Free vibration of the complex cable system − An exact method using symbolic computation

With the increase of the span and height of modern engineering structures, the design length and complexity of the cable structure are constantly increasing, whose dynamic problem has become the key to structural design, performance monitoring and maintenance, and vibration control. Therefore, it is necessary to study and develop a unified dynamic analysis theory for complex cable system to meet the requirements of calculation accuracy and efficiency. In view of this, a unified dynamic analysis method for dynamic analysis of complex cable system is proposed in this paper on the basis of the classical dynamic stiffness method. In this paper, the dynamic stiffness method has been enhanced in multiple aspects, which not only retains the advantages of high computational efficiency and wide application range but also overcomes its technical bottlenecks in analysis of shallow-sag cable system considering the damping effect, composite cable systems, and multisegment cable systems. The proposed method can not only be used to the structural design of the complex cable system but also be extended to the vibration control of the system during the service period.

Dynamic stiffness analysis of toroidal shells

Exact dynamic analysis of multi-segment cable systems

Dynamic stiffness method and CUF-based component-wise theories applied to free vibration analysis of solid beams, thin-walled structures and reinforced panels

Two new methods for calculating vibration problems—the dynamic stiffness method and the mobility method—have been introduced in recent years. Each of these methods offers certain advantages over the older vibration theory. This article is an at tempt to unify these two methods so that the best features of each are included in one theory. By means of this theory it is possible to determine the resonance and antiresonance frequencies and the relative amplitudes of vibration of a mechanical system. The effect of the position of torque application on the vibration characteristics of a system are discussed. The application of the theory is demonstrated by a few examples including the problem of the pendulum damper.

Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method has been extended to frame structures with uniform or non-uniform, straight or curved, damped or undamped beam members. An orthonormal condition is suggested here for the natural modes resulting from the dynamic stiffness method; modal analysis in the classical sense is then made possible. Modes corresponding to repeated natural frequencies are discussed in detail. An expansion theorem for expanding from a finite number of degrees of freedom by means of an infinite number of modes is validated by means of the frequency-dependent shape functions. Distributed modal participation factors are introduced for distributed excitations.

Harmonic response analysis of coupled plate structures using the dynamic stiffness method

The dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. The exact dynamic stiffness matrix is found directly from the analytical solutions of the basic governing differential equations of motion. The Poisson effect, shear deformation, rotary inertia, in-plane deformation are considered in the analysis. Application of the derived dynamic stiffness matrix to several particular laminated beams is discussed. The influences of Poisson effect, material anisotropy, slenderness and end condition on the natural frequencies of the beams are investigated. The numerical results are compared with the existing solutions in literature whenever possible to demonstrate and validate the present method.

The dynamic stiffness method is used to investigate the free vibration behaviour of a functionally graded beam (FGB). The material properties of the FGB are assumed to vary in the thickness direction based on a power-law. The kinetic and potential energies of the beam are formulated using the Timoshenko beam theory. The governing differential equations of motion in free vibration for the FGB are derived using Hamilton’s principle. The analytical expressions for axial force, shear force and bending moments at any cross-section of the FGB are obtained as a by-product of the Hamiltonian formulation. The differential equations are solved in closed analytical form for harmonic oscillation. The dynamic stiffness matrix of the FGB is then formulated by relating the amplitudes of forces and displacements at the ends of the beam. The Wittrick-Williams algorithm is used as solution technique to yield natural frequencies and mode shapes of the FGB. A parametric study is carried out by varying significant beam parameters and boundary conditions. The investigation required a substantial amount of validation exercise to confirm the predictable accuracy of the dynamic stiffness method. The results are discussed and some concluding remarks are made.

Dynamic stiffness analysis of follower force

Dynamic Stiffness Analysis of Follower Moments

A dynamic stiffness method is presented for the vibrations of plate structures that are reinforced by eccentric stiffeners. The model incorporates both out-of-plane and in-plane deformations of the plates and the stiffeners. Based on the relationship between the forces and displacements along the common edges of the plate or beam elements, the dynamic stiffness formulae for the plate and the beam elements are derived, respectively. The globally assembled dynamic stiffness matrix is then obtained using the finite element method so that the dynamics of built-up stiffened plates can be readily addressed by using the present method. Compared to the conventional finite element model, the dynamic stiffness model can provide very accurate solutions using only one element over each uniform plate and beam member, regardless of its geometry.

Dynamic stiffness method for space frames under distributed harmonic loads

Application of the dynamic stiffness method in the vibration analysis of stiffened composite plates