The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with...The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.展开更多
Long-term load forecasting (LTLF) is a challenging task because of the complex relationships between load and factors affecting load. However, it is crucial for the economic growth of fast developing countries like Ch...Long-term load forecasting (LTLF) is a challenging task because of the complex relationships between load and factors affecting load. However, it is crucial for the economic growth of fast developing countries like China as the growth rate of gross domestic product (GDP) is expected to be 7.5%, according to China’s 11th Five-Year Plan (2006-2010). In this paper, LTLF with an economic factor, GDP, is implemented. A support vector regression (SVR) is applied as the training algorithm to obtain the nonlinear relationship between load and the economic factor GDP to improve the accuracy of forecasting.展开更多
As the existing heating load forecasting methods are almostly point forecasting,an interval forecasting approach based on Support Vector Regression (SVR) and interval estimation of relative error is proposed in this p...As the existing heating load forecasting methods are almostly point forecasting,an interval forecasting approach based on Support Vector Regression (SVR) and interval estimation of relative error is proposed in this paper.The forecasting output can be defined as energy saving control setting value of heating supply substation;meanwhile,it can also provide a practical basis for heating dispatching and peak load regulating operation.By means of the proposed approach,SVR model is used to point forecasting and the error interval can be gained by using nonparametric kernel estimation to the forecast error,which avoid the distributional assumptions.Combining the point forecasting results and error interval,the forecast confidence interval is obtained.Finally,the proposed model is performed through simulations by applying it to the data from a heating supply network in Harbin,and the results show that the method can meet the demands of energy saving control and heating dispatching.展开更多
The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is...The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.展开更多
It is important to have a reasonable estimation of sediment transport rate with respect to its significant role in the planning and management of water resources projects. The complicate nature of sediment transport i...It is important to have a reasonable estimation of sediment transport rate with respect to its significant role in the planning and management of water resources projects. The complicate nature of sediment transport in gravel-bed rivers causes inaccuracies of empirical formulas in the prediction of this phenomenon. Artificial intelligences as alternative approaches can provide solutions to such complex problems. The present study aimed at investigating the capability of kernel-based approaches in predicting total sediment loads and identification of influential parameters of total sediment transport. For this purpose, Gaussian process regression(GPR), Support vector machine(SVM) and kernel extreme learning machine(KELM) are applied to enhance the prediction level of total sediment loads in 19 mountain gravel-bed streams and rivers located in the United States. Several parameters based on two scenarios are investigated and consecutive predicted results are compared with some well-known formulas. Scenario 1 considers only hydraulic characteristics and on the other side, the second scenario was formed using hydraulic and sediment properties. The obtained results reveal that using the parameters of hydraulic conditions asinputs gives a good estimation of total sediment loads. Furthermore, it was revealed that KELM method with input parameters of Froude number(Fr), ratio of average velocity(V) to shear velocity(U*) and shields number(θ) yields a correlation coefficient(R) of 0.951, a Nash-Sutcliffe efficiency(NSE) of 0.903 and root mean squared error(RMSE) of 0.021 and indicates superior results compared with other methods. Performing sensitivity analysis showed that the ratio of average velocity to shear flow velocity and the Froude number are the most effective parameters in predicting total sediment loads of gravel-bed rivers.展开更多
A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic...A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.展开更多
This research studies short-term electricity load prediction with a large-scalelinear programming support vector regression (LP-SVR) model. The LP-SVR is compared with other three non-linear regression models: Collob...This research studies short-term electricity load prediction with a large-scalelinear programming support vector regression (LP-SVR) model. The LP-SVR is compared with other three non-linear regression models: Collobert’s SVR, Feed-Forward Neural Networks (FFNN), and Bagged Regression Trees (BRT). The four models are trained to predict hourly day-ahead loads given temperature predictions, holiday information and historical loads. The models are trained on-hourly data from the New England Power Pool (NEPOOL) region from 2004 to 2007 and tested on out-of-sample data from 2008. Experimental results indicate that the proposed LP-SVR method gives the smallest error when compared against the other approaches. The LP-SVR shows a mean absolute percent error of 1.58% while the FFNN approach has a 1.61%. Similarly, the FFNN method shows a 330 MWh (Megawatts-hour) mean absolute error, whereas the LP-SVR approach gives a 238 MWh mean absolute error. This is a significant difference in terms of the extra power that would need to be produced if FFNN was used. The proposed LP-SVR model can be utilized for predicting power loads to a very low error, and it is comparable to FFNN and over-performs other state of the art methods such as: Bagged Regression Trees, and Large-Scale SVRs.展开更多
