This study presents axially Forced vibration of a cracked nanorod under harmonic external dynamically load. In constitutive equation of problem, the nonlocal elasticity theory is used. The Crack is modelled as an axial spring in the crack section. In the axial spring model, the nonrod separates two sub-nanorods and the flexibility of the axial spring represents the effect of the crack. Boundary condition of the nanorod is selected as fixed-free and a harmonic load is subjected at the free end of the nanorod. Governing equation of the problem is obtained by using equilibrium conditions. In the solution of the governing equation, analytical solution is presented and exact expressions are obtained for the Forced vibration problem. On the solution method, the separation of variable is implemented and the Forced vibration displacements are obtained exactly. In the open literature, the Forced vibration analysis of the cracked nanorod has not been investigated broadly. The objective of this study is to fill this blank for cracked nanorods. In numerical results, influences of the crack parameter, position of crack, the nonlocal parameter and dynamic load parameters on Forced vibration responses of the cracked nanorod are presented and discussed.

Mechanical systems with structural symmetries present vibration properties that allow the calculation to be easier and the analysis time to decrease. The paper aims to use the properties involved by the symmetries that exist in mechanical systems for the analysis of the Forced response to vibrations. Thus, the study of the properties of systems with symmetries or with identical parts is expanded. Based on a classic model, the characteristic properties that appear in this case are obtained and the advantages of using these properties are revealed. On an example consisting of a truck equipped with two identical engines, the way of applying these properties in the calculation and the resulting advantages is presented.

In this paper, a numerical solution procedure is presented for the free and Forced vibration of a piezoelectric nanowireunder thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenkobeam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken intoconsideration. Using Hamilton’ s principle, the nonlocal governing differential equations are derived. The governingequations and the related boundary conditions are discretized by using the differential quadrature method (DQM). Thenumerical results are obtained for both free and Forced vibration of piezoelectric nanowires. The present results arevalidated by available results in the literature. The effects of the nonlocal parameter together with the other parameterssuch as residual surface stress, temperature change and external electric voltage on the size-dependent Forced vibrationof the piezoelectric nanowires are studied. It is shown that the nonlocal effect (small scale effect) plays a prominentrole in the Forced vibration of piezoelectric nanowires and this effect cannot be neglected for small externalcharacteristic lengths. The resonant frequency increases with increasing the residual surface stress. In addition, as thesurface elastic constant increases, the resonant frequency of PNWs increases, while the surface piezoelectric constanthas a decreasing effect on the resonant frequency.

The implementation of new techniques and design of new elements have been an important issues among finite element researchers. In this regard, a designed super element has been applied to analyze a series of dynamic problems. Findings indicate that in large structure analysis the same results as the conventional method can be obtained when applying a few super elements. The time required for dynamic analysis using a super element is significantly smaller than the regular finite element. In this paper, the Forced vibration of laminated composite rectangular plates is analyzed. The dynamic response of the plate, using a four-super element, is obtained. In-plane deformation, as well as bending deformation, is included in the model. The current computational model is a simple and efficient way to predict the dynamic behavior of the laminated composite plate.

This paper deals with the harmonic Forced vibration of a circular plate surface bonded by two piezoelectric layers, based on the Kirchhoff plate model.The electric potential field in the piezoelectric layer is assumed such that the Maxwell static electricity equation is satisfied. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The solutions are expressed by elementary Bessel functions. The results are verified by those obtained from finite-element analysis as well as the findings stated in the literature.

Dynamic properties of Shahid Rajaee Concrete Arch Dam were identified by Forced vibration tests and then compared with FE model results. Forced vibration tests on the dam were performed with two exciter units on the dam crest for alternative conditions of in-phase and out-of-phase cases. Test records were processed using PSD, CSD and Coherence Spectra through MATLAB software. Consistent conformity between experimental and computational 8 middle modes of the Dam-Reservoir-Foundation system was achieved by the particular algorithm proposed in this research.