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• Construction of transparent boundary conditions (TBCs) for exural wave cavity scattering in two dimensions, ensuring the satisfaction of the sommerfeld radiation conditions. • Deduction of a decomposed problem for the biharmonic plate wave equation using two auxiliary functions and establishment of the unique-ness of the solution for the decomposed problem. • Proposal of the linear _nite element method with interior penalty term (IP-FEM) and boundary penalty term (BP-FEM) to solve the coupled boundary helmholtz and modi_ed helmholtz equations, leading to stable numerical solutions. • Introduction of an analytical solution for exural wave scattering by a circular cavity with a clamped boundary, facilitating comparative analysis. Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order plate wave equation on an unbounded domain, making it challenging to solve directly using the regular linear finite element method (FEM). In this paper, we propose two numerical methods, the interior penalty FEM (IP-FEM) and the boundary penalty FEM (BP-FEM) with a transparent boundary condition (TBC), to study flexural wave scattering by an arbitrary-shaped cavity on an infinite thin plate. Both methods decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary. A TBC is then constructed based on the analytical solutions of the Helmholtz and modified Helmholtz equations in the exterior domain, effectively truncating the unbounded domain into a bounded one. Using linear triangular elements, the IP-FEM and BP-FEM successfully suppress the oscillation of the bending moment of the solution on the cavity boundary, demonstrating superior stability and accuracy compared to the regular linear FEM when applied to this problem. [ABSTRACT FROM AUTHOR]

Bolted flanges in aero-engine casings exhibit a nonlinear response when subjected to forced vibration. The current models for the structural dynamic analysis of bolted flanges are accurate, but they are cumbersome for the design of new structures. These models either require model updating from modal testing, or they require a large number of nonlinear elements. This study presents a new lump model that accounts for the nonlinear phenomena of partial clearance and friction, and has analytical parameters related to the flange geometry. The model was implemented in finite element analysis and compared with an experiment where a test structure is excited by an electromechanical shaker. The lump model predicts the structural response better than a traditional linear method; yet it does not require model updating, and it uses a very limited number of nonlinear elements. The model is therefore well suited for the early design phase of new aero-engine casings. This study supports the use of geometric lump models in the field of nonlinear structural dynamics. [ABSTRACT FROM AUTHOR]

Blade crack is one of the most common blade failures of rotating machines which may lead to catastrophic accidents. Although many nonlinear vibrations of breathing crack have been investigated, there are few reports on the axial-bending coupling vibration caused by crack. With the aim of providing physical insight into the mechanisms of axis-bending coupling due to crack, a novel axial-bending coupled breathing crack model (ABCBCM) for the rotating blade is proposed in this study. The proposed ABCBCM is analytically formulated based on the Timoshenko beam theory and Castigliano's principle, and validated by comparing the natural and dynamic characteristics with the finite element model (FEM) and experimental tests. In addition, the effects of boundary conditions (rotational speed), crack parameters (crack depth and crack location) and loading conditions (excitation load) on the vibration characteristics of the cracked blade are investigated. The results indicate that the blade axial response is more sensitive to the nonlinearity caused by the breathing crack than the bending response; the axial-bending coupling caused by the crack changes the equilibrium position of the axial and bending displacement; the phase portrait of axial response and the orbit of axial-bending displacement are effective methods to detect breathing crack; and the axial displacement amplitude ratio and the axial acceleration amplitude ratio also are valuable indicators to estimate the severity of the blade crack. The proposed model can provide valuable insights for fault diagnosis and safety monitoring of cracked blade. • A novel axial-bending coupled breathing crack model (ABCBCM) for the cracked blade with rotational effects is proposed. • The proposed model can simulate the crack-caused axial-bending vibration without additional bending moment. • The phase portrait of axial response and orbit of axial-bending displacement are used to investigate the cracked blade. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents finite element formulae for calculating accurately the internal forces, namely bending moment and shear force, of Bernoulli–Euler beams under moving vehicles. The formulae for evaluating these internal forces are derived based on the dynamic equilibrium conditions and the solution procedure is also given. The correctness of the proposed formulae is verified by comparing with available closed-form solutions. The internal forces of simply supported and continuous beams subjected to moving vehicles are obtained by several methods. The numerical results show that the proposed formulae are efficient and accurate in predicting the internal forces. [Copyright &y& Elsevier]

Abstract: We investigated the restructuring behavior of colloidal aggregates by means of the discrete element method. We used a recently proposed model [V. Becker, H. Briesen, Physical Review E 78 (6) (2008) 061404] for tangential inter-particle forces, capable of supporting bending moments. We extended this model by the capability of supporting torsional moments. The time evolution of the aggregates’ radius of gyration was tracked and a power law relation between the number of primary particles and the final radius of gyration was found. For the hydrodynamic drag forces the free-draining approximation is employed. We investigated the quality of the free-draining approximation by fully resolved finite element simulations for small aggregates. We found that the free-draining approximation overestimates the drag forces and we identified the usage of effective shear rates as a possible ansatz for reduced modeling of hydrodynamic forces. [Copyright &y& Elsevier]