The present paper aims at modeling suspended sediment load(SSL) using heuristic data driven methodologies, e.g. Gene Expression Programming(GEP) and Support Vector Machine(SVM) in three successive hydrometric stations...The present paper aims at modeling suspended sediment load(SSL) using heuristic data driven methodologies, e.g. Gene Expression Programming(GEP) and Support Vector Machine(SVM) in three successive hydrometric stations of Housatonic River in U.S. The simulations were carried out through local and cross-station data management scenarios to investigate the interrelations between the SSL values of upstream/downstream stations. The available scenarios were applied to predict SSL values using GEP to obtain the best models. Then, the best models were predicted by SVM approach and the obtained results were compared with those of GEP. The comparison of the results revealed that the SVM technique is more capable than the GEP for modeling the SSL through the both local and cross-station data management strategies. Besides, local application seems to be better than cross-station application for modeling SSL. Nevertheless, the cross-station application demonstrated to be a valid methodology for simulating SSL, which would be of interest for the stations with lack of observational data. Also, the prediction capability of conventional Sediment Rating Curve(SRC) method was compared with those of GEPand SVM techniques. The obtained results revealed the superiority of GEP and SVM-based models over the traditional SRC technique in the studied stations.展开更多
Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a rea...Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a reasonable prediction, authors have applied and compared two features extraction technique presented by kernel partial least square regression and kernel principal component regression, and both of them are carried out by polynomial and Gaussian kernels to map the original features’ to high dimension features’ space, and then draw new predictor variables known as scores and loadings, while kernel principal component regression draws the predictor features to construct new predictor variables without any consideration to response vector. In contrast, kernel partial least square regression does take the response vector into consideration. Models are simulated by three different cities’ electric load data, which used historical load data in addition to weekends and holidays as common predictor features for all models. On the other hand temperature has been used for only one data as a comparative study to measure its effect. Models’ results evaluated by three statistic measurements, show that Gaussian Kernel Partial Least Square Regression offers the more powerful features and significantly can improve the load prediction performance than other presented models.展开更多
Structural health monitoring(SHM)in service has attracted increasing attention for years.Load localization on a structure is studied hereby.Two algorithms,i.e.,support vector machine(SVM)method and back propagation ne...Structural health monitoring(SHM)in service has attracted increasing attention for years.Load localization on a structure is studied hereby.Two algorithms,i.e.,support vector machine(SVM)method and back propagation neural network(BPNN)algorithm,are proposed to identify the loading positions individually.The feasibility of the suggested methods is evaluated through an experimental program on a carbon fiber reinforced plastic laminate.The experimental tests involve in application of four optical fiber-based sensors for strain measurement at discrete points.The sensors are specially designed fiber Bragg grating(FBG)in small diameter.The small-diameter FBG sensors are arrayed in 2-D on the laminate surface.The testing results indicate that the loading position could be detected by the proposed method.Using SVM method,the 2-D FBG sensors can approximate the loading location with maximum error less than 14 mm.However,the maximum localization error could be limited to about 1 mm by applying the BPNN algorithm.It is mainly because the convergence conditions(mean square error)can be set in advance,while SVM cannot.展开更多
An adaptive load balancing scheme is proposed to balance the load in ad hoc networks. The new scheme can be applied in most on-demand routing protocols resulting in significant performance improvement. The proposed sc...An adaptive load balancing scheme is proposed to balance the load in ad hoc networks. The new scheme can be applied in most on-demand routing protocols resulting in significant performance improvement. The proposed scheme is applied to the ad hoc on-demand distance vector （AODV） routing protocol. Simulation results show that the network load is balanced on the whole, and performance in packet loss rate, routing overhead and average end-to-end delay is also improved.展开更多
A reliable seismic-resistant design of structures is achieved in accordance with the seismic design codes by designing structures under seven or more pairs of earthquake records. Based on the recommendations of seismi...A reliable seismic-resistant design of structures is achieved in accordance with the seismic design codes by designing structures under seven or more pairs of earthquake records. Based on the recommendations of seismic design codes, the average time-history responses （ATHR） of structure is required. This paper focuses on the optimal seismic design of reinforced concrete （RC） structures against ten earthquake records using a hybrid of particle swarm optimization algorithm and an intelligent regression model （IRM）. In order to reduce the computational time of optimization procedure due to the computational efforts of time-history analyses, IRM is proposed to accurately predict ATHR of structures. The proposed IRM consists of the combination of the subtractive algorithm （SA）, K-means clustering approach and wavelet weighted least squares support vector machine （WWLS-SVM）. To predict ATHR of structures, first, the input-output samples of structures are classified by SA and K-means clustering approach. Then, WWLS-SVM is trained with few samples and high accuracy for each cluster. 9- and 18-storey RC frames are designed optimally to illustrate the effectiveness and practicality of the proposed IRM. The numerical results demonstrate the efficiency and computational advantages of IRM for optimal design of structures subjected to time-history earthquake loads.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
基金Project supported by the National Natural Science Foundation of China(No.42207182)the Research Grants Council of the Hong Kong Special Administrative Region Government of China(Nos.HKU 17207518 and R5037-18)。
文摘The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.
