In this paper, He's energy balance method is applied to nonlinear oscillators. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We proved that the energy balance is very effective, convenient and does not require any linearization or small perturbation. In contradicts of the conventional methods, He's Energy Balance method (HEBM) using just one iteration, leads us to high accuracy of solutions. Energy Balance method is very effective, convenient and adequately accurate to both linear and nonlinear problems in physics and engineering.

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Sandy soils constitute a large part of the soils of northern part of Iran. The construction of structures on these soils will have some problems due to lack of proper strength properties. On the other hand, in recent years, bottles of Polyethylene terephthalate (PET) plastic such as water and soda bottles have resulted an environmental threat due to their prolonged durability in the environment. Utilization of these materials for soil improvement seems to be a sustainable approach. In this research, the effect of recycled PET on mechanical properties of Babolsar sandy soil is investigated through an extensive experimental analysis carried out using direct shear and consolidated drained (CD) triaxial compression tests. Various concentrations of PET were mixed to sand with 3%, 5% and 7% cement content. The curing time and relative density of samples was 7 days and 70%, respectively. The results showed that addition of this fiber improves strength parameters such as cohesion and internal friction angle. Furthermore, the effect of the fiber is less marked with an increase in cement content in samples. The samples with 3% cement were showed better results in both direct shear and tiaxial tests. By adding 0.5% and 1% PET fibers to the samples containing 3% cement at 100 kPa pressure, the ratio of strength in direct shear tests was increased 13% and 24%, respectively, and in the triaxial test was increased 50% and 93%, respectively.

Recent research works demonstrated that the interaction between the loads and the carrying structure's boundary which is related to the inertia of the load is an influential factor on the dynamic response of the structure. Although effects of the inertia in moving loads were considered in many works, very few papers can be found on the inertial effects of the stationary loads on structures. In this paper, an elastodynamic formulation was employed to investigate the dynamic response of a homogeneous isotropic elastic half-space under an inertial strip foundation subjected to a time-harmonic force. Fourier integral transformation was used to solve the system of Poisson-type partial differential equation considering the boundary conditions and the inertial effects. Steepest descent method was employed to obtain the approximate far-field displacements and stresses. A numerical example is presented to illustrate the methodology and typical results.

An analytical approach has been applied to obtain the solution of Navier's equation for a homogeneous, isotropic half-space under an inertial foundation subjected to a time-harmonic loading. Displacement potentials were used to change the Navier's equation to a system of wave-type equations. Calculus of variation was employed to demonstrate the contribution of the foundation's inertial effects as boundary conditions. Use of the Fourier transformation method for the system of Poisson-type equations and applying the boundary conditions yielded the transformed surface displacement field. Direct contour integration has been employed to achieve the surface waves. In order to clarify the foundation's inertial effects, related coefficients were defined and a parametric study was conducted. Final results revealed that increasing the mass per unit length of the foundation or the frequency of the applied harmonic load intensifies the inertial effect factors. On the other hand, an increase in strip width or Poisson's ratio would imply reduction in the inertial effect factors.