scholarly journals Three-Dimensional Semianalytical Solutions for Piezoelectric Laminates Subjected to Underwater Shocks

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Xu Liang ◽  
Wenbin Lu ◽  
Ronghua Zhu ◽  
Changpeng Ye ◽  
Guohua Liu
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Electric Potential ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Inversion Method ◽  
Variation Principle ◽  
The Laplace Transform

In this study, a piezoelectric laminate is analyzed by applying the Laplace transform and its numerical inversion, Fourier transform, differential quadrature method (DQM), and state space method. Based on the modified variation principle for the piezoelectric laminate, the fundamental equations for dynamic problems are derived. The solutions for the displacement, stress, electric potential, and dielectric displacement are obtained using the proposed method. Durbin’s inversion method for the Laplace transform is adopted. Four boundary conditions are discussed through the DQM. The proposed method is validated by comparing the results with those of the finite element method (FEM). Moreover, this semianalytical method is further extended to describe the dynamic response of piezoelectric laminated plates subjected to underwater shocks by introducing Taylor’s fluid-structure interaction algorithm. Both air-backed and water-backed laminated plates are investigated, and the effect of the fluid is examined. In the time domain, the electric potential and displacements of sample points are calculated under four boundary conditions. The present method is shown to be accurate and can be a useful method to calculate the dynamic response of underwater laminated sensors.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

The solution of theoretical seismic problems by best rational function approximations for Laplace transform inversion

1975 ◽  
Vol 65 (4) ◽  
pp. 927-935
Author(s):  
I. M. Longman ◽  
T. Beer
Keyword(s):  
Laplace Transform ◽  
Rational Function ◽  
High Accuracy ◽  
Time Variable ◽  
Inversion Method ◽  
The Laplace Transform ◽  
Previously Treated ◽  
The Mean ◽  
Function Approximations ◽  
Laplace Transform Inversion

Abstract In a recent paper, the first author has developed a method of computation of “best” rational function approximations ḡn(p) to a given function f̄(p) of the Laplace transform operator p. These approximations are best in the sense that analytic inversion of ḡn(p) gives a function gn(t) of the time variable t, which approximates the (generally unknown) inverse f(t) of f̄(p in a minimum least-squares manner. Only f̄(p) but not f(t) is required to be known in order to carry out this process. n is the “order” of the approximation, and it can be shown that as n tends to infinity gn(t) tends to f(t) in the mean. Under suitable conditions on f(t) the convergence is extremely rapid, and quite low values of n (four or five, say) are sufficient to give high accuracy for all t ≧ 0. For seismological applications, we use geometrical optics to subtract out of f(t) its discontinuities, and bring it to a form in which the above inversion method is very rapidly convergent. This modification is of course carried out (suitably transformed) on f̄(p), and the discontinuities are restored to f(t) after the inversion. An application is given to an example previously treated by the first author by a different method, and it is a certain vindication of the present method that an error in the previously given solution is brought to light. The paper also presents a new analytical method for handling the Bessel function integrals that occur in theoretical seismic problems related to layered media.

scholarly journals Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads

2012 ◽  
Vol 19 (3) ◽  
pp. 333-347 ◽  
Author(s):  
R. Abu-Mallouh ◽  
I. Abu-Alshaikh ◽  
H.S. Zibdeh ◽  
Khaled Ramadan
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Damping Characteristics ◽  
The Laplace Transform ◽  
The Right

This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity. The damping characteristics of the beams are described in terms of fractional derivatives of arbitrary orders. In the analysis where initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to obtain the analytical solution of the investigated problems. Subsequently, curves are plotted to show the dynamic response of different beams under different sets of parameters including different orders of fractional derivatives. The curves reveal that the dynamic response increases as the order of fractional derivative increases. Furthermore, as the order of the fractional derivative increases the peak of the dynamic deflection shifts to the right, this yields that the smaller the order of the fractional derivative, the more oscillations the beam suffers. The results obtained in this paper closely match the results of papers in the literature review.

Propagation of Discontinuities in Coupled Thermoelastic Problems

1968 ◽  
Vol 35 (3) ◽  
pp. 489-494 ◽  
Author(s):  
B. A. Boley ◽  
R. B. Hetnarski
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Applied Strain ◽  
Transform Domain ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Thermoelastic Problems

The character and magnitude of traveling discontinuities in one-dimensional coupled transient thermoelastic problems are studied. For this purpose, 16 different fundamental problems are considered in detail, by examination of the nature of the solutions in the Laplace-transform domain. These problems correspond to various combinations of applied strain or stress as mechanical variables, and of applied temperature or heat flux as thermal variables. A system of classification of discontinuities is devised, which permits the results of the 16 problems to be extended to some general conclusions as to the character of the discontinuities in cases of arbitrary boundary conditions.