Abstract: In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant–Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation. [Copyright &y& Elsevier]

[Display omitted] • The proposed sensor can detect the bending moment and torque in a self-decoupled manner, without any decoupling algorithm. • The proposed sensor can work passively, without onboard batteries or external power. • The proposed sensor can work wirelessly, without connecting wires. • The proposed sensor can work dynamically and in underwater environment. In this study, a bending moment and torque detecting sensor that works in a passive, wireless, and self-decoupled manner was proposed, analyzed, fabricated, and tested. The sensor was composed mainly of a bending moment deforming ring, a torque deforming sheet, and a cardan. The bending moment deforming ring bore the bending moment separately and the torque deforming sheet withstood the torque individually. The self-decoupling operation of the bending moment and torque was realized by the cardan. Then, the bending moment and the torque were measured separately. The decoupling operation was based on the mechanical structure. Two pieces of magnetostrictive material were pasted on the bending moment deforming ring and torque deforming sheet as the sensing material. The passive and wireless characteristics were fulfilled based on the Villari effect. Finite element method (FEM) analysis was conducted to verify the decoupling principle and acquire the most appropriate position for the sensing material. Experiments were carried out to test the performance of the sensor. The experimental results demonstrated the sensor had a good self-decoupling ability with maximum decoupling error of 1.43%. The sensor was able to work dynamically with an average voltage change ratio of 1.87%. Furthermore, the sensor showed advantages of being passive, and wireless, and had the ability to work in a liquid environment. Therefore, the sensor can be installed on a cutting tool holder of a machine center to detect the compound force on the cutting tool. [ABSTRACT FROM AUTHOR]

In this study, a method of analysis is presented for investigating the effects of elastic foundation and fluid on the dynamic response characteristics (natural frequencies and associated mode shapes) of rectangular Kirchhoff plates. For the interaction of the Kirchhoff plate–Pasternak foundation, a mixed-type finite element formulation is employed by using the Gâteaux differential. The plate finite element adopted in this study is quadrilateral and isoparametric having four corner nodes, and at each node four degrees of freedom are present (one transverse displacement, two bending moments and one torsional moment). Therefore, a total number of 16 degrees-of-freedom are assigned to each element. A consistent mass formulation is used for the eigenvalue solution in the mixed finite element analysis. The plate structure considered is assumed clamped or simply supported along its edges and resting on a Pasternak foundation. Furthermore, the plate is fully or partially in contact with fresh water on its one side. For the calculation of the fluid–structure interaction effects (generalized fluid–structure interaction forces), a boundary element method is adopted together with the method of images in order to impose an appropriate boundary condition on the fluid''s free surface. It is assumed that the fluid is ideal, i.e., inviscid, incompressible, and its motion is irrotational. It is also assumed that the plate–elastic foundation system vibrates in its in vacuo eigenmodes when it is in contact with fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. At the fluid–structure interface, continuity considerations require that the normal velocity of the fluid is equal to that of the structure. The normal velocities on the wetted surface of the structure are expressed in terms of the modal structural displacements, obtained from the finite element analysis. By using the boundary integral equation method the fluid pressure is eliminated from the problem, and the fluid–structure interaction forces are calculated in terms of the generalized hydrodynamic added mass coefficients (due to the inertial effect of fluid). To asses the influences of the elastic foundation and fluid on the dynamic behavior of the plate structure, the natural frequencies and associated mode shapes are presented. Furthermore, the influence of the submerging depth on the dynamic behavior is also investigated. [Copyright &y& Elsevier]

This paper presents a new method to compute the sound radiation emanating from a thin plate structure due to complex inputs that include normal force and in-plane bending moments. A set of new formulas for the sound radiation of baffled and unbaffled plates are derived by substituting the moment components of the plates with the equivalent couples using finite difference analysis. This approach allows to calculate sound power purely by the input location and amplitude of each component. Thus, it enables faster, more accurate calculations than the existing methods such as the average radiation efficiency analysis and the radiation mode analysis. Based on these calculations, the vibroacoustic characteristics of a simply supported rectangular plate are analyzed. The computational results are in good agreement with the finite element analysis results. It is suggested to keep the grid spacing less than 2.5% of the shortest dimension of the target structure to accurately calculate the moment mobility. Accurate sound power can also be obtained by downsampling the grid to satisfy k a < 0.2 within the frequency band of interest. Furthermore, a sound reduction method is proposed by analyzing each structural mode's contribution to the sound radiation. Using the proposed methodology, sound power at a specific frequency or multi-frequency range can be reduced or amplified by changing the location and angle of the complex inputs. • Sound radiation from a thin plate due to complex inputs was calculated. • A more intuitive method was proposed compared to radiation efficiency based method. • Computational time was reduced and the calculation accuracy was improved. • The proposed method was verified by comparison with finite element analysis. • Sound can be reduced by changing location and angle of the complex inputs. [ABSTRACT FROM AUTHOR]