Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
非线性能量阱(nonlinear energy sink,NES)在减振和能量采集领域具有重要价值。尽管立方刚度NES及含立方刚度的双稳态NES已受广泛研究,但精确实现指定立方刚度的方法鲜有讨论。为此针对基于欧拉曲梁实现的NES开展研究,通过减小曲梁回复...非线性能量阱(nonlinear energy sink,NES)在减振和能量采集领域具有重要价值。尽管立方刚度NES及含立方刚度的双稳态NES已受广泛研究,但精确实现指定立方刚度的方法鲜有讨论。为此针对基于欧拉曲梁实现的NES开展研究,通过减小曲梁回复力与一个特定的理想非线性回复力之间的相对偏差,来实现NES中精确的立方刚度。基于欧拉梁理论得到圆弧梁和折线梁的初始刚度公式,用于设计曲梁长度。基于有限元方法求解了不同曲梁形状的非线性回复力,确定了能够实现立方刚度的圆弧梁和折线梁形状,并得到了满足相对偏差要求的临界位移拟合公式。基于以上两个公式总结出一套快速设计曲梁的方法,通过合理调节形状和截面尺寸使曲梁的回复力在需要的变形区间内逼近于理想非线性回复力。与有限元仿真进行对比,推导的解析公式可以对大初始挠度曲梁的初始刚度进行精确计算,设计出的NES回复力与目标之间的相对偏差绝对值小于1%。该设计方法有助于更精准、高效地设计NES,为曲梁实现非线性弹簧提供了新的设计方法。展开更多
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
文摘非线性能量阱(nonlinear energy sink,NES)在减振和能量采集领域具有重要价值。尽管立方刚度NES及含立方刚度的双稳态NES已受广泛研究,但精确实现指定立方刚度的方法鲜有讨论。为此针对基于欧拉曲梁实现的NES开展研究,通过减小曲梁回复力与一个特定的理想非线性回复力之间的相对偏差,来实现NES中精确的立方刚度。基于欧拉梁理论得到圆弧梁和折线梁的初始刚度公式,用于设计曲梁长度。基于有限元方法求解了不同曲梁形状的非线性回复力,确定了能够实现立方刚度的圆弧梁和折线梁形状,并得到了满足相对偏差要求的临界位移拟合公式。基于以上两个公式总结出一套快速设计曲梁的方法,通过合理调节形状和截面尺寸使曲梁的回复力在需要的变形区间内逼近于理想非线性回复力。与有限元仿真进行对比,推导的解析公式可以对大初始挠度曲梁的初始刚度进行精确计算,设计出的NES回复力与目标之间的相对偏差绝对值小于1%。该设计方法有助于更精准、高效地设计NES,为曲梁实现非线性弹簧提供了新的设计方法。