The analysis of inter-laminar stress and electric potential for a laminated piezoelectric plate with interfacial damage

2011 ◽  
Vol 16 (8) ◽  
pp. 793-811 ◽  
Author(s):  
Fu Yiming ◽  
Li Sheng
Keyword(s):  
Electric Potential ◽  
Degrees Of Freedom ◽  
Piezoelectric Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Variation Principle ◽  
Interfacial Damage ◽  
Load Models ◽  
Non Linear ◽  
Piezoelectric Plates

This paper presents a non-linear model for laminated piezoelectric plates with inter-laminar mechanical and electrical damage. The model is based on the general six-degrees-of-freedom plate theory, and the discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the variation principle, the three-dimensional non-linear equilibrium differential equations of simply supported laminated piezoelectric plates with interfacial damage are derived. Then, an analytical solution is presented by using the finite difference method. In numerical examples, the effects of different damage values, load models, and electric boundary conditions on the inter-laminar stress and electric potential profile of a laminated piezoelectric plate with interfacial imperfections are investigated.

Parametric study of three-dimensional vibration of viscoelastic cylindrical shells on different boundary conditions

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2567-2579 ◽  
Author(s):  
Siamak Mohajel Sadeghi ◽  
Akbar Alibeigloo
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Radius Ratio ◽  
Radial Coordinate ◽  
Different Boundary Conditions ◽  
Space Technique ◽  
Frequency Behavior

In this research based on theory of elasticity, free vibration behavior of a viscoelastic cylindrical shell with different boundary conditions is studied. A constitutive equation for viscoelastic material is assumed to obey the Boltzmann model and Poisson's ratio is held to be constant. Moreover, the Prony series is used to model time dependent modulus of elasticity. Governing equations of motions for simply-supported edges conditions are solved analytically using the state-space technique along the radial coordinate and the Fourier series method along the axial and circumferential directions. In the case of other edges condition a semi-analytical solution is employed by using the differential quadrature method instead of Fourier series solutions. It is worthy to note before solving the problem, that the Laplace transform is employed to convert governing differential equations from the time-domain into the Laplace domain. Then, validation of the present formulation is performed by comparing the numerical results with those published in the literature. Finally, effect of viscoelastic properties, boundary conditions, the thickness-to-radius ratio and length-to-radius ratio on the frequency behavior are studied.

A result on the Laplace transform associated with the sticky Brownian motion on an interval

2020 ◽  
pp. 2150031
Author(s):  
Shiyu Song
Keyword(s):  
Brownian Motion ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Laplace Transforms ◽  
Perturbation Approach ◽  
Integrated Process ◽  
Modified Bessel Function ◽  
Airy Functions ◽  
Occupation Times ◽  
The Laplace Transform

In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab. 45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially equivalent to solving the associated differential equations with boundary conditions. We obtain the explicit expression for the joint Laplace transform in terms of the modified Bessel function and Airy functions.

scholarly journals The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method

2020 ◽  
pp. 146134842094657
Author(s):  
Xu Liang ◽  
Zeng Cao ◽  
Yu Deng ◽  
Xue Jiang ◽  
Xing Zha ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Fourier Series Expansion ◽  
Pasternak Foundation

This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate.

Effects of Impact on the Behavior of a Flexible Multiple Disk Clutch and Brake

1987 ◽  
Vol 109 (4) ◽  
pp. 416-421 ◽  
Author(s):  
Kosuke Nagaya
Keyword(s):  
Dynamic Response ◽  
Laplace Transform ◽  
Dynamic Behavior ◽  
Circular Plate ◽  
Static Load ◽  
Equation Of Motion ◽  
Dynamic Loads ◽  
The Laplace Transform ◽  
The Impact

This paper discusses the dynamic behavior of a flexible multiple disk clutch subjected to dynamic loads. The expressions for obtaining the dynamic response and the transmission torque of the clutch have been derived from the equation of motion of a circular plate by applying the Laplace transform procedure. The results for the clutch subjected to a static load have also been obtained. The comparison between both static and dynamic results has been made to clarify the effect of the impact of the load on the behavior of the clutch.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

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