文摘Long-term load forecasting (LTLF) is a challenging task because of the complex relationships between load and factors affecting load. However, it is crucial for the economic growth of fast developing countries like China as the growth rate of gross domestic product (GDP) is expected to be 7.5%, according to China’s 11th Five-Year Plan (2006-2010). In this paper, LTLF with an economic factor, GDP, is implemented. A support vector regression (SVR) is applied as the training algorithm to obtain the nonlinear relationship between load and the economic factor GDP to improve the accuracy of forecasting.
基金Sponsored by the National 11th 5-year Plan Key Project of Ministry of Science and Technology of China (Grant No.2006BAJ01A04)
文摘As the existing heating load forecasting methods are almostly point forecasting,an interval forecasting approach based on Support Vector Regression (SVR) and interval estimation of relative error is proposed in this paper.The forecasting output can be defined as energy saving control setting value of heating supply substation;meanwhile,it can also provide a practical basis for heating dispatching and peak load regulating operation.By means of the proposed approach,SVR model is used to point forecasting and the error interval can be gained by using nonparametric kernel estimation to the forecast error,which avoid the distributional assumptions.Combining the point forecasting results and error interval,the forecast confidence interval is obtained.Finally,the proposed model is performed through simulations by applying it to the data from a heating supply network in Harbin,and the results show that the method can meet the demands of energy saving control and heating dispatching.
基金Supported by the Program of Yunnan Provincial Institute of Communications Planning,Design and Research (2011(D)11-b)
文摘The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.
文摘It is important to have a reasonable estimation of sediment transport rate with respect to its significant role in the planning and management of water resources projects. The complicate nature of sediment transport in gravel-bed rivers causes inaccuracies of empirical formulas in the prediction of this phenomenon. Artificial intelligences as alternative approaches can provide solutions to such complex problems. The present study aimed at investigating the capability of kernel-based approaches in predicting total sediment loads and identification of influential parameters of total sediment transport. For this purpose, Gaussian process regression(GPR), Support vector machine(SVM) and kernel extreme learning machine(KELM) are applied to enhance the prediction level of total sediment loads in 19 mountain gravel-bed streams and rivers located in the United States. Several parameters based on two scenarios are investigated and consecutive predicted results are compared with some well-known formulas. Scenario 1 considers only hydraulic characteristics and on the other side, the second scenario was formed using hydraulic and sediment properties. The obtained results reveal that using the parameters of hydraulic conditions asinputs gives a good estimation of total sediment loads. Furthermore, it was revealed that KELM method with input parameters of Froude number(Fr), ratio of average velocity(V) to shear velocity(U*) and shields number(θ) yields a correlation coefficient(R) of 0.951, a Nash-Sutcliffe efficiency(NSE) of 0.903 and root mean squared error(RMSE) of 0.021 and indicates superior results compared with other methods. Performing sensitivity analysis showed that the ratio of average velocity to shear flow velocity and the Froude number are the most effective parameters in predicting total sediment loads of gravel-bed rivers.
基金supported by National Natural Science Foundation of China (Nos. U1333201, 11502123 and 11262012 )
文摘A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.
文摘This research studies short-term electricity load prediction with a large-scalelinear programming support vector regression (LP-SVR) model. The LP-SVR is compared with other three non-linear regression models: Collobert’s SVR, Feed-Forward Neural Networks (FFNN), and Bagged Regression Trees (BRT). The four models are trained to predict hourly day-ahead loads given temperature predictions, holiday information and historical loads. The models are trained on-hourly data from the New England Power Pool (NEPOOL) region from 2004 to 2007 and tested on out-of-sample data from 2008. Experimental results indicate that the proposed LP-SVR method gives the smallest error when compared against the other approaches. The LP-SVR shows a mean absolute percent error of 1.58% while the FFNN approach has a 1.61%. Similarly, the FFNN method shows a 330 MWh (Megawatts-hour) mean absolute error, whereas the LP-SVR approach gives a 238 MWh mean absolute error. This is a significant difference in terms of the extra power that would need to be produced if FFNN was used. The proposed LP-SVR model can be utilized for predicting power loads to a very low error, and it is comparable to FFNN and over-performs other state of the art methods such as: Bagged Regression Trees, and Large-Scale SVRs.
