In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.
This paper examines the free lateral vibration of a cracked nano-beam based on Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). Due to the importance and application of nanostructures, their mechanical and mechanical properties are essential. The governing equations and boundary conditions related to using the Hamilton principle have been extracted. The beam separation with the nano-beams division into two parts attached to the Torsion spring is modeled. The model calls the excess strain energy due to crack and increases the discontinuity in the deflection slope. This study investigated the effects of crack propagation, crack intensity, material length scale parameter, and various nonlocal parameters. A comparison of previous studies has been published, where a good agreement is observed. The results show that the parameters mentioned above play an important role in dynamical behavior.
Today, due to the many applications of sandwich beams in industry, studying the forced vibrations of these structures is important. In these structures, amplifiers are used to improve mechanical properties. In this paper, metal-based graphene (copper) is used to improve the mechanical properties. This research uses a functionally graded (FG) graphene-reinforced copper-based composite (GRCC) sandwich beam and FG soft porous core, subjected to two moving loads and located on an elastic foundation. The equations are derived using Soldatos’ higher-order shear deformation theory in axial and transverse directions. The exact problem under the magnetic field is solved using the Laplace method, which has not been done. The advantages of this method are the simplicity of solving and reducing to zero the error percentage that exists in numerical solutions. The results are compared with previous works. Finally, the effect of various parameters such as magnetic, porosity coefficient, elastic constant, thickness ratio, and velocity of moving load on the dynamic response of the sandwich beam is investigated. It should be noted that the results can be used to construct this type of structure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.