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Structural Dynamics
Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subjected to dynamic loading. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis. Structural analysis is mainly concerned with finding out the behavior of a physical structure when subjected to force. This action can be in the form of load due to the weight of things such as people, furniture, wind, snow, etc. or some other kind of excitation such as an earthquake, shaking of the ground due to a blast nearby, etc. In essence all these loads are dynamic, including the self-weight of the structure because at some point in time these loads were not there. The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Analysis
Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on physical structures and their components. In contrast to theory of elasticity, the models used in structural analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis uses ideas from applied mechanics, materials science and applied mathematics to compute a structure's deformations, internal forces, stresses, support reactions, velocity, accelerations, and stability. The results of the analysis are used to verify a structure's fitness for use, often precluding physical tests. Structural analysis is thus a key part of the engineering design of structures. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spring (device)
A spring is a device consisting of an Elasticity (physics), elastic but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed or extended. Springs can Energy storage, store energy when compressed. In everyday use, the term most often refers to coil springs, but there are many different spring designs. Modern springs are typically manufactured from spring steel. An example of a non-metallic spring is the Bow (weapon), bow, made traditionally of flexible Taxus baccata, yew wood, which when Bow draw, drawn stores energy to propel an arrow. When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing force approximately proportional to its change in length (this approximation breaks down for larger deflections). The ''rate'' or ''spring constant'' of a spring is the change in the force it exerts, divided by the cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inertia
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his Newton%27s_laws_of_motion#First, first law of motion (also known as The Principle of Inertia). It is one of the primary manifestations of mass, one of the core quantitative properties of physical systems. Newton writes: In his 1687 work ''Philosophiæ Naturalis Principia Mathematica'', Newton defined inertia as a property: History and development Early understanding of inertial motion Joseph NeedhamProfessor John H. Lienhard points out the Mozi (book), Mozi – based on a Chinese text from the Warring States period (475–221 BCE) – as having given the first description of inertia. Before the European Renaissance, the prevailing theory of motion in western philosophy was that of Aristotle (384–322 BCE). On the surface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing Function (differential Equations)
In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables. In effect, it is a constant for each value of ''t''. In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting solution can often be determined using a superposition of linear combinations of the homogeneous solutions and the forcing term. For example, f(t) is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: ay'' + by' + cy = f(t) References Differential equations {{mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Moment Of Area
The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I (for an axis that lies in the plane of the area) or with a J (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension, when working with the International System of Units, is meters to the fourth power, m4, or inches to the fourth power, in4, when working in the Imperial System of Units or the US customary system. In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam. In order to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. The term modulus is derived from the Latin root term '' modus'', which means ''measure''. Definition Young's modulus, E, quantifies the relationship between tensile or compressive stress \sigma (force per unit ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Principles In Structural Mechanics
Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in solid mechanics. They can also be used for obtaining approximate solutions of fairly complex systems, bypassing the difficult task of solving the set of governing partial differential equations. General principles * Virtual work principle **Principle of virtual displacements **Principle of virtual forces ***Unit dummy force method * Modified variational principles Elastic systems * Minimum total potential energy principle * Principle of stationary total complementary potential energy * Castigliano's first theorem (for forces) Linear elastic systems * Castigliano's second theorem (for di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillations
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximum amplitude response in the system. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases. All systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure; when there is very little damping this frequency is approximately equal to, but slightly above, the resonant frequency. When an Oscillation, oscillat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a linear system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Damping Ratio
In physical systems, damping is the loss of energy of an oscillating system by dissipation. Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. Examples of damping include viscous damping in a fluid (see Viscosity, viscous Drag (physics), drag), Friction, surface friction, radiation, Electrical resistance and conductance, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. Damping not based on energy loss can be important in other oscillating systems such as those that occur in ecology, biological systems and Bicycle_and_motorcycle_dynamics#Lateral_motion_theory, bikes (ex. Suspension (mechanics)). Damping is not to be confused with friction, which is a type of dissipative force acting on a system. Friction can cause or be a factor of damping. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
