Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation

Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.

Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping

In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.

A Compact Difference Method for Viscoelastic Plate Vibration Equation

In this paper, a fourth-order viscoelastic plate vibration equation is transformed into a set of two second-order differential equations by introducing an intermediate variable. A three-layer compact difference scheme for the initial-boundary value problem of the viscoelastic plate vibration equation is established. Then the stability and convergence of the difference scheme are analyzed by the energy method, and the convergence order is <img src="Edit_0a250b60-7c3c-4caf-8013-5e302d6477ab.png" alt="" />. Finally, some numerical examples are given of which results verify the accuracy and validity of the scheme.

ANALYSIS OF SOUND RADIATION FROM THE RING-STIFFENED CYLINDRICAL SHELL COATED WITH VISCOELASTIC LAYER IN FLUID MEDIUM

The Donnell theory of shell is applied to describe shell motion and layer motion is described by means of three-dimensional Navier equations.Using deformation harmonious condi- tions of the interface,the effects of stiffeners and layer are treated as reverse forces and moments acting on the cylindrical shell.In studying the acoustic field produced by vibration of the sub- merged ring-stiffened cylindrical coated shell,the structure dynamic equation,Helmholtz equation in the fluid field and the continuous conditions of the fluid-structure interface compose the cou- pling vibration equation of the sound-fluid-structure.The extract of sound pressure comes down to the extract of coupling vibration equation.By use of the solution of the equation,the influ- ences of hydrostatic pressure,physical characters and geometric parameters of the layer on sound radiation are discussed.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

ANALYTICAL SOLUTION OF RADIATION SOUND PRESSURE OF DOUBLE CYLINDRICAL SHELLS IN FLUID MEDIUM

The Donnell theory of shell was applied to describe shell motion. The inner and outer shells were stiffened by transverse components. Using deformation harmonious conditions of the interface, the effects of stiffeners were treated as reverse forces and moments on the double cylindrical shell. In the acoustic field produced by vibration and sound radiation of the double shell, the structure dynamic equation, Helmholtz equation in the fluid field and the continuity conditions of the surface of fluid-structure compose the vibration equation coupled by the sound-fluid-structure. The extract of acoustic pressure comes down to the extract of coupling vibration equation. The near field acoustic pressure can be solved directly by complicated calculational methods.

Vibration Measurement of Pedestrian Bridge Using Double Magnetic Suspension Vibrator Based on Wavelet Analysis

Aiming at the problem of pedestrian bridge vibration measurement,a vibration measurement system of pedestrian bridge with dual magnetic suspension vibrator structure was designed according to absolute vibration measurement principle. The relationship between the magnetic repulsion force of vibrator and its displacement was obtained by the experimental method and the least square fitting method. The vibration equations of two magnetic suspension vibrators were deduced respectively,and the measurement sensitivity of the system was deduced. The amplitude-frequency characteristic of the system was studied. A simulation model of vibrator measurement system with double magnetic suspension vibrator was established. The analysis shows that the sensitivity of the vibration measurement system with double magnetic suspension vibrator is higher than that with single magnetic suspension vibrator. The four vibration waveforms were measured,that is,no one passes through a pedestrian bridge,there are cars running under the pedestrian bridge,single pedestrian passes through the pedestrian bridge and multiple pedestrians pass through the pedestrian bridge. The multi-scale one-dimensional wavelet decomposition function was used to analyze the vibration signals. The vibration characteristics were obtained using one dimension wavelet decomposition function under four different conditions. Finally,the vibration waveforms of four cases were reconstructed. The measured results show that the vibration measurement system of pedestrian bridge with double magnetic suspension vibrator structure has high measurement sensitivity. The design has a certain value to monitor a pedestrian bridge.

Nonlinear vibration of corrugated shallow shells under uniform load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green＇s function. To solve the integral-differential equations, expansion method is used to obtain Green＇s function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells .

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

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For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.

Elastic Wave Scattering and Dynamic Stress Concentrations in Stretching Thick Plates with Two Cutouts by Using the Refined Dynamic Theory

Based on the refined dynamic equation of stretching plates, the elastic tensio compression wave scattering and dynamic stress concentrations in the thick plate with two cutouts are studied. In view of the problem that the shear stress is automatically satisfied under the free boundary condition, the generalized stress of the first-order vanishing moment of shear stress is considered. The numerical results indicate that, as the cutout is thick, the maximum value of the dynamic stress factor obtained using the refined dynamic theory is 19% higher than that from the solution of plane stress problems of elastic dynamics.