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The polar finite element is utilized to examine the dynamic characteristics of the horizontal cylindrical shells taking into account sloshing effect. The proposed method is developed by integrating the structural shape functions that are derived on basis of exact solution of equations of motion of shell, the polar finite element and the Sander's thin-walled shell theory. Furthermore, a rigorous fluid-structure interaction analysis is carried out based on the simultaneous solving of the governing equations of the solid and the fluid domains. Moreover, the natural frequencies and the mode shapes of the system are obtained, and the numerical results are compared with available experimental outcomes. By this mean, the accuracy of the presented method is examined thoroughly and it is concluded that the proposed method, in comparisons with other theoretical approaches, is much more accurate under all practical conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic analysis of Euler–Bernoulli beams at the resonant condition. The governing partial differential equation of the problem is converted into an ordinary differential equation by applying the well-known Fourier transform. The solution develops a Green’s function method which involves establishing the Green’s function of the problem, applying the pertinent boundary conditions of the beam. Due to the special conditions of the resonant situation, a significant obstacle arises during the derivation of the Green’s function. In order to overcome this hurdle, however, the Fredholm Alternative Theorem is employed; and it is shown that the modified Green’s function of the beam may still be achievable. Furthermore, the necessary requirement so that the resonant response will be found is introduced. A special case which refers to a case in the absence of resonance is also included, for some verification purposes. [ABSTRACT FROM AUTHOR]

Abstract: A new modal technique is proposed for dynamic analysis of concrete arch dam–reservoir systems in frequency domain. The approach relies on the new mode shapes that are entitled “ideal-coupled modes”. These modes are employed in somehow similar to decoupled modes of the dam–reservoir system. However, they are actually coupled modes of ideal systems which correspond to fictitious systems. These are calculated by assuming incompressible fluid to obtain the first set and massless solid idealization to compute the second set. These two ideal systems are replacing the actual system temporarily just to obtain the mode shapes. It should be realized that although, these ideal mode shapes are not the true coupled modes of the original system, they are utilized to solve the true coupled problem. It is also worthwhile to emphasize that the employed mode shapes can be envisaged as some kind of Ritz vectors for the original system. The accuracy of the proposed technique is examined thoroughly and it is concluded that ideal-coupled procedure is very accurate under all practical conditions. It is also shown that the decoupled modal approach proposed in a previous study can be considered as a special case of the present more general procedure. [Copyright &y& Elsevier]

Abstract: The accurate dynamic analysis of concrete arch dams relies heavily on employing a three-dimensional semi-infinite fluid element. The usual method for calculating the impedance matrix of this fluid hyper-element is dependent on the solution of a complex eigenvalue problem for each frequency. In the present study, a modified efficient procedure is proposed, which simplifies this procedure significantly, and results in great computational time savings. Moreover, the accuracy of this technique is examined thoroughly and it is concluded that modified efficient procedure is also extremely accurate under all practical conditions. It is also shown that the original efficient method proposed in a previous study can be considered as a special case of the present more general procedure. [Copyright &y& Elsevier]

In this paper, a new system of damage detection equations for damage identification of cylindrical shells is developed based on classic finite element method, incomplete noisy modal data and model updating. Classic finite element technique in conjunction with Sander's thin shell theory is deployed in order to construct the finite element model of cylindrical shells and compute vibration data. To overcome the difficulty of incomplete data, "system equivalent reduction expansion process" (SEREP) method is applied to find a proper complete approximation of incomplete modal data. The proposed system is usually ill-posed due to noisy data and ill-conditioned system derived from the model updating process. To tackle this issue, a constraint as a regularization parameter is employed in model updating problem to differentiate potentially damaged elements and undamaged elements. This constraint is imposed on the model updating process by defining a Reduction Index (RI) and forcing severities of undamaged elements to tend to zero. Furthermore, the presented system is non-square and large depending on the number of structural unknowns. For these reasons, Biconjugate gradient (BCG) method along with an appropriate preconditioner are employed to solve the system of equations. Not only does the preconditioner stabilize the solution against numerical errors and inaccuracies caused by noisy data, but also it alters the system to a square one. Numerical studies are performed to demonstrate the efficiency of the presented method. Moreover, a statistical analysis is carried out to evaluate the effect of different sequences of random noises on the damage detection results. Findings show that the proposed method is capable of detecting the severities and sites of damages for cylindrical shells in the presence of noisy data. • Presenting a new method for damage detection of cylindrical shells based on Sander's theory and using incomplete modal data. • Conducting statistical analysis in order to examine the influence of noisy data on the damage detection results. • Using model updating strategy in conjunction with a new constraint to minimize the numerical and measurement errors. • Employing a preconditioner so as to guarantee the robustness of solution and switch the non-square system to a square one. [ABSTRACT FROM AUTHOR]