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Go to Editorial ManagerFourier series and finite element analysis are utilized to obtain the solution of simply supported beams resting on elastic foundations with different loadings in order to arrive at a free vibration. The equation of the free vibration of beam on elastic foundation is derived and solved. Good agreement has been obtained between the results of the present study Fourier and finite element analysis and other previous solutions. The effect of modulus of subgrade reaction, axial tension force (foundation modulus) and beam depth on the behavior is studied.
The free vibration analysis of rotating multi-layered cylindrical shell is investigated based on the first order shear deformation theory (FSDT) of shell. Cylindrical shell consists of three layers; outer and inner layers are isotropic material and the middle layer is a functionally graded material (FGM). The material properties for middle layer are assumed to be graded in the thickness direction. Based on Hamilton’s principle, the equilibrium equations and the equations of motion are derived and then solved by using the differential quadrature method (DQM) as a numerical tool. MATLAB software was adopted for programming the equations and the related boundary condition. The effect of (FGM) layer thickness, angular speed, index power law, circumferential wave number on the natural frequency of the clamped-clamped rotating cylindrical shell were examined. The numerical results showed that a reasonable agreement between the present study and analytical data available in the literature.
In this research, we investigate the nonlinear vibration of functionally graded carbon nanotubes (FG-CNTs) for simply supported sandwich cylindrical panels. The sandwich consisting of three layers formed of (FG-CNTs) and isotropic material as (CNT, ALMINUME, CNT). Mechanical properties of the sandwich media are acquired according to a re?ned rule of blend approach. The governing equations were derived using a first-order deformation theory (FOSDT). Four kinds of carbon nanotubes of sandwich cylindrical panels were analyzed. The volume fraction of CNTs is varied. The properties of nonlinear responses and free vibration are studied. The numerical approach employs the fourth-order Runge-Kutta and Galerkine procedure. Which conducted for the dynamic analysis of the panels to present the natural frequencies and non-linear dynamic response expression. The results show that; the natural frequencies and the nonlinear vibration amplitude decrease with the volume fraction and thickness ratio increase. The nonlinear vibration amplitude response increases when increasing the excitation force. The initial imperfection and the elastic foundation have a minor impact on the nonlinear vibration response of the panel. The Pasternak Foundation has a larger impact than the Winkler foundation. The structure formed of FG-CNT present an excellent choice for high-performance of engineering applications.
Pressure vessels are the heart of plants and oil refineries stations. In many engineering applications such vessels can be subjected to periodic loading either internally due to the charging and discharging process or externally due to the excitation from other nearby components such as pumps, compressors or from seismic. So that in spite of a good design according static assumption it may be critical in dynamics. In this work a horizontal pressure vessel with accessories subjected to liquefied petroleum gas pressure LPG is considered. Three models of different head types are investigated herein namely; Deep torispherical, Elliptical 2:1 and Hemispherical. The design and material selections are chosen as per ASME. For practical service many accessories are attached to the vessel such as manhole, supports, inlet and outlet opining. Finite Element method via ANSYS R18.2 is introduced for the numerical analysis. The fatigue life in case of fully reversed cyclic loading are estimated and located. Vibration characteristics such as mode shapes and natural frequencies for the lowest five modes are evaluated and compared. It is found that the fatigue life can be increased as higher as 180% for hemi- spherical head as compared with deep torispherical head pressure vessel and the lowest four natural frequencies are nearly identical for all models, however significant change observed in the fifth natural frequency.
In this paper, a dynamic analysis has been carried out on zoned earthdam subjected to earthquake excitation in which pore water pressure, effective stresses and displacements are calculated. The finite element method is used and the computer program Geo-Studio is adopted in the analysis through its sub-programs SEEP/W and QUAKE/W. A case study is considered to be Khassa Chai dam which is located on Khassa Chai river north of Iraq and consists of zoned embankment with a total length of 3.34 km. The selected earthquake for the analysis is El-Centro earthquake with a period of 10 sec and different amplitudes of acceleration. The time of the analysis is taken as 600 sec. with a time step (?t = 0.05 sec.) to investigate the behavior of the soil for a period of time after the earthquake has stopped, a free vibration period is included in the analysis. It was concluded that the value of pore water pressure generated at the base of the core is greater than that in the upper parts of dam. The horizontal and vertical effective stresses continue to decrease during the period of analysis 600 sec. which indicates that the soil continues to weaken during this period, the horizontal displacement increases with depth of the point from the crest and the largest horizontal displacement will be at the base of the dam at time 60 sec and There is attenuation of the acceleration to some degree depending on the amplitude of the input horizontal acceleration. The maximum horizontal displacement decreases by about 37%, 45% and 49% when using a horizontal drain 2 m thick at the downstream under a peak acceleration of 0.05g, 0.1g and 0.2g, respectively.
Openings in reinforced concrete (RC) slabs are usually created as a result of variations in construction function, architectural or mechanical necessities. Heavy equipment loads resulting from mechanical system of any building are often carried by RC slabs. Even the static analysis and design of RC slabs with opening is not clearly stated in the available international Codes, dynamic analytical solution for such structure is complex._x000D_ In this paper, numerical analysis based on finite element approach is utilized to implement the modal analysis of RC slabs. Opening size and position was parametrically studied. Slab natural frequency or periods in addition to, the mode shape were registered. The results showed that the opening size and position involved in RC slab had a significant change in the value of natural frequency and period for the high level modes. The material nonlinearity affect on free vibration analysis of RC opening slab with different levels of stiffness modifiers was taken into account. The dynamic characteristics of RC opening slab as a function of stiffness modifier degree was numerically measured for six mode shapes. The paper found that a reduction in stiffness modifier value greatly reduce the .natural frequency of RC opening slab.