scholarly journals Dynamic Response Analysis of a Thin Plate with Partially Constrained Layer Damping Optimization under Moving Loads for Various Boundary Conditions

2021 ◽  
Vol 11 (7) ◽  
pp. 3282
Author(s):  
Yun Qin ◽  
Qinghua Song ◽  
Zhanqiang Liu ◽  
Jiahao Shi
Keyword(s):  
Dynamic Response ◽  
Loss Factor ◽  
Lagrange Equation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Response Analysis ◽  
Constrained Layer Damping ◽  
Moving Loads ◽  
Damping Loss Factor

In this paper, the vibration analysis of a partially constrained layer damping plate subjected to moving loads is investigated. In addition, the first four order damping loss factor of the system is optimized with the location of partially constrained layer damping as a design variable. The equations of motion of a partially constrained layer damping plate are derived through the Lagrange equation based on first order shear deformation theory (FSDT). Next, using an extended Rayleigh–Ritz solution together with the penalty method expresses the unknown displacement terms, and the differential quadrature method is proposed to obtain the dynamic response of the system in the time domain. A multi-population genetic algorithm (MPGA) is employed to deal with the optimization of the damping loss factor of a partially constrained layer damping plate. To ensure the accuracy of the method presented in this study, the numerical results are comprehensively verified by experiments and open literature. The optimization results show that the damping loss factor increases when the position of the patch is close to the constraint boundary, and the best strategy is to optimize the low order damping loss factor of the system under moving loads. It is believed that the research results are of interest to engineering science.

Nonlinear Dynamics Analysis of a Laminated Printed Wiring Board

2002 ◽  
Vol 124 (2) ◽  
pp. 77-84 ◽  
Author(s):  
Xiaoling He ◽  
Robert E. Fulton
Keyword(s):  
Dynamic Response ◽  
Large Deflection ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Printed Wiring Board ◽  
High Acceleration ◽  
Dynamic Stress Field ◽  
Laminate Theory ◽  
Wiring Board ◽  
Nonlinear Elastic

Nonlinear laminate theory is applied for the printed wiring board (PWB) dynamic response analysis. Equations of motion for the nonlinear elastic deformation of the isotropic laminates are derived for the dynamic response of a simply supported PWB. Numerical results are generated for the nonlinear response characterization of the PWB deformation. Comparisons are made between the response of linear and nonlinear systems. Results show that PWB is in large deflection under high acceleration or certain pressure load. Nonlinear theory gives more accurate results for the large deflection than the linear theory does. Besides, lamina stresses are analyzed and illustrated from finite difference computation. The analytical derivation in modal approach and the stress analysis provide the basis for PWB reliability studies, especially the defect and failure induced by the dynamic stress field.

Dynamic Response Analysis of Large Latticed Space Structures

1989 ◽  
Vol 4 (1) ◽  
pp. 25-42 ◽  
Author(s):  
A.R. Kukreti ◽  
N.D. Uchil
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Time ◽  
Space Structures ◽  
Response Analysis ◽  
Actual System ◽  
Large Space ◽  
Element Analysis ◽  
Dynamic Response Analysis

In this paper an alternative method for dynamic response analysis of large space structures is presented, for which conventional finite element analysis would require excessive computer storage and computational time. Latticed structures in which the height is very small in comparison to its overall length and width are considered. The method is based on the assumption that the structure can be embedded in its continuum, in which any fiber can translate and rotate without deforming. An appropriate kinematically admissable series function is constructed to descrbe the deformation of the middle plane of this continuum. The unknown coefficients in this function are called the degree-of-freedom of the continuum, which is given the name “super element.” Transformation matrices are developed to express the equations of motion of the actual systems in terms of the degrees-of-freedom of the super element. Thus, by changing the number of terms in the assumed function, the degrees-of-freedom of the super element can be increased or decreased. The super element response results are transformed back to obtain the desired response results of the actual system. The method is demonstrated for a structure woven in the shape of an Archimedian spiral.

Vibration control of magnetostrictive plate under multi- physical loads via trigonometric higher order shear deformation theory

2015 ◽  
Vol 23 (19) ◽  
pp. 3057-3070 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Z Khoddami Maraghi ◽  
H Khani Arani
Keyword(s):  
Elastic Medium ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Feedback Gain ◽  
First Time ◽  
Free Vibration Response

For the first time in this research, a feedback control system is used to study the free vibration response of rectangular plate made of magnetostrictive material. In this regard, magnetostrictive plate (MsP) is analyzed by trigonometric higher order shear deformation theory that involved six unknown displacement functions and does not require shear correction factor. The MsP is supported by elastic medium as Pasternak foundation which considers both normal and shears modules. Also the MsP undergoes in-plane forces in x and y directions. Considering simply supported boundary condition, six equations of motion are derived using Hamilton’s principle and solved by differential quadrature method. Results indicate the effect of aspect ratio, thickness ratio, elastic medium, compression and tension loads on vibration behavior of MsP. Also, findings show the controller effect of velocity feedback gain to minimize the frequency as far as other parameters become ineffective. These findings can be used to active noise and vibration cancellation systems in many structures.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

Temperature-dependent vibration analysis of a FG viscoelastic cylindrical microshell under various thermal distribution via modified length scale parameter: a numerical solution

2017 ◽  
Vol 26 (1-2) ◽  
pp. 9-24 ◽  
Author(s):  
Hamed Safarpour ◽  
Kianoosh Mohammadi ◽  
Majid Ghadiri
Keyword(s):  
Boundary Conditions ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Temperature Dependent

