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1.
A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. Advantages of the method over classical methods are discussed, and it is concluded that the method is most advantageous when used for a structure with frequency and/or temperature dependent damping properties, or when the non-proportional part of the damping is local. The technique suggested can easily be applied to structural modification problems if there is no additional degree-of-freedom due to the modifying structure.  相似文献   

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In this paper, an analytical method is proposed for solving the free vibration of cracked functionally graded material (FGM) beams with axial loading, rotary inertia and shear deformation. The governing differential equations of motion for an FGM beam are established and the corresponding solutions are found first. The discontinuity of rotation caused by the cracks is simulated by means of the rotational spring model. Based on the transfer matrix method, then the recurrence formula is developed to get the eigenvalue equations of free vibration of FGM beams. The main advantage of the proposed method is that the eigenvalue equation for vibrating beams with an arbitrary number of cracks can be conveniently determined from a third-order determinant. Due to the decrease in the determinant order as compared with previous methods, the developed method is simpler and more convenient to analytically solve the free vibration problem of cracked FGM beams. Moreover, free vibration analyses of the Euler–Bernoulli and Timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method. These advantages of the proposed procedure would be more remarkable as the increase of the number of cracks. A comprehensive analysis is conducted to investigate the influences of the location and total number of cracks, material properties, axial load, inertia and end supports on the natural frequencies and vibration mode shapes of FGM beams. The present work may be useful for the design and control of damaged structures.  相似文献   

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A method for the dynamic analysis of continuously and non-proportionally damped plates is discussed. The method is quite general and suitable for various damping treatments, such as in multilayer plates with damping layers. The transverse vibrations of partially coated plates under harmonic excitation are analyzed by the proposed method. The results of the undamped modal analysis made by classical finite element methods are used in the suggested lumped parameter analysis. The receptance matrices of coated plates have been computed at undamped natural frequencies. The computational results have been verified by comparison with experimental values for partially and fully coated rectangular plates.  相似文献   

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Modern modal control techniques are applied to the design of dynamic absorbers for the control of transient vibrations of internally damped thin uniform beams. Parameters and locations of single and dual absorbers are chosen so that the overall system approximates a desired characteristic polynomial.  相似文献   

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This paper presents a method for the dynamic analysis of continuously and non-proportionally damped plates in bending modes. The damping can be in the form of constrained or unconstrained layers. The method is an extension of the equivalent dampers method discussed in a previous paper, in which the damping matrix of a discretized plate is replaced by a diagonal equivalent damping matrix. Each diagonal element represents an equivalent damper inserted between the structure and ground. In this method the number of equivalent dampers is reduced so that the receptance matrix of the damped structure can be obtained economically by a direct matrix method. The receptances of two different partially coated plates in transverse directions are computed by the method suggested. The verification of the results is demonstrated by comparison with the experimental values and also with the theoretical values obtained by the equivalent dampers method. The method presented can also be applied to the transverse vibration analysis of plates with discrete damping inserts.  相似文献   

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In this paper, a method of stability analysis for the large amplitude, steady state response of a non-linear beam under periodic excitation is presented. The stability problem is investigated by studying the behavior of a small perturbation of the steady state response which results in a coupled Hill-type equation. The problem is transformed by the harmonic balance method into an eigenvalue problem of a non-symmetric matrix. The effectiveness and the accuracy of the proposed method for a Mathieu equation are examined and the application to the stability analysis of the non-linear vibrations of a beam is presented.  相似文献   

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A Timoshenko beam finite element is presented which has three nodes and two degrees of freedom per node, namely the values of the lateral deflection and the cross-sectional rotation. The element properties are based on a coupled displacement field; the lateral deflection is interpolated as a quintic polynomial function and the cross-sectional rotation is linked to the deflection by specifying satisfaction of the governing differential equation of moment equilibrium in the absence of the rotary inertia term. Numerical results confirm that this procedure does not preclude convergence to true Timoshenko theory solutions since rotary inertia is included in lumped form at element ends. The new Timoshenko beam element has good convergence characteristics and where comparison can be made in numerical studies it is shown to be generally more efficient than previous elements.  相似文献   

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Inverse iteration is extended to internally and/or externally damped natural vibration. Each iteration involves one matrix multiplication and one linear equation solution of order n. The symmetric band form of the original undamped eigenvalue problem is preserved. If the undamped mode is taken as the first approximation, the inverse iteration will converse to the corresponding damped mode in about four iterations. However, the one step method is divergent for heavy damping. Therefore, it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations. The method is successful for both discrete systems and distributed systems. The implementation is very simple by means of complex arithmetic which is readily available in many FORTRAN compilers.  相似文献   

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This paper studies free vibration of axially functionally graded beams with non-uniform cross-section. A novel and simple approach is presented to solve natural frequencies of free vibration of beams with variable flexural rigidity and mass density. For various end supports including simply supported, clamped, and free ends, we transform the governing equation with varying coefficients to Fredholm integral equations. Natural frequencies can be determined by requiring that the resulting Fredholm integral equation has a non-trivial solution. Our method has fast convergence and obtained numerical results have high accuracy. The effectiveness of the method is confirmed by comparing numerical results with those available for tapered beams of linearly variable width or depth and graded beams of special polynomial non-homogeneity. Moreover, fundamental frequencies of a graded beam combined of aluminum and zirconia as two constituent phases under typical end supports are evaluated for axially varying material properties. The effects of the geometrical and gradient parameters are elucidated. The present results are of benefit to optimum design of non-homogeneous tapered beam structures.  相似文献   

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This paper addresses the issue of design of a passive vibration absorber in the presence of uncertainties in the forcing frequency. A minimax problem is formulated to determine the parameters of a vibration absorber which minimize the maximum motion of the primary mass over the domain of the forcing frequency. The limiting solutions corresponding to the forcing frequency being unrestricted and to that where the forcing frequency is known exactly, are shown to match those available in the literature. The transition of the optimal vibration absorber parameters between the extreme two cases is presented and the solutions are generalized by permitting the mass ratio of the absorber mass and the primary mass to be design parameters. For the specific case where the primary system is undamped, detailed analysis is presented to determine the transition of the optimal vibration absorber parameters between three distinct domains of solutions.  相似文献   

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This paper deals with higher-order theories for the analysis of free vibration of beam structures. Refined theories are implemented by the application of the Unified Formulation by the first author which allows one to introduce any-order expansions of the displacement unknowns over the beam sections. The selection of the most appropriate theory is made by using a so-called axiomatic–asymptotic approach which permits one to retain only those terms of the displacement expansion which have been established to be significant with respect to an assigned control parameter. The finite element method is used to provide numerical solutions. Various beam sections as well as boundary conditions are considered. Depending on the vibration modes (bending, torsion, etc.), quite different theories are selected. In general, the number of the effective terms of the resultant theories is much lower than the full expansion case amount. The nature of these terms can differ very much as different beam geometries and boundary conditions are considered. It has been concluded that the method proposed appears to be suitable and convenient to establish the most appropriate beam theory for a given problem; it leads, in fact, to the cheapest computational model for a given accuracy.  相似文献   

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Free vibration analysis of planar curved beams by wave propagation   总被引:1,自引:0,他引:1  
In this paper, a systematic approach for the free vibration analysis of a planar circular curved beam system is presented. The system considered includes multiple point discontinuities such as elastic supports, attached masses, and curvature changes. Neglecting transverse shear and rotary inertia, harmonic wave solutions are found for both extensional and inextensional curved beam models. Dispersion equations are obtained and cut-off frequencies are determined. Wave reflection and transmission matrices are formulated, accounting for general support conditions. These matrices are combined, with the aid of field transfer matrices, to provide a concise and efficient method for the free vibration problem of multi-span planar circular curved beams with general boundary conditions and supports. The solutions are exact since the effects of attenuating wave components are included in the formulation. Several examples are presented and compared with other methods.  相似文献   

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In this paper, an analytical procedure for free vibrations of shear-deformable two-layer beams with interlayer slip is developed. The effect of transverse shear flexibility of two layers is taken into account in a general way by assuming that each layer behaves as a Timoshenko beam element. Therefore, the layers have independent shear strains that depend indeed on their own shear modulus. This is the main improvement of the proposed model compared to existing models where the transverse shear flexibility is ignored or taken into account in a simplified way in which the shear strains of both layers are assumed to be equal whatever the shear modulus of the layers. In the proposed model, the two layers are connected continuously and the partial interaction is considered by assuming a continuous relationship between the interface shear flow and the corresponding slip. Based on these key assumptions, the governing differential equation of the problem is derived using Hamilton's principle and is analytically solved. The solutions for the eigenfrequencies and eigenmodes of four single span two-layer beams with classical Euler boundary conditions, i.e. pinned-pinned, clamped-clamped, clamped-pinned and clamped-free, are presented. Next, some numerical applications dealing with these four beams are carried out in order to compare the eigenfrequencies obtained with the proposed model against two existing models which consider different kinematic assumptions. Finally, a parametric study is conducted with the aim to investigate the influence of varying material and geometric parameters on the eigenfrequencies, such as shear stiffness of the connectors, span-to-depth ratios, flexural-to-shear moduli ratios and layer shear moduli ratios.  相似文献   

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