文摘The present paper aims at modeling suspended sediment load(SSL) using heuristic data driven methodologies, e.g. Gene Expression Programming(GEP) and Support Vector Machine(SVM) in three successive hydrometric stations of Housatonic River in U.S. The simulations were carried out through local and cross-station data management scenarios to investigate the interrelations between the SSL values of upstream/downstream stations. The available scenarios were applied to predict SSL values using GEP to obtain the best models. Then, the best models were predicted by SVM approach and the obtained results were compared with those of GEP. The comparison of the results revealed that the SVM technique is more capable than the GEP for modeling the SSL through the both local and cross-station data management strategies. Besides, local application seems to be better than cross-station application for modeling SSL. Nevertheless, the cross-station application demonstrated to be a valid methodology for simulating SSL, which would be of interest for the stations with lack of observational data. Also, the prediction capability of conventional Sediment Rating Curve(SRC) method was compared with those of GEPand SVM techniques. The obtained results revealed the superiority of GEP and SVM-based models over the traditional SRC technique in the studied stations.
文摘Accurate load prediction plays an important role in smart power management system, either for planning, facing the increasing of load demand, maintenance issues, or power distribution system. In order to achieve a reasonable prediction, authors have applied and compared two features extraction technique presented by kernel partial least square regression and kernel principal component regression, and both of them are carried out by polynomial and Gaussian kernels to map the original features’ to high dimension features’ space, and then draw new predictor variables known as scores and loadings, while kernel principal component regression draws the predictor features to construct new predictor variables without any consideration to response vector. In contrast, kernel partial least square regression does take the response vector into consideration. Models are simulated by three different cities’ electric load data, which used historical load data in addition to weekends and holidays as common predictor features for all models. On the other hand temperature has been used for only one data as a comparative study to measure its effect. Models’ results evaluated by three statistic measurements, show that Gaussian Kernel Partial Least Square Regression offers the more powerful features and significantly can improve the load prediction performance than other presented models.
基金supported by the National Natural Science Foundation of China(Nos.11402112,51405223)
文摘Structural health monitoring(SHM)in service has attracted increasing attention for years.Load localization on a structure is studied hereby.Two algorithms,i.e.,support vector machine(SVM)method and back propagation neural network(BPNN)algorithm,are proposed to identify the loading positions individually.The feasibility of the suggested methods is evaluated through an experimental program on a carbon fiber reinforced plastic laminate.The experimental tests involve in application of four optical fiber-based sensors for strain measurement at discrete points.The sensors are specially designed fiber Bragg grating(FBG)in small diameter.The small-diameter FBG sensors are arrayed in 2-D on the laminate surface.The testing results indicate that the loading position could be detected by the proposed method.Using SVM method,the 2-D FBG sensors can approximate the loading location with maximum error less than 14 mm.However,the maximum localization error could be limited to about 1 mm by applying the BPNN algorithm.It is mainly because the convergence conditions(mean square error)can be set in advance,while SVM cannot.
基金Project supported by the Science Foundation of Shanghai Municipal Commission of Science and Technology （Grant No.045115012）, and the Shanghai Leading Academic Discipline Project （Grant No.T0102）
文摘An adaptive load balancing scheme is proposed to balance the load in ad hoc networks. The new scheme can be applied in most on-demand routing protocols resulting in significant performance improvement. The proposed scheme is applied to the ad hoc on-demand distance vector （AODV） routing protocol. Simulation results show that the network load is balanced on the whole, and performance in packet loss rate, routing overhead and average end-to-end delay is also improved.
文摘A reliable seismic-resistant design of structures is achieved in accordance with the seismic design codes by designing structures under seven or more pairs of earthquake records. Based on the recommendations of seismic design codes, the average time-history responses （ATHR） of structure is required. This paper focuses on the optimal seismic design of reinforced concrete （RC） structures against ten earthquake records using a hybrid of particle swarm optimization algorithm and an intelligent regression model （IRM）. In order to reduce the computational time of optimization procedure due to the computational efforts of time-history analyses, IRM is proposed to accurately predict ATHR of structures. The proposed IRM consists of the combination of the subtractive algorithm （SA）, K-means clustering approach and wavelet weighted least squares support vector machine （WWLS-SVM）. To predict ATHR of structures, first, the input-output samples of structures are classified by SA and K-means clustering approach. Then, WWLS-SVM is trained with few samples and high accuracy for each cluster. 9- and 18-storey RC frames are designed optimally to illustrate the effectiveness and practicality of the proposed IRM. The numerical results demonstrate the efficiency and computational advantages of IRM for optimal design of structures subjected to time-history earthquake loads.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
