The real mecheanics model of pantographs is analyzed with master/slave freedom technique in this paper The element stiffness matrix of pantograph and the free vibration equations under hybrid coordinate are derived.

Based on simplified Donnel shell theory and acoustic wave propagation equation in a pipe with fully developed turbulent flow, free vibration equations of fluid flowing piping system were derived. Types of wave corresponding to various circumference mode ( n =0, 1, 2, 5) and various axial wavenumber were analyzed in details. The fundamental types of wave were determined which were responsible for vibration energy transmission in pipe.

Based on Bernoulli equation,the mechanism of solid-fluid interaction was analyzed,and the free vibration equations of solid-fluid interaction rectangular containers with elastic bottoms were established.

Based on Maxwell, Kelvin, generalized Kelvin and Poyting-Thomson(P-TH) models, the free vibration equations of viscoelastic thin plate are derived, and the analytical solutions to the natural frequencies are given for thin rectangular plate on Maxwell and kelvin models. Their dynamic behaviors are analysed and compared.

In this paper, the alternate iteration method is used in static analysis of cable truss hybrid structural system, and the simplified non damping free vibration equations have been drawn.

Based on Maxwell,Kelvin,three elements models of viscoelastic foundations,the free vibration equations of viscoelastic foundation plate on viscoelastic foundations are derived. And the analytical solutions to the natural frequencies are given for viscoelastic rectangular plates of Kelvin and three elements models on Kelvin viscoeastic foundations. Their dynamic behaviors are analyzed and compared for different models.

With the elastic bearing, the model of elastic bending beam was firstly used to simulate the cable and deck of cable-stayed bridge. The dynamic governing equations of beam of multi-cables and one girder composite structure were derived by Hamilton’s principle and the free vibration equations of beam with consideration of axial force.

The time domain free vibration equations of motion are obtained by applying the principle of virtual work, and are mapped into the frequency domain by the harmonic balance method.

With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established.

Currently used finite dynamic elements are all expressed by frequency expansions of both mass and stiffness matrices, namelyThus, for a finite dynamic element a set of mass and stiffness matrices of successive orders must be established, In the present paper the impedance matrixfor finite dynamic element is proposed.Basing upon; this new concept, instead of deriving mass and stiffness matrix expansion terms separately, only expansion terms D'f s of D(ω) are to be derived, hence the formulation of finite dynamic...

Currently used finite dynamic elements are all expressed by frequency expansions of both mass and stiffness matrices, namelyThus, for a finite dynamic element a set of mass and stiffness matrices of successive orders must be established, In the present paper the impedance matrixfor finite dynamic element is proposed.Basing upon; this new concept, instead of deriving mass and stiffness matrix expansion terms separately, only expansion terms D'f s of D(ω) are to be derived, hence the formulation of finite dynamic element is simplified significantly. Furthermore, the incorrect stiffness matrix term K1 derived in some previous studies is avoided automatically. Thus the second order finite dynamic element free vibration equation can be consistent with the conventional finite element equation. It is shown that there exist definite relations between the mass-stiffness matrix pair and the impedance matrix expansion terms, namelyThe finite dynamic element impedance matrices of two dimensional membrane, rectangular and triangular plate elements as well as one dimensional bar and beam elements are established.The element shape function vector a is expanded inThe α'i s are derived as follows:For a×b rectangular membrane, the governing equations are and the boundary conditions areFinal results obtained area0 is determined to be the same as for the conventional finite element method, while the remaining aif s are found by Galerkin method.For plate elements the procedures of derivation are similar to that just mentioned above.Illustrative examples of membrane and cantilever plates both rectangular an triangular are worked out, numerical results are compared with those obtained by conventional method.In the present paper the finite dynamic element method is shown to be a special case of higher order Guyan reduction. Thus, from Guyan reduction analysis a frequency limitation criterion and error estimation formula for finite dynamic element are established. Numerical checks confirm the feasibility of these formulas.

Taking the advantages of Spline Function Substructure Method and Synthetic Discrete Method, the authors propose a new method for dynamic property analysis of high-rise tube structures. For the purpose of analysis Plane stress element with four nodal points of orthogonal anisotropy is derived. In addition, an analytical method of independent column substructures is given. In defining the displacement patterns of nodal points, the cubic B-spline function and variant intervals spline function are used in vertical...

Taking the advantages of Spline Function Substructure Method and Synthetic Discrete Method, the authors propose a new method for dynamic property analysis of high-rise tube structures. For the purpose of analysis Plane stress element with four nodal points of orthogonal anisotropy is derived. In addition, an analytical method of independent column substructures is given. In defining the displacement patterns of nodal points, the cubic B-spline function and variant intervals spline function are used in vertical and horizontal (peripheral) directions, respectively. With generalized displacements as unknowns the horizonto-torsional coupled free vibration equations are established. The numbers of D. O. F. are only related to the term number of horizontal displacement functions but not to the storey number. Clear concept, high accuracy and less computation are the advantages of the proposed method. The numerical results of the examples show a good agreement with those of model experiments.

In this paper, Frame-Shear wall structure is divided into frame substructure and shear wall substructure by cutting the connecting beams. The vibration equation for shear wall substructure is set up according to Timoshenko Cantilever beam. The vibration equation for frame substructure is set up according to frame structure. The mode synthesis technique is used to set up the free vibration equation of frame shear wall structure. A numerical example shows that our method is simpler...

In this paper, Frame-Shear wall structure is divided into frame substructure and shear wall substructure by cutting the connecting beams. The vibration equation for shear wall substructure is set up according to Timoshenko Cantilever beam. The vibration equation for frame substructure is set up according to frame structure. The mode synthesis technique is used to set up the free vibration equation of frame shear wall structure. A numerical example shows that our method is simpler and more precise.