AbstractIn this article, the vibrational analysis of temperature-dependent cylindrical functionally graded (FG) microshells surrounded by viscoelastic a foundation is investigated by means of the modified couple stress theory (MCST). MCST is applied to this model to be productive in design and analysis of micro actuators and micro sensors. The modeled cylindrical FG microshell, its equations of motion and boundary conditions are derived by Hamilton’s principle and the first-order shear deformation theory (FSDT). For the first time, in the present study, functionally graded length scale parameter which changes along the thickness has been considered in the temperature-dependent cylindrical FG microshell. The accuracy of the present model is verified with previous studies and also with those obtained by analytical Navier method. The novelty of the current study is consideration of viscoelastic foundation, various thermal loadings and size effect as well as satisfying various boundary conditions implemented on the temperature-dependent cylindrical FG microshell using MCST. Generalized differential quadrature method (GDQM) is applied to discretize the equations of motion. Then, some factors are investigated such as the influence of length to radius ratio, damping, Winkler and Pasternak foundations, different temperature changes, circumferential wave numbers, and boundary conditions on natural frequency of the cylindrical FG microshell. The results have many applications such as modeling of microrobots and biomedical microsystems.

scholarly journals Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads

2019 ◽  
Vol 9 (10) ◽  
pp. 2162 ◽  
Author(s):  
Lizhong Jiang ◽  
Yuntai Zhang ◽  
Yulin Feng ◽  
Wangbao Zhou ◽  
Zhihua Tan
Keyword(s):  
Dynamic Response ◽  
Analytical Method ◽  
Amplitude Spectrum ◽  
Analytical Calculation ◽  
Response Analysis ◽  
Moving Loads ◽  
Analytical Expression ◽  
Simply Supported ◽  
Beam System ◽  
Double Beam

The dynamic response of a simply supported double-beam system under moving loads was studied. First, in order to reduce the difficulty of solving the equation, a finite sin-Fourier transform was used to transform the infinite-degree-of-freedom double-beam system into a superimposed two-degrees-of-freedom system. Second, Duhamel’s integral was used to obtain the analytical expression of Fourier amplitude spectrum function considering the initial conditions. Finally, based on finite sin-Fourier inverse transform, the analytical expression of dynamic response of a simply supported double-beam system under moving loads was deduced. The dynamic response under successive moving loads was calculated by the analytical method and the general FEM software ANSYS. The analysis results show that the analytical method calculation results are consistent with ANSYS’ calculation, thus validating the analytical calculation method. The simply supported double-beam system had multiple critical speeds, and the flexural rigidity significantly affected both peak vertical displacement and critical speed.

Dynamic Response Analysis and Comparative Study of Circular Cylindrical Shell Subjected to Radial Impact

2007 ◽  
Vol 51 (02) ◽  
pp. 94-103
Author(s):  
Li Xuebin
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Normal Mode ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Mode Theory ◽  
Normal Mode Theory ◽  
Exact Derivation

Following Flu¨ gge's exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of a circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The responses of displacements, strain, and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.

Loads Moving on Beam Supported by Layered Elastic Foundation

1980 ◽  
Vol 102 (2) ◽  
pp. 295-302 ◽  
Author(s):  
V. N. Shah ◽  
R. D. Cook ◽  
T. C. Huang
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Variable Coefficients ◽  
Moving Loads ◽  
Numerical Illustration ◽  
Concentrated Force ◽  
Winkler Model ◽  
First Case ◽  
Mass Damper ◽  
Pasternak Model

A finite element method is applied to analyze the dynamic response of a beam supported by layered inertial foundation and subjected to moving loads. The foundation is represented by the modified Pasternak model or by the Winkler model. The moving loads are simulated by a concentrated force, a point-mass or a spring-mass-damper system. The equations of motion are represented by a system of second-order ordinary differential equations with variable coefficients. Newmark’s method of constant average acceleration is used to integrate these equations. Two test cases are analyzed for numerical illustration. In the first case, the dynamic response of a beam supported by the modified Pasternak model and subjected to a moving concentrated force is analyzed. In the second, the dynamic response of a beam supported by the Winkler model and subjected to a moving spring-mass-damper system is analyzed. The results from these two cases are compared with those obtained by the transfer matrix method.

scholarly journals Rocking Response Analysis of Self-Centering Walls under Ground Excitations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaobin Hu ◽  
Qinwang Lu ◽  
Yang Yang
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Elastic Stiffness ◽  
The Self ◽  
Response Analysis ◽  
Seismic Excitations ◽  
Parametric Studies ◽  
Initial Force ◽  
Rocking Response

This paper presents a numerical procedure to simulate the rocking response of self-centering walls under ground excitations. To this aim, the equations of motion that govern the dynamic response of self-centering walls are first formulated and then solved numerically, in which three different self-centering wall structural systems are considered, that is, (i) including the self-weight of the wall only, (ii) including posttensioned tendon, and (iii) including both posttensioned tendon and dampers. Following the development of the numerical procedure, parametric studies are then carried out to investigate the influence of a variety of factors on the dynamic response of the self-centering wall under seismic excitations. The investigation results show that within the cases studied in this paper the installation of posttensioned tendon is capable of significantly enhancing the self-centering ability of the self-centering wall. In addition, increasing either the initial force or the elastic stiffness of the posttensioned tendon can reduce the dynamic response of the self-centering wall in terms of the rotation angle and angular velocity, whereas the former approach is found to be more effective than the latter one. It is also revealed that the addition of the dampers is able to improve the energy dissipation capacity of the self-centering wall. Furthermore, for the cases studied in this paper the yield strength of the dampers appears to have a more significant effect on the dynamic response of the self-centering wall than the elastic stiffness of the dampers.

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