Direct method for solution variational problems by using Hermite polynomials

Yari, Ayatollah; Mirnia, Mir Kamal

doi:10.5269/bspm.39925

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…As known, Eq. ( 18) provides the exact solution of a secondorder homogeneous PDE (in the classical form) as shown in Yari and Mirnia (2021) and Abramowitz and Stegun (1965). However, Eqs.…”

Section: Numerical Solutionsmentioning

confidence: 99%

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Zacchei

Brasil

2023

Arab J Geosci

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Anti-seismic devices are employed to implement the best performance of the structures under earthquakes. In this paper, semi-active tuned mass dampers (SA-TMDs) are studied by considering several combinations of variable friction forces and external disturbances. The variable damping model is used, where the goal consists in estimating the external actions to find the best friction force for system dampening. In particular, general, sinusoidal, and Gaussian dynamic loadings are considered. To obtain the response of the structure and dampers, several numerical solutions have been implemented. Probabilistic and determines analyses have been also developed to study different damper characteristics. Results show that a SA-TMD can reduce the structure displacements up to ~ 70.0% indicating a good performance in controlling different oscillations. This technology not only preserves the integrity of a structure mitigating its vibrations but also improves the life of occupants and their safety and comfort. This is beneficial from the perspective of practical application, and it is an advancement with respect to this theme.

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“…As known, Eq. ( 18) provides the exact solution of a secondorder homogeneous PDE (in the classical form) as shown in Yari and Mirnia (2021) and Abramowitz and Stegun (1965). However, Eqs.…”

Section: Numerical Solutionsmentioning

confidence: 99%

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Zacchei

Brasil

2023

Arab J Geosci

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“…However, it can be used to get HPs approximated solution. Thus, HPs in x and t are introduced by the series, generating function and identity, respectively [51,53]: and satisfy in the following relation [53]:…”

Section: Non-constant Diffusivitymentioning

confidence: 99%

Multifactorial Chloride Ingress Model for Reinforced Concrete Structures Subjected to Unsaturated Conditions

Zacchei

Bastidas‐Arteaga

2022

Buildings

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The attack of chloride ions is one of the most important factors affecting reinforced concrete (RC) durability. Chloride ingress into concrete is usually studied by assuming constant diffusivity and constant surface chloride concentration. However, these two approximations could badly estimate the chloride concentration in RC structures and then the lifetime assessment. Several factors influence the chloride concentration and ingress mechanisms in the convection area. In this paper, a new multifactorial and multiphase model to account for some effects on chloride surface concentrations in the convection zone is proposed. 136 values have been collected to identify the position and the chloride concentration in the border between the diffusion and convection zones. In addition, a time-dependent multifactorial diffusivity is considered. Diffusivity, which is the key parameter of the mechanical diffusion accounts in this paper for the water/cement ratio, chloride binding, temperature, concrete age, internal humidity, concrete deformation, and damage. The surface chloride model considers environment humidity, temperature, superficial concrete irregularities, and convection area of concrete. Advanced numerical solutions have been carried out to consider space and time dependencies in the model. Results show that the error function-based solutions could underestimate the chloride concentration C for periods < 10 years and for concrete depths > 4.0 cm in comparison with the proposed model.

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“…Therefore, various direct techniques based on orthogonal functions and polynomial series have been used to solve the VPs. An overall view of these methods can be explored in the research work provided by Schechter (1967), Hwang and Shih (1983), Razzaghi et al (2012), Mashayekhi et al (2012), Haddai et al (2012), Zarebnia and Birjandi (2012), Zarebnia and Sarvari (2014), Jaber (2015), Yari et al (2017), Yari and Mirnia (2021) and Shiri and Baleanu (2019). Also, Baleanu et al (2018) and Shiri et al (2021) introduced the applications of an operational matrix method based on orthogonal polynomials.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets

Rayal

Verma

2020

Journal of Vibration and Control

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In this study, an approximation method with an integral operational matrix based on the Muntz wavelets basis is presented to solve the variational problems of moving or fixed boundary conditions and a computational algorithm is given for the suggested approach. First, the integral operational matrix is created through the Muntz wavelets. Then, by using this integral operational matrix with Lagrange multipliers, the present approach reduces the variational problem into the system of algebraic equations. This approach is examined by some illustrative examples, and the acquired results prove that the suggested approach can solve the variational problems effectively with higher accuracy. The proposed approach yields better and comparable results with some other existing schemes given in the literature. The approximate wavelet solutions derived by the suggested approach are very identical to the corresponding exact solution.

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Direct method for solution variational problems by using Hermite polynomials

Cited by 6 publications

References 24 publications

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Multifactorial Chloride Ingress Model for Reinforced Concrete Structures Subjected to Unsaturated Conditions

Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets

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