion and are made of polymers with remarkable linear dissipation, that leads to decay of any of linear or shock waves at short distances. Nonlinear elasticity of materials results in generation of strain solitons even under short-run and reversible (elastic) loading. Theoretical and experimental research has been performed to prove the existence of long bulk strain solitary waves produced by a laser-induced impact in nonlinearly elastic isotropic wave guides. New experiments in lengthy bars (over 0.5 m) confirm that bulk solitons do not reveal any considerable amplitude decay and shape transformation, while linear or shock waves disappear at much shorter distance completely. Decrement values are small, indeed, and estimated first for elastic nonlinear strain waves dissipation in polymeric bars. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]