Alexandre de M. Wahrhaftig | UFBA - Federal University of Bahia (original) (raw)
Papers by Alexandre de M. Wahrhaftig
The present paper investigates the properties of an alternative material to be used in marine eng... more The present paper investigates the properties of an alternative material to be used in marine engineering field. It is a composite material based on a sandwich configuration, which is both rigid and light, made of expanded polystyrene and fiberglass. This material has several atractives as section modulus improver, besides technical and economical advantages, like low price and weight, commercially available, various dimensions, and easy to manipulate. Mathematical simulations are used to analyze the behavior of the proposed material based on finite element method. Ultimately, this paper aims to contribute with a unique study which will motivate future investigations regarding to extend the application of this material to construction of ships, boats and serve as an academic guide for future references in the naval architecture field.
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016
Numerical Simulations in Engineering and Science
For a complete analysis of vibration, the stiffness of a structure must have two characteristics:... more For a complete analysis of vibration, the stiffness of a structure must have two characteristics: one corresponding to conventional stiffness and the other to the geometric stiffness. Thus, the total stiffness takes form where the model to be used to represent any behavior of the material is introduced to the first part via the modulus of elasticity. The second is the geometric stiffness, through which it is possible to linearize a geometric nonlinear problem. To consider both aspects, a mathematical model based on the Rayleigh method has been elaborated. Two systems were numerically studied. First, the occurrence of resonance in the vibration of a prestressed reinforced concrete beam has been investigated. The results indicated resonant and non-resonant schemes between the natural frequency of the beam and the frequency of the engine. To the second system, the first natural frequency of a slender, 40-m-high concrete mobile phone mast, was calculated, and an evaluation of the structural collapse was performed. To the both systems, the cross section of reinforced concrete was treated by the theory for the homogenized section in order to consider the presence of the steel, and the viscoelasticity of the concrete was taken into account through a three-parameter rheological model.
Abstract. Beams and columns constitute a continuous system with infinite degrees of freedom. To s... more Abstract. Beams and columns constitute a continuous system with infinite degrees of freedom. To study the behavior of these systems the use of discretization techniques is required. However, one can associate them to a system with a single degree of freedom, restricting the form in which the system will deform and write their properties as a function of the generalized coordinate. This technique is the called Rayleigh Method and is a resource largely used to study the vibration of elastic systems. However, actual structures are systems more complex than simple beams and columns, because they have properties varying along its length. In such cases, the use of the Rayleigh Method should be done by parts and its integrals resolved within the limits established for each interval, being the generalized properties calculated for each segment of the structure. The actual structure selected for this study is a metallic high slenderness pole for which the frequency of the first vibration mod...
Buckling and free vibration analysis of non-prismatic columns using optimized shape functions and Rayleigh method
European Journal of Mechanics - A/Solids
The matrix stiffness of structures under axial compression loads is different from the convention... more The matrix stiffness of structures under axial compression loads is different from the conventional matrix stiffness. In slender structures, the stiffness changing due to geometric nonlinearity is one very important point in bulking analysis. For these structures, the stability analysis by dynamic method is usually required. The Rayleigh's method is a simple and easy way to consider the geometric nonlinearity effect on slender cantilevered structure stability analysis.
Effect of Creep in the Fundamental Frequency and Stability of a Slender Wooden Column of Composite Section
Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. ... more Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. Creep may change the purely elastic parameters determined in wood characterization initial tests, as its behavior depends on the rheology of the material, even under a constant stress level. Mathematically, creep can be characterized by models in which the immediate elastic deformation is increased by a viscous deformation, resulting in a temporal function. For this reason, the calculation of the natural frequency of vibration and the stability verification of a slender column should include the reducing effects of stiffness both of axial force and creep. The first one can be considered through the geometrical portion and the second one by the introduction, in the conventional portion, of a variable elasticity modulus over time, obtained in relation to the adopted rheological model. A numerical simulation was performed to evaluate the aspects above, considering a bar compressed by a forc...
The Brazilian Code on the design of structures subjected to Wind forces is NBR 6123/88 – Forces d... more The Brazilian Code on the design of structures subjected to Wind forces is NBR 6123/88 – Forces due to wind on buildings [1]. It gives three ways how to consider the effects of wind for design purposes. The engineer may choose one or the other according to the fundamental mode frequency and the height of the building. In Brazil, as the transference to private enterprise of the mobile cellular telephone system in the 90’s years occurred very rapidly, there was not time for the professionals involved in the design of the structures for telecommunications to adapt their models and they kept using the ones they were used to. Thus, the projects for the telecommunications poles were based on the method given by item 4 of NBR 6123/88, which we will call in this paper static model. Even though the Brazilian Code gives indications of how to compute the dynamic response to wind, many doubts on how to compute frequencies, damping rations and modal shape still persist to this day. This paper is...
Influência Da Rigidez Geométrica Na Resposta Dinâmica De Um Poste De Telefonia Celular Sob Carregamento De Vento Influence of the Geometric Stifiness in the Dynamic Response of a Cellular Telephony Pole Under Wind Excitation
The procedures for the consideration of the dynamic effect due to the wind in slender structures,... more The procedures for the consideration of the dynamic effect due to the wind in slender structures, adopted for NBR 6123/87, had disrespected the influence of the axial load in the stiffness geometric of the structure, on the contrary of this it praises linear models of verification. In slender structures, where the stiffness changes due to geometric nonlinearity, linear models do not obtain to describe the structural behavior exactly. The poles of cellular telephony consist in typical cases of structures whose dynamic analysis must include the influence of the stiffness geometric in the calculation of the natural frequency, starting point of the
Updating the bearing capacity, stresses, and strain for retrofitting reinforced concrete towers of the cellular and internet system
To retrofit reinforced concrete telecommunication towers, it is necessary to update their paramet... more To retrofit reinforced concrete telecommunication towers, it is necessary to update their parameters because the structure’s bearing capacity is no longer the same as at the initial moment of commi...
Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight
Journal of Vibration Engineering & Technologies
Latin American Journal of Solids and Structures
This study focused on improving the design of slender structures with reinforced concrete (RC) te... more This study focused on improving the design of slender structures with reinforced concrete (RC) telecommunication towers as the main application. Analytical procedure based on Rayleigh's method to compute the first natural vibration frequency and the critical buckling load was development. All the nonlinearities present in the system were considered, in addition to the soil-structure interaction and the variation of the geometric properties along the length of the structure. The geometric nonlinearity and imperfections of the tower structure were computed as functions of the axial load using a geometric stiffness matrix. Further, the material nonlinearity was accounted for by reducing the flexural stiffness. As concrete structures exhibit viscoelasticity, creep was calculated using the Eurocode 2 model. The soilstructure interaction was modeled as a set of distributed springs. To validate the proposed method, the first frequency and critical buckling load were compared with those yielded by FEM simulations. The frequency results were in good agreement with those of the FEM simulations, indicating that the proposed method is sufficiently accurate for use in engineering design applications and easy to implement. On the other hand, the buckling load results obtained using the proposed method and FEM differed significantly, motivating further investigation.
Vibration analysis of mobile phone mast system by Rayleigh method
Applied Mathematical Modelling
Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016
Plurais Revista Multidisciplinar Da Uneb, Dec 1, 2013
Os autores expressam seus agradecimentos pelo apoio dado pela CAPES e CNPq, ambas agências brasil... more Os autores expressam seus agradecimentos pelo apoio dado pela CAPES e CNPq, ambas agências brasileiras de fomento. Agradecem também à agência de fomento à pesquisa do Estado de São Paulo, FAPESP.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.
The present paper investigates the properties of an alternative material to be used in marine eng... more The present paper investigates the properties of an alternative material to be used in marine engineering field. It is a composite material based on a sandwich configuration, which is both rigid and light, made of expanded polystyrene and fiberglass. This material has several atractives as section modulus improver, besides technical and economical advantages, like low price and weight, commercially available, various dimensions, and easy to manipulate. Mathematical simulations are used to analyze the behavior of the proposed material based on finite element method. Ultimately, this paper aims to contribute with a unique study which will motivate future investigations regarding to extend the application of this material to construction of ships, boats and serve as an academic guide for future references in the naval architecture field.
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016
Numerical Simulations in Engineering and Science
For a complete analysis of vibration, the stiffness of a structure must have two characteristics:... more For a complete analysis of vibration, the stiffness of a structure must have two characteristics: one corresponding to conventional stiffness and the other to the geometric stiffness. Thus, the total stiffness takes form where the model to be used to represent any behavior of the material is introduced to the first part via the modulus of elasticity. The second is the geometric stiffness, through which it is possible to linearize a geometric nonlinear problem. To consider both aspects, a mathematical model based on the Rayleigh method has been elaborated. Two systems were numerically studied. First, the occurrence of resonance in the vibration of a prestressed reinforced concrete beam has been investigated. The results indicated resonant and non-resonant schemes between the natural frequency of the beam and the frequency of the engine. To the second system, the first natural frequency of a slender, 40-m-high concrete mobile phone mast, was calculated, and an evaluation of the structural collapse was performed. To the both systems, the cross section of reinforced concrete was treated by the theory for the homogenized section in order to consider the presence of the steel, and the viscoelasticity of the concrete was taken into account through a three-parameter rheological model.
Abstract. Beams and columns constitute a continuous system with infinite degrees of freedom. To s... more Abstract. Beams and columns constitute a continuous system with infinite degrees of freedom. To study the behavior of these systems the use of discretization techniques is required. However, one can associate them to a system with a single degree of freedom, restricting the form in which the system will deform and write their properties as a function of the generalized coordinate. This technique is the called Rayleigh Method and is a resource largely used to study the vibration of elastic systems. However, actual structures are systems more complex than simple beams and columns, because they have properties varying along its length. In such cases, the use of the Rayleigh Method should be done by parts and its integrals resolved within the limits established for each interval, being the generalized properties calculated for each segment of the structure. The actual structure selected for this study is a metallic high slenderness pole for which the frequency of the first vibration mod...
Buckling and free vibration analysis of non-prismatic columns using optimized shape functions and Rayleigh method
European Journal of Mechanics - A/Solids
The matrix stiffness of structures under axial compression loads is different from the convention... more The matrix stiffness of structures under axial compression loads is different from the conventional matrix stiffness. In slender structures, the stiffness changing due to geometric nonlinearity is one very important point in bulking analysis. For these structures, the stability analysis by dynamic method is usually required. The Rayleigh's method is a simple and easy way to consider the geometric nonlinearity effect on slender cantilevered structure stability analysis.
Effect of Creep in the Fundamental Frequency and Stability of a Slender Wooden Column of Composite Section
Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. ... more Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. Creep may change the purely elastic parameters determined in wood characterization initial tests, as its behavior depends on the rheology of the material, even under a constant stress level. Mathematically, creep can be characterized by models in which the immediate elastic deformation is increased by a viscous deformation, resulting in a temporal function. For this reason, the calculation of the natural frequency of vibration and the stability verification of a slender column should include the reducing effects of stiffness both of axial force and creep. The first one can be considered through the geometrical portion and the second one by the introduction, in the conventional portion, of a variable elasticity modulus over time, obtained in relation to the adopted rheological model. A numerical simulation was performed to evaluate the aspects above, considering a bar compressed by a forc...
The Brazilian Code on the design of structures subjected to Wind forces is NBR 6123/88 – Forces d... more The Brazilian Code on the design of structures subjected to Wind forces is NBR 6123/88 – Forces due to wind on buildings [1]. It gives three ways how to consider the effects of wind for design purposes. The engineer may choose one or the other according to the fundamental mode frequency and the height of the building. In Brazil, as the transference to private enterprise of the mobile cellular telephone system in the 90’s years occurred very rapidly, there was not time for the professionals involved in the design of the structures for telecommunications to adapt their models and they kept using the ones they were used to. Thus, the projects for the telecommunications poles were based on the method given by item 4 of NBR 6123/88, which we will call in this paper static model. Even though the Brazilian Code gives indications of how to compute the dynamic response to wind, many doubts on how to compute frequencies, damping rations and modal shape still persist to this day. This paper is...
Influência Da Rigidez Geométrica Na Resposta Dinâmica De Um Poste De Telefonia Celular Sob Carregamento De Vento Influence of the Geometric Stifiness in the Dynamic Response of a Cellular Telephony Pole Under Wind Excitation
The procedures for the consideration of the dynamic effect due to the wind in slender structures,... more The procedures for the consideration of the dynamic effect due to the wind in slender structures, adopted for NBR 6123/87, had disrespected the influence of the axial load in the stiffness geometric of the structure, on the contrary of this it praises linear models of verification. In slender structures, where the stiffness changes due to geometric nonlinearity, linear models do not obtain to describe the structural behavior exactly. The poles of cellular telephony consist in typical cases of structures whose dynamic analysis must include the influence of the stiffness geometric in the calculation of the natural frequency, starting point of the
Updating the bearing capacity, stresses, and strain for retrofitting reinforced concrete towers of the cellular and internet system
To retrofit reinforced concrete telecommunication towers, it is necessary to update their paramet... more To retrofit reinforced concrete telecommunication towers, it is necessary to update their parameters because the structure’s bearing capacity is no longer the same as at the initial moment of commi...
Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight
Journal of Vibration Engineering & Technologies
Latin American Journal of Solids and Structures
This study focused on improving the design of slender structures with reinforced concrete (RC) te... more This study focused on improving the design of slender structures with reinforced concrete (RC) telecommunication towers as the main application. Analytical procedure based on Rayleigh's method to compute the first natural vibration frequency and the critical buckling load was development. All the nonlinearities present in the system were considered, in addition to the soil-structure interaction and the variation of the geometric properties along the length of the structure. The geometric nonlinearity and imperfections of the tower structure were computed as functions of the axial load using a geometric stiffness matrix. Further, the material nonlinearity was accounted for by reducing the flexural stiffness. As concrete structures exhibit viscoelasticity, creep was calculated using the Eurocode 2 model. The soilstructure interaction was modeled as a set of distributed springs. To validate the proposed method, the first frequency and critical buckling load were compared with those yielded by FEM simulations. The frequency results were in good agreement with those of the FEM simulations, indicating that the proposed method is sufficiently accurate for use in engineering design applications and easy to implement. On the other hand, the buckling load results obtained using the proposed method and FEM differed significantly, motivating further investigation.
Vibration analysis of mobile phone mast system by Rayleigh method
Applied Mathematical Modelling
Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016
Plurais Revista Multidisciplinar Da Uneb, Dec 1, 2013
Os autores expressam seus agradecimentos pelo apoio dado pela CAPES e CNPq, ambas agências brasil... more Os autores expressam seus agradecimentos pelo apoio dado pela CAPES e CNPq, ambas agências brasileiras de fomento. Agradecem também à agência de fomento à pesquisa do Estado de São Paulo, FAPESP.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.
J Braz. Soc. Mech. Sci. Eng., 2013
In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsi... more In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.