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.

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.

In this paper, an analytical study of the Forced Vibrations of hexapod table is studied. Considering external force as a time sinusoid force, Forced Vibrations of the platform are investigated. Resonance frequencies and Vibrations of the moving platform are also calculated in different directions. The results of the analytical approach are verified using FEM simulation. Modelling the harmonic milling forces, a careful examination of the Forced Vibration are carried out in different cutting conditions and different configurations. Resonance frequencies and the range of Vibrations are then calculated. Finally, knowing the resonance frequencies and the Vibrations of hexapod table, different configurations of the table, which results in dynamic instability, are investigated.

This study focuses on the investigation of intelligent form-finding and Vibration Analysis of a triangular polyhedral tensegrity that is enclosed within a sphere and subjected to external loads. The nonlinear dynamic equations of the system are derived using the Lagrangian approach and the finite element method. The proposed form-finding approach, which is based on a basic genetic algorithm, can determine regular or irregular tensegrity shapes without dimensional constraints. Stable tensegrity structures are generated from random configurations and based on defined constraints (nodes located on the sphere, parallelism, and area of upper and lower surfaces), and shape finding is performed using the fitness function of the genetic algorithm and multi-objective optimization goals. The genetic algorithm's efficacy in determining the shape of structures with unpredictable configurations is evaluated in two distinct scenarios: one involving a known connection matrix and the other involving fixed or random member positions (struts and cables). The shapes obtained from the algorithm suggested in this study are validated using the force density approach, and their Vibration characteristics are examined. The findings of the comparative study demonstrate the efficacy of the proposed methodology in determining the Vibrational behavior of tensegrity structures through the utilization of intelligent shape seeking techniques.

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.

Cylindrical shells are used tremendously in many engineering fields such as ships, submarines, and fuel tanks in airplanes. In many cases, shells are exposed to dynamic loads. One of the dynamic loads in shells is internal moving pressure. Analysis of cylindrical stiffened shells under moving internal pressure are investigated in this research. Equations of motion are based on classic shell theory and derived from Hamilton’s method. Boundary conditions are assumed simply support. Displacement components are assumed Fourie double series based on boundary conditions. Equations of motions are solved by Galerkin weighted functions method for calculation of natural frequency and dynamic response of cylindrical shells under moving internal pressure. Codes in FORTRAN are used to derive the natural frequency and dynamic response of cylindrical shells. Results are compared with other references and Abaqus software. The effect of geometrical parameters on natural frequency and dynamic response of cylindrical shells under moving internal pressure are investigated finally and results for stiffened shells and unstiffened shells with different stiffeners are compared.

This work proposes a geometrically non-linear vibratory study of a functional gradation beam reinForced by surface-bonded piezoelectric fibers located on an arbitrary number of supports and subjected to excitation forces and thermoelectric changes. The non-linear formula is based on Hamilton's principle combined with spectral Analysis and developed using Euler-Bernoulli's beam theory. In the case of a non-linear Forced response, numerical results of a wide range of amplitudes are given based on the approximate multimodal method close to the predominant mode. In order to test the methods implemented in this study, examples are given and the results are very consistent with those of the literature. It should also be noted that the thermal charge, the electrical charge, the volume fraction of the structure, the thermal properties of the material, the harmonic force and the number of supports have a great influence on the Forced non-linear dynamic response of the piezoelectrically functionally graded structure.

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.