Sharif Digital Repository

In this paper, a continuous model for flexural vibration of beams with a vertical edge crack including the effects of shear deformation and rotary inertia is presented. The crack is assumed to be an open-edge crack perpendicular to the neutral plane. A quasi-linear displacement filed is suggested for the beam, and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle. The equation of motion is solved with a modified weighted residual method, and the natural frequencies and mode shapes are obtained. The results are compared to the results of similar model with Euler–Bernoulli assumptions and finite element model... 

The present study deals with vibrational behavior of two joined cross-ply laminated conical shells. The natural frequencies and mode shapes are investigated. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, cylindrical and conical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell type and Hamilton's principle. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section of the cones. The equations are solved assuming trigonometric response in... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

The free vibrations analysis of liquid sloshing is carried out for arbitrary axisymmetric containers under low-gravity condition using boundary element method. A potential flow theory is used to model the flow field and the free-surface Laplace-Young equation is used to model the surface tension effect. The obtained governing equations are solved using eigenanalysis techniques to determine the natural frequencies and mode shapes of the sloshing liquid. The results for a circular cylindrical container are compared to the analytical values and very good agreement is achieved for the slipping and anchored contact line assumptions. Furthermore, some baffled containers are also analysed and the... 

The objective of this work is to design electrostatic actuators for a CMOS-MEMS nano-newton capacitive force sensor to suppress vertical vibrations disturbances. Electrostatic actuators are selected because the movable part of this force sensor is anchored to the fixed parts. In the first step, we propose a framework for simulation of the force sensor based on finite element method. The proposed model is modified utilizing comparison between the simulation and experimental models to improve the performance of the model. Then, 14 pairs of electrostatic actuators are designed for applying the control algorithm and their pull-in voltage is calculated. In next step, Modal Analysis is applied to... 

The potentials of carbon nanotubes (CNTs) as mechanical resonators for atomic-scale mass sensing are presented. To this aim, a nonlocal continuum-based model is proposed to study the dynamic behavior of bridged single-walled carbon nanotube-based mass nanosensors. The carbon nanotube (CNT) is considered as an elastic Euler–Bernoulli beam with von Kármán type geometric nonlinearity. Eringen’s nonlocal elastic field theory is utilized to model the interatomic long-range interactions within the structure of the CNT. This developed model accounts for the arbitrary position of the deposited atomic-mass. The natural frequencies and associated mode shapes are determined based on an eigenvalue... 

Carbon nanoscroll (CNS) is a graphene sheet rolled into a spiral structure with great potential for different applications in nanotechnology. In this paper, an equivalent open shell model is presented to study the vibration behavior of a CNS with arbitrary boundary conditions. The equivalent parameters used for modeling the carbon nanotubes are implemented to simulate the CNS. The interactions between the layers of CNS due to van der Waals forces are included in the model. The uniformly distributed translational and torsional springs along the boundaries are considered to achieve a unified solution for different boundary conditions. To study the vibration characteristics of CNS, total energy... 

In this paper a new approach is introduced for structural health monitoring of offshore jacket platforms. The procedure uses the measured ambient vibration responses and the corresponding readable natural frequencies and mode shapes of the structural system. Since offshore platforms are composed of heavy topsides supported by jacket structures, participation of the first mode is dominant in each direction in the response of the structure under field excitations. Moreover, ambient vibrations such as wave loads and boat impacts only excite the first modes of the structure. Therefore, it is difficult to find higher modes and the pertinent frequencies by use of accelerometers data. The... 

In this paper a nonlinear pedal like microresonator made of Functionally Graded material is introduced and modeled. Using Lagrangian formulation nonlinear equations of motion of the system are derived and the natural frequencies and mode shapes are extracted by linear analysis. The effects of various parameters such as geometry, FG material index and DC voltages on the natural frequencies and mode shapes are investigated. Static pull-in voltages of the system are obtained and it is found that depending on the type of actuation, both softening and hardening behaviors can be observed in the system. The results are compared with previous studies and finite element method where a good agreement... 

Rings are widely used in mechanical equipment, and their fitness may undergo some damage under severe vibration. In these structures, functionally graded rings can be used to optimize the resistance, energy consumption, and fitness. Due to their complexity, the finite-element analysis may be implemented using special elements. Enhancement of accuracy and minimization of time consumption play an important role in the analysis of these rings. In this study, a new cylindrical superelement for the FGM rings is designed and implemented to facilitate the vibration analysis of the rings. The power-law distribution is used for the modeling of the FGM rings in the thickness direction. Natural... 

In this paper a new continuous model for vibration analysis of a beam with an open edge crack is presented. A quasi-linear displacement filed is suggested for the beam and the strain and stress fields are calculated. The equation of motion of the beam is calculated using the Hamilton principle. The calculated equation of motion is solved with a modified weighted residual method and the natural frequencies and mode shapes are obtained. The results are compared with those obtained by finite element method and an excellent agreement has been observed. The presented model is a simple and accurate method for analysis of the cracked beam behavior near or far from the crack tip  

The paper presents the experimental and analytical model analysis of a steel-girder arch bridge. The field test is carried out by ambient vibration testing under traffic excitations. Both the peak picking method in the frequency domain and the stochastic subspace identification method in the time domain are used for the output-only model identification. A good agreement in identified frequencies has been found between the two methods. It is further demonstrated that the stochastic subspace method provides better mode shapes. The three-dimensional finite element models are constructed and an analytical model analysis is then performed to generate natural frequencies and mode shapes